Statistik mit Excel: Beschreibende Statistik für jedermann, 3. Auflage

Wolf-Gert Matthäus, Jörg Schulze Statistik mit Excel Wolf-Gert Matthäus, Jörg Schulze Statistik mit Excel Beschreibe...

Author: Wolf-Gert Matthäus | Jörg Schulze

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Wolf-Gert Matthäus, Jörg Schulze

Statistik mit Excel

Wolf-Gert Matthäus, Jörg Schulze

Statistik mit Excel Beschreibende Statistik für jedermann 3., überarbeitete und erweiterte Auflage

Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar.

1. Auflage 2003 2. Auflage 2005 3., überarbeitete und erweiterte Auflage 2008 Alle Rechte vorbehalten © B.G. Teubner Verlag / GWV Fachverlage GmbH, Wiesbaden 2008 Lektorat: Ulrich Sandten / Kerstin Hoffmann

Der B.G. Teubner Verlag ist ein Unternehmen von Springer Science+Business Media. www.teubner.de Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Umschlaggestaltung: Ulrike Weigel, www.CorporateDesignGroup.de Druck und buchbinderische Verarbeitung: Strauss Offsetdruck, Mörlenbach Gedruckt auf säurefreiem und chlorfrei gebleichtem Papier. Printed in Germany

ISBN 978-3-8351-0159-3

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báåÑ~ÅÜÉë=^Äò®ÜäÉå=ãáí=ZÄHLENWENN KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPV=

PKO=

hä~ëëÉåÄáäÇìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQS=

PKOKN= = hä~ëëÉåòìçêÇåìåÖ=ãáí=ÇÉê=cìåâíáçå=WENNKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQT= PKOKO= = aáÉ=cìåâíáçå=VERWEIS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQV= PKOKP= = aáÉ=cìåâíáçå=HÄUFIGKEIT KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRM= PKOKQ= = a~ë=tÉêâòÉìÖ=HISTOGRAMM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRM=

U===================================================================================================fåÜ~äíëîÉêòÉáÅÜåáë= PKP=

jçÇ~äïÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRO=

PKQ=

e®ìÑáÖâÉáíÉå=îçå=m~~êÉåW=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ=

PKQKN= = ^ìÑÖ~ÄÉåëíÉääìåÖ=ìåÇ=_ÉòÉáÅÜåìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ= PKQKO= = eÉêëíÉääìåÖ=ÉáåÉê=ÉáåÑ~ÅÜÉå=máîçíJq~ÄÉääÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ= PKQKP= = cÉäÇÉáåëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRT= PKQKQ= = mê®ëÉåí~íáçå=îçå=máîçíJq~ÄÉääÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRV= PKQKR= = ^Äò®ÜäÉå=ãáííÉäë=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RV= PKQKS= = s~êá~ÄäÉ=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSN= PKQKT= = máîçíJq~ÄÉääÉå=ãáí=a~íìãë~åÖ~ÄÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SO= PKR=

^ÄëçäìíÉ=pìããÉåÜ®ìÑáÖâÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ST=

= = Q=

dê~ÑáëÅÜÉ=a~êëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SV=

= QKN=

eáëíçÖê~ããÉW=tÉêâòÉìÖ=HISTOGRAMM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSV=

QKO=

aáÉ= F11 JjÉíÜçÇÉ=òìê=eÉêëíÉääìåÖ=îçå=dê~ÑáâÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TO=

QKOKN= = wìë~ããÉåÜ®åÖÉåÇÉ=a~íÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTO= QKOKO= = káÅÜí=òìë~ããÉåÜ®åÖÉåÇÉ=a~íÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTS= QKP=

wÉáíêÉáÜÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTS=

QKQ=

pâ~äáÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUM=

QKQKN= = _ÉÇÉìíìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UM= QKQKO= = içÖ~êáíÜãáëÅÜÉ=pâ~äáÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UO= QKR=

dê~ÑáëÅÜÉ=a~êëíÉääìåÖ=îçå=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UQ=

QKS=

a~êëíÉääìåÖ=îçå=~ÄëçäìíÉå=pìããÉåÜ®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUS=

QKSKN= = _ÉêÉáíë=ÄÉêÉÅÜåÉíÉ=pìããÉåÜ®ìÑáÖâÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK US= QKSKO= = NMMJmêçòÉåíJaá~Öê~ããÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUT= QKSKP= = NMMJmêçòÉåíJaá~Öê~ããÉ=áã=wÉáí~Ää~ìÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUU= = = R=

oÉä~íáîÉ=e®ìÑáÖâÉáíÉåI=ÉãéáêáëÅÜÉ=sÉêíÉáäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VN=

= RKN=

_ÉêÉÅÜåìåÖ=êÉä~íáîÉê=e®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVN=

RKO=

bñÅÉä=êÉÅÜåÉí=Ñ~äëÅÜ=>\ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VP=

RKP=

hìãìäáÉêíÉ=êÉä~íáîÉ=e®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVU=

=

fåÜ~äíëîÉêòÉáÅÜåáë= S=

V

pí~íáëíáëÅÜÉ=j~≈ò~ÜäÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP=

= SKN=

jáííÉäïÉêíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP=

SKNKN= = jÉÇá~å=ìåÇ=~êáíÜãÉíáëÅÜÉë=jáííÉä=EaìêÅÜëÅÜåáííF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP= SKNKO= = tÉáíÉêÉ=jáííÉäïÉêíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKO=

píêÉììåÖëã~≈ÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT=

SKOKN= = pé~ååïÉáíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKOKO= = jáííäÉêÉ=~ÄëçäìíÉ=^ÄïÉáÅÜìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKOKP= = bãéáêáëÅÜÉ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=ìåÇ=s~êá~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMU= SKOKQ= = báåëÅÜìÄW=kçêã~äîÉêíÉáäìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMV= SKP=

pÅÜáÉÑÉ=ìåÇ=t∏äÄìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNP=

SKQ=

aáÉ=sÉêÑΩÜêìåÖW=mçéìä~íáçåëâÉååÖê∏≈Éå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNQ=

= = T=

hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV=

= TKN=

aÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=îçå=_ê~î~áëJmÉ~êëçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV=

TKNKN= = _ÉÖêáÑÑI=_ÉÇÉìíìåÖI=_ÉêÉÅÜåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV= TKNKO= = eÉêëíÉääìåÖ=ÇÉê=mìåâíïçäâÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOM= TKO=

oÉÖêÉëëáçå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOP=

TKOKN= = _ÉêÉÅÜåìåÖ=ÇÉê=oÉÖêÉëëáçåëâçåëí~åíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOP= TKOKO= = oÉÅÜåìåÖ=ãáí=ÇÉã=tÉêâòÉìÖ=REGRESSION KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOS= TKP=

jìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOV=

TKQ=

káÅÜíäáåÉ~êÉ=wìë~ããÉåÜ®åÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN=

TKQKN= = dêìåÇä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN= TKQKO= = qê~åëÑçêã~íáçåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPR= = = U=

wÉáíêÉáÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPT=

= UKN=

_ÉÖêáÑÑ=ìåÇ=bêÑ~ëëìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPT=

UKO=

bñéÉêáãÉåíÉääJîáëìÉääÉ=qêÉåÇÉêãáííäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPU=

UKP=

iáåÉ~êÉ=wÉáíêÉáÜÉå=ìåÇ=ÇáÉ=TRENDJcìåâíáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQN=

UKQ=

däÉáíÉåÇÉê=aìêÅÜëÅÜåáíí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQQ=

===================================================================================================fåÜ~äíëîÉêòÉáÅÜåáë= NM UKR=

dêìåÇä~ÖÉå=ÇÉê=wÉáíêÉáÜÉå~å~äóëÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQT=

UKRKN= = ^ìÑÄ~ì=ÇÉë=~ÇÇáíáîÉå=wÉáíêÉáÜÉåãçÇÉääë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQU= UKRKO= = däÉáíÉåÇÉ=aìêÅÜëÅÜåáííÉ=ìåÇ=Ç~ë=~ÇÇáíáîÉ=wÉáíêÉáÜÉåãçÇÉääKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRM= UKRKP= = i~åÖÑêáëíáÖÉ=qêÉåÇë=ÉêâÉååÄ~ê=ã~ÅÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRN= UKRKQ= = jçå~íëíóéáëÅÜÉ=^ÄïÉáÅÜìåÖÉå=ÄÉêÉÅÜåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRO= UKRKR= = p~áëçåÄÉêÉáåáÖíÉ=wÉáíêÉáÜÉ=ÄÉêÉÅÜåÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRS= UKRKS= = ^ìëÄäáÅâKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRT= = = V=

fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=

= VKN=

dêìåÇë®íòäáÅÜÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=

VKO=

fãéçêí=~ìë=jpJ^ÅÅÉëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=

VKP=

báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSN=

VKQ=

wìÖêáÑÑ=~ìÑ=âçåâêÉíÉ=a~íÉåÄ~åâÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP=

VKQKN= = jáÅêçëçÑí=pniJpÉêîÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP= VKQKO= = lê~ÅäÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP= VKR=

bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSR=

VKRKN= = a~íÉå=áãéçêíáÉêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSR= VKRKO= = a~íÉå=îáëì~äáëáÉêÉå=ìåÇ=~âíìÉää=Ü~äíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSV= = = ^åÜ~åÖ=NW=sçã=mêçÄäÉã=òìê=bñÅÉäJi∏ëìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTN= = = ^åÜ~åÖ=OW=_Éá=bñÅÉä=OMMT=áëí=ã~åÅÜÉë=~åÇÉêëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTV= = = iáíÉê~íìê= = KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMN= = = p~ÅÜïçêíîÉêòÉáÅÜåáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= = = =

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1

Grundlagen

1.1

Statistische Grundbegriffe

aÉå=dÉÖÉåëí~åÇ=ÇÉê=ëí~íáëíáëÅÜÉå=råíÉêëìÅÜìåÖ=åÉååí=ã~å=jÉêâã~äëíê®ÖÉêK=aÉê=jÉêâJ ã~äëíê®ÖÉê=áëí=ÇÉê=qê®ÖÉê=ÇÉê=áåíÉêÉëëáÉêÉåÇÉå=ëí~íáëíáëÅÜÉå=fåÑçêã~íáçåÉåK= aáÉ= jÉåÖÉ= ~ääÉê= jÉêâã~äëíê®ÖÉêI= ÇáÉ= ΩÄÉêÉáåëíáããÉåÇÉ= ^ÄÖêÉåòìåÖëãÉêâã~äÉ= ÄÉëáíòÉåI= ÄÉòÉáÅÜåÉí=ã~å=~äë=dêìåÇÖÉë~ãíÜÉáíK= báå=jÉêâã~ä=áëí=ÇáÉàÉåáÖÉ=báÖÉåëÅÜ~Ñí=ÇÉë=jÉêâã~äëíê®ÖÉêëI=ÇáÉ=ÄÉá=ÇÉê=ëí~íáëíáëÅÜÉå=råJ íÉêëìÅÜìåÖ=îçå=fåíÉêÉëëÉ=áëíK= aÉê=tÉêíI=ÇÉê=Ç~åå=ÄÉá=ÇÉê=_ÉçÄ~ÅÜíìåÖI=_ÉÑê~ÖìåÖI=jÉëëìåÖ=çÇÉê=ÇìêÅÜ=ÉáåÉå=w®ÜäîçêJ Ö~åÖ=ÄÉáã=jÉêâã~äëíê®ÖÉê=ÑÉëíÖÉëíÉääí=ïáêÇI=ïáêÇ=~äë=jÉêâã~äëïÉêí=çÇÉê=jÉêâã~äë~ìëéê®J ÖìåÖ=ÄÉòÉáÅÜåÉíK== j~å=ìåíÉêëÅÜÉáÇÉí=òïáëÅÜÉå=èì~äáí~íáîÉå=ìåÇ=èì~åíáí~íáîÉå=jÉêâã~äÉåW== tÉåå= ÇÉå= jÉêâã~äë~ìëéê®ÖìåÖÉå= äÉÇáÖäáÅÜ= k~ãÉå= çÇÉê= hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= òìÖÉJ çêÇåÉí=ïÉêÇÉåI=ëéêáÅÜí=ã~å=îçå=èì~äáí~íáîÉå=jÉêâã~äÉåK== = Merkmal

Merkmalsausprägung (Merkmalswert)

_ÉêìÑ=

_®ÅâÉêI=iÉÜêÉêI=häÉãéåÉêI=fåÖÉåáÉìê=

sçêíê~ÖëïÉáëÉ=

fåíÉêÉëë~åíI=ä~åÖïÉáäáÖI=Éêíê®ÖäáÅÜ=

q~ÄK=N~W=_ÉáëéáÉäÉ=ÑΩê=èì~äáí~íáîÉ=jÉêâã~äÉ= _Éëáíòí=Ç~ÖÉÖÉå=Ç~ë=jÉêâã~ä=ÉáåÉ=ãÉëëÄ~êÉ=aáãÉåëáçå=çÇÉê=â~åå=Éë=áå=jÉåÖÉåÉáåÜÉáJ íÉå=~ìëÖÉÇêΩÅâí=ïÉêÇÉåI=ëç=ëéêáÅÜí=ã~å=îçå=ÉáåÉã=èì~åíáí~íáîÉå=jÉêâã~äK= = Merkmal

Merkmalsausprägung (Merkmalswert)

^äíÉê=Eg~ÜêÉF=

ÁI=RI=NUI=ÁI=UVI=Á=

_ÉåòáåîÉêÄê~ìÅÜ=EiáíÉêLNMM=âãF=

PIRX=Á=X=QIU=X=Á=X=TIP=X=Á=X=NOIR=X=Á=

q~ÄK=NÄW=_ÉáëéáÉäÉ=ÑΩê=èì~åíáí~íáîÉ=jÉêâã~äÉ=

=

káããí=Éáå=èì~åíáí~íáîÉë=jÉêâã~ä=åìê=ÉáåáÖÉ=îÉêëÅÜáÉÇÉåÉ=tÉêíÉ=~åI=ëç=ëéêáÅÜí=ã~å=îçå= ÉáåÉã=ÇáëâêÉíÉå=jÉêâã~ä=EòK=_K=jáí~êÄÉáíÉêò~ÜäI=e~ìëÜ~äíëÖê∏≈ÉI=hÑòJ_Éëí~åÇFK==== h~åå=Éáå=jÉêâã~ä=Ç~ÖÉÖÉå=EíÜÉçêÉíáëÅÜF=ìåÉåÇäáÅÜ=îáÉäÉ=tÉêíÉ=~ååÉÜãÉåI=ëç=ÜÉá≈í=Ç~ë= jÉêâã~ä=ëíÉíáÖ=EòK=_K=h∏êéÉêÖê∏≈ÉI=dÉëÅÜïáåÇáÖâÉáíI=aìêÅÜãÉëëÉê=ÉáåÉë=_~ìíÉáäëFK==

1.2

Datenniveau, Skalierung der Merkmale

aáÉ=bêãáííäìåÖ=îçå=jÉêâã~äëïÉêíÉå=ÉêÑçäÖí=ÇìêÅÜ=ÉáåÉå=w®ÜäîçêÖ~åÖ=çÇÉê=ÇìêÅÜ=jÉëëìåÖI= _ÉÑê~ÖìåÖI=_ÉçÄ~ÅÜíìåÖK= aáÉ= bêÖÉÄåáëëÉ= ïÉêÇÉå= ÉåíïÉÇÉê= ìåãáííÉäÄ~ê= çÇÉê= ãáí= eáäÑÉ= ÉáJ åÉë=pâ~äáÉêìåÖëîÉêÑ~ÜêÉåë=áå=ÉáåÉ=pâ~ä~=~ÄÖÉÄáäÇÉíK==

=

=NU

=

N==dêìåÇä~ÖÉå=

aáÉëÉ=Eëí~íáëíáëÅÜÉF=jÉëëJpâ~ä~=áëí=Ç~åå=Ç~ë=fåëíêìãÉåíI=ãáí=ÇÉã=ÇáÉ=jÉêâã~äëïÉêíÉ=ÉêãáíJ íÉäí=ïÉêÇÉåK=^ìÑ=ÇÉê=pâ~ä~=ïÉêÇÉå=ÇáÉ=ã∏ÖäáÅÜÉå=jÉêâã~äëïÉêíÉI=Ñ~ääë=ã∏ÖäáÅÜI=å~ÅÜ=ÄÉJ ëíáããíÉã=lêÇåìåÖëéêáåòáé=~äë=pâ~äÉåïÉêíÉ=~ÄÖÉíê~ÖÉåK== aáÉ=pâ~äÉå=ïÉêÇÉå=ÖÉï∏ÜåäáÅÜ=áå== J=h~êÇáå~äëâ~äÉå= J=lêÇáå~äëâ~äÉå= J=kçãáå~äëâ~äÉå= ìåíÉêÖäáÉÇÉêíK== gÉ=å~ÅÜ=^êí=ÇÉê=pâ~ä~=ëéêáÅÜí=ã~å=Ç~åå=~ìÅÜ=îçå=ÇÉã=òìÖÉÜ∏êáÖÉå=káîÉ~ì=ÇÉê=a~íÉå=Ea~J íÉååáîÉ~ìFK=

1.2.1

Kardinalskala (metrische Skala)

tÉåå=ÇáÉ=a~íÉå=áåíÉêî~ääJ=çÇÉê=Ç~êΩÄÉê=Üáå~ìë=ëçÖ~ê=åçÅÜ=ê~íáçå~ä=ëâ~äáÉêí=ëáåÇI=Ç~åå= ëéêáÅÜí=ã~å=îçå=â~êÇáå~ä=ëâ~äáÉêíÉå=a~íÉå=EçÇÉê=ãÉíêáëÅÜ=ëâ~äáÉêíÉå=a~íÉåFK=aáÉëÉ=a~íÉå= Ü~ÄÉå=Ç~ë=Ü∏ÅÜëíÉ=a~íÉååáîÉ~ìK==

Intervallskala j~å= ëéêáÅÜí= îçå= áåíÉêî~ääëâ~äáÉêíÉå= a~íÉåI= ïÉåå= ÇáÉ= ^ìëéê®ÖìåÖÉå= ÉáåÉë= jÉêâã~äë= áå= ÉáåÉ=o~åÖçêÇåìåÖ=ÖÉÄê~ÅÜí=ïÉêÇÉå=â∏ååÉå=ìåÇ=ïÉåå=òìë®íòäáÅÜ=åçÅÜ=ÄÉëíáããí=ïÉêJ ÇÉå= â~ååI= áå= ïÉäÅÜÉã= ^ìëã~≈= ëáÅÜ= òïÉá= îÉêëÅÜáÉÇÉåÉ= jÉêâã~äë~ìëéê®ÖìåÖÉå= ìåíÉêJ ëÅÜÉáÇÉåK== = Merkmal

Merkmalsausprägung (Merkmalswert)

rÜêòÉáí=

QWMMWMMI=UWNTWRSI=NOWRVWOOI=Á=

qÉãéÉê~íìê=Eáå=dê~Ç=`ÉäëáìëF=

JPQI=JNOI=RSI=OMMI=Á=

h~äÉåÇÉêòÉáí=

NKNKOMMMI=ONKNOKOMMOI=UKNKOMPRI=Á=

q~ÄK=NKOW=_ÉáëéáÉäÉ=ÑΩê=áåíÉêî~ääëâ~äáÉêíÉ=a~íÉå= fåíÉêî~ääëâ~äáÉêíÉ=a~íÉå=äáÉÖÉå=~äë=w~ÜäÉåïÉêíÉ=EåìãÉêáëÅÜÉ=tÉêíÉF=îçêK=t®ÜêÉåÇ=Éë=çÑÑÉåJ ëáÅÜíäáÅÜ=ìåëáååáÖ=áëíI=ÇáÉ=rÜêòÉáíÉå=Q=rÜê=ìåÇ=NO=rÜê=Ç~ÜáåÖÉÜÉåÇ=òì=áåíÉêéêÉíáÉêÉåI=Ç~ëë= Éë=łìã=NO=rÜê=ÇêÉáã~ä=ëç=ëé®í=áëí=ïáÉ=ìã=Q=rÜêI=áëí=ÇáÉ=^ìëë~ÖÉ=çÑÑÉåÄ~ê=ëáååîçääI=Ç~ëë= łîçå=Q=rÜê=Äáë=U=rÜê=ÖÉå~ìëç=îáÉä=wÉáí=îÉêÖÉÜí=ïáÉ=îçå=R=rÜê=Äáë=V=rÜêK== páååîçää=ëáåÇ=~ìÅÜ=ÇáÉ=^åÖ~ÄÉå=ÇÉê=ãáííäÉêÉå=qÉãéÉê~íìê=EaìêÅÜëÅÜåáííëïÉêíF=ëçïáÉ=ïÉáíÉJ êÉê=ëí~íáëíáëÅÜÉê=j~≈ò~ÜäÉå=EëáÉÜÉ=^ÄëÅÜåáíí=S=~ìÑ=pÉáíÉ=NMPFK=

Verhältnisskala (Ratioskala) j~å= ëéêáÅÜí= Ç~êΩÄÉê= Üáå~ìë= ëçÖ~ê= îçå= ê~íáçå~ä=ëâ~äáÉêíÉå=a~íÉåI= ïÉåå= ÇÉê= pâ~äÉåïÉêí= kìää=ÇÉã=å~íΩêäáÅÜÉåI=~ÄëçäìíÉå=kìääéìåâí=ÉåíëéêáÅÜíK=kÉÖ~íáîÉ=tÉêíÉ=ëáåÇ=Ç~ãáí=ìåã∏ÖJ äáÅÜK=pçãáí=ÉêÜ®äí=åÉÄÉå=ÇÉã=ÉáåÑ~ÅÜÉå=^Äëí~åÇ=EÇáÉ=aáÑÑÉêÉåòF=~ìÅÜ=ÇÉê=nìçíáÉåí=EÇ~ë= sÉêÜ®äíåáëF=ÉáåÉ=ëáååîçääÉ=_ÉÇÉìíìåÖK=== a~ë=sÉêÜ®äíåáë=ä®ëëí=ëáÅÜ=Ç~ÄÉá=~ìÅÜ=áåíÉêéêÉíáÉêÉåW== jáí=TO=g~ÜêÉå=áëí=Éáå=jÉåëÅÜ=ëÉÅÜëã~ä=ëç=~äí=ïáÉ=ãáí=NO=g~ÜêÉåK=báå=báåâçããÉå=îçå=PSMMM= bìêç=áëí=åìê=Éáå=cΩåÑíÉä=ÇÉë=NUMMMMJbìêçJbáåâçããÉåë=ìëïK== =

=

=

NKO==a~íÉååáîÉ~ìI=pâ~äáÉêìåÖ=ÇÉê=jÉêâã~äÉ= Merkmal

NV

Merkmalsausprägung (Merkmalswert)

báåâçããÉå=Eáå=qëÇK=bìêçF=

MI=ÁI=NOI=ÁI=PSI=ÁI=NOMI=Á=

dÉïáÅÜí=EâÖF=

MI=ÁI=QRI=ÁI=USI=ÁI=NOPI=Á=

^äíÉê=Eg~ÜêÉF=

MI=ÁI=NOI=ÁI=OQI=ÁI=TUI=Á=

q~ÄK=NKPW=_ÉáëéáÉäÉ=ÑΩê=ê~íáçå~ä=ëâ~äáÉêíÉ=a~íÉå=

1.2.2

Ordinalskala

^äë= pâ~äÉåïÉêíÉ= ïÉêÇÉå= åìê=hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= ~ÄÖÉíê~ÖÉåK= _Éáã= sÉêÖäÉáÅÜ=òïÉáÉê= jÉêâã~äëíê®ÖÉê= â~åå= áã= c~ääÉ= ÇÉê= sÉêëÅÜáÉÇÉå~êíáÖâÉáí= åìê= áÜêÉ= o~åÖÑçäÖÉ= ÑÉëíÖÉëíÉääí= ïÉêÇÉåK=aáÑÑÉêÉåòÉå=ëáåÇ=åáÅÜí=áåíÉêéêÉíáÉêÄ~êK== lêÇáå~ä=ëâ~äáÉêíÉ=a~íÉå=ÄÉëáíòÉå=åìê=åçÅÜ=ãáííäÉêÉë=a~íÉååáîÉ~ìK== = Merkmal

Merkmalsausprägung (Merkmalswert)

pÅÜìäåçíÉ=

ëÉÜê=ÖìíI=ÖìíI=ÄÉÑêáÉÇáÖÉåÇI=~ìëêÉáÅÜÉåÇI=ã~åÖÉäÜ~Ñí=

qÉãéÉê~íìêÉãéÑáåÇÉå=

ÜÉá≈I=ï~êãI=ä~ìï~êãI=â~äíI=ëÉÜê=â~äí==

^äíÉêëÖêìééÉ=

háåÇI=gìÖÉåÇäáÅÜÉêI=bêï~ÅÜëÉåÉêI=dêÉáë=

q~ÄK=NKQW=_ÉáëéáÉäÉ=ÑΩê=çêÇáå~ä=ëâ~äáÉêíÉ=a~íÉå= _Éá=çêÇáå~ä=ëâ~äáÉêíÉå=a~íÉå=â∏ååÉå=áããÉêÜáå=ÇáÉ=e®ìÑáÖâÉáíÉå=~ÄÖÉò®Üäí=ïÉêÇÉåX=òìë®íòJ äáÅÜ= â∏ååÉå= îÉêÖäÉáÅÜÉåÇÉ= ^ìëë~ÖÉå= ïáÉ= ÄÉëëÉêLëÅÜäÉÅÜíÉêI= ãÉÜêLïÉåáÖÉê= ìK= ®K= ÖÉã~ÅÜí= ïÉêÇÉåK== _ÉêÉÅÜåìåÖÉå=îçå=jáííÉäïÉêíÉå=çÇÉê=ïÉáíÉêÉå=ëí~íáëíáëÅÜÉå=j~≈ò~ÜäÉå=çêÇáå~ä=ëâ~äáÉêíÉê= a~íÉå=ëáåÇ=áã=~ääÖÉãÉáåÉå=åáÅÜí=ëáååîçääK==

1.2.3

Nominalskala

^äë=pâ~äÉåïÉêíÉ=ïÉêÇÉå=k~ãÉå=~ÄÖÉíê~ÖÉåX=Éë=â~åå=åìê=ÇáÉ=däÉáÅÜÜÉáí=çÇÉê=råÖäÉáÅÜJ ÜÉáí=ÖÉéêΩÑí=ïÉêÇÉåK== kçãáå~ä=ëâ~äáÉêíÉ=a~íÉå=ÄÉëáíòÉå=Ç~ë=ìåíÉêëíÉ=a~íÉååáîÉ~ìK=aáÉ=q~ÄÉääÉ=NKR=ÉåíÜ®äí=ÉáåáÖÉ= _ÉáëéáÉäÉ=ÑΩê=åçãáå~ä=ëâ~äáÉêíÉ=a~íÉåK= = Merkmal

Merkmalsausprägung (Merkmalswert)

dÉëÅÜäÉÅÜí=

ã®ååäáÅÜI=ïÉáÄäáÅÜ=

c~ãáäáÉåëí~åÇ=

äÉÇáÖI=îÉêÜÉáê~íÉíI=ÖÉëÅÜáÉÇÉåI=îÉêïáíïÉí=

miwJ_ÉêÉáÅÜ=

MI=NI=OI=ÁI=V=

q~ÄK=NKRW=_ÉáëéáÉäÉ=ÑΩê=åçãáå~ä=ëâ~äáÉêíÉ=a~íÉå= aáÉ=^åÖ~ÄÉ=îçå=^Äëí®åÇÉå=ìåÇLçÇÉê=lêÇåìåÖëÄÉòáÉÜìåÖÉå=òïáëÅÜÉå=òïÉá=jÉêâã~äëíê®ÖÉêå= áëí= ~åÜ~åÇ= ÇÉê= hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= åáÅÜí= ã∏ÖäáÅÜK= ^ìÅÜ= ïÉåå= ÇáÉëÉ= EòìÑ®ääáÖF= ëçÖ~ê= ~ìë= w~ÜäÉå=ÄÉëíÉÜÉå=ëçääíÉåW=aÉê=miwJ_ÉêÉáÅÜ=U=áëí=âÉáåÉëÑ~ääë=łÄÉëëÉê=~äë=ÇÉê=miwJ_ÉêÉáÅÜ=SK== råÇ=ï~ë=ëçääíÉ=~ìÅÜ=ÇáÉ=ëáååäçëÉ=aáÑÑÉêÉåò=łmiwJ_ÉêÉáÅÜ=T=ãáåìë=miwJ_ÉêÉáÅÜ=P=~ìëë~ÖÉå\==

=

=OM

=

N==dêìåÇä~ÖÉå=

kçÅÜ= âìêáçëÉê= ï®êÉ=ÉëI= ïÉåå= ã~å= ÇáÉ= mçëíäÉáíò~Üä= VVVVV= ~äë= łÇêÉáã~ä= ëç= Öêç≈LÖìíLKKK= ïáÉ= ÇáÉ=mçëíäÉáíò~Üä=PPPPP=ÄÉòÉáÅÜåÉå=ïΩêÇÉK=

1.3

Verarbeitungsmöglichkeiten von Daten

a~ë= jÉëëåáîÉ~ì= ÇÉê= a~íÉå= ÄÉëíáããí= ïÉáíÖÉÜÉåÇ= ÇáÉ= j∏ÖäáÅÜâÉáíÉå= ìåÇ= dêÉåòÉå= ÇÉê= a~íÉå~å~äóëÉW= gÉ= åáÉÇêáÖÉê= Ç~ë=a~íÉååáîÉ~ì= áëíI= ÇÉëíç= ÖÉêáåÖÉê=áëí= Ç~ë= ^å~äóëÉéçíÉåòá~ä= ÇÉê=sÉêÑ~ÜêÉå=ìåÇ=ÇÉëíç=ÖÉêáåÖÉê=áëí=ÇÉê=fåÑçêã~íáçåëÖÉÜ~äí=ÇÉê=jÉêâã~äëïÉêíÉK== = Skalentyp Empirische Operationen

Nominalskala Bestimmung von Gleichheit und Ungleichheit

Ordinalskala Zusätzlich: Bestimmung einer Rangfolge z. B. x
Statistische Maßzahlen (Beispiele)

Häufigkeit, Modalwert

Zusätzlich: Median, Quantile, Prozentrangwerte

Zusammenhangsmaße

Kontingenzkoeffizient Vierfelderkoeffizient

Beispiele

Nummerierung von Fußballspielern, Kontonummern, Quantifizierung von dichotomen Merkmalen (z. B. Geschlecht)

Zusätzlich: Rangkorrelationskoeffizient (SpearmansRho, Kendalls Tau) Schulnoten, Richter’sche Erdbebenskala, Testrohwerte

Intervallskala Zusätzlich: Intervalle gleich (z. B. 10-7≅7-4) willkürlich festgelegter Nullpunkt Zusätzlich: Arithmetisches Mittel, Standardabweichung, Schiefe, Exzeß Zusätzlich: Korrelations-, Regressionskoeffizienten

Verhältnisskala Zusätzlich: Bestimmung gleicher Verhältnisse (z. B. x/y ≅ y/z ) absoluter Nullpunkt Zusätzlich: Geometrisches Mittel, Variationskoeffizient

Temperatur (nach Celsius, Fahrenheit, Reaumur)

Länge, Masse, Zeit, Winkel, Temperatur (nach Kelvin)

Siehe Intervallskala

q~ÄK=NKSW=j∏ÖäáÅÜâÉáíÉå=ìåÇ=dêÉåòÉå=ÄÉá=îÉêëÅÜáÉÇÉåÉå=a~íÉåJkáîÉ~ìë= jáí=ëáåâÉåÇÉã=a~íÉååáîÉ~ì=Ñ~ääÉå=Ç~ë=fåÑçêã~íáçåëåáîÉ~ì=ëçïáÉ=ÇáÉ=j∏ÖäáÅÜâÉáíÉå=òìê= _ÉêÉÅÜåìåÖ=~ìëë~ÖÉâê®ÑíáÖÉê=ëí~íáëíáëÅÜÉê=j~≈ò~ÜäÉå= ìåÇ= òìê= ^åÖ~ÄÉ=îçå=wìë~ããÉåJ Ü~åÖëã~≈ÉåK= få=ÇÉê=q~ÄÉääÉ=NKS=ëáåÇ=~ääÉ=j∏ÖäáÅÜâÉáíÉå=ìåÇ=báåëÅÜê®åâìåÖÉå=ëÅÜçå=Éáåã~ä=òìë~ããÉåJ ÖÉëíÉääíX=~ìÑ=ÇáÉ=ÖÉå~ååíÉå=_ÉÖêáÑÑÉ=ïáêÇ=áå=ÇÉå=ÑçäÖÉåÇÉå=h~éáíÉäå=áã=aÉí~áä=ÉáåÖÉÖ~åÖÉåK=

=

NKQ==w~ÜäÉå=Ó=ÇáÉ=Öêç≈Éå=sÉêÑΩÜêÉê=

1.4

=

ON

Zahlen — die großen Verführer

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Hotel 4 Sterne

Hotel 3 Sterne

Hotel 2 Sterne

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Hotel 4 Sterne

Privatquartier

Jugendherberge

Hotel 3 Sterne

Hotel 2 Sterne

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2

Datenerfassung und -verwaltung

2.1

Mehrdimensionales Datenmaterial

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2.1.1

Überschriften

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Separierung des Datenbestandes sáÉäÉ=^åäÉáíìåÖÉå=ÑΩê=bñÅÉäJj~≈å~ÜãÉå=ÄÉÖáååÉå=ãáí=ÇÉê=^ìÑÑçêÇÉêìåÖI=ÇÉå=q~ÄÉääÉåâìêJ ëçê=áå=áêÖÉåÇÉáåÉ=wÉääÉ=ÇÉë=a~íÉåÄÉëí~åÇÉë=òì=ëÉíòÉå=Ó=ìåÇ=Ç~åå=ïÉáíÉêÉ=_ÉÇáÉåÜ~åÇäìåJ ÖÉå=îçêòìåÉÜãÉåK== bñÅÉä= áëí= å®ãäáÅÜ= áå= ÇÉê= i~ÖÉI= ëÉäÄëí= ÇáÉ= dêÉåòÉå= ÉáåÉë= a~íÉåÄÉëí~åÇÉë= ÉêâÉååÉå= òì= â∏ååÉåK=a~ë=Éêëé~êí=òÉáíê~ìÄÉåÇÉë=j~êâáÉêÉåK== ^ääÉêÇáåÖë=ëÉíòí=Ç~ë=îçê~ìëI=Ç~ëë=ÇÉê=a~íÉåÄÉëí~åÇ=ëÉé~êáÉêí=áëíW= báå=a~íÉåÄÉëí~åÇ=áëí=ëÉé~êáÉêíI=ïÉåå=Éê=ÇìêÅÜ=ãáåÇÉëíÉåë=ÉáåÉ=iÉÉêòÉáäÉ=ìåÇ=iÉÉêëé~äíÉ= îçå=~åÇÉêÉå=fåÜ~äíÉå=ÇÉë=q~ÄÉääÉåÄä~ííÉë=ÖÉíêÉååí=áëíK==

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2.1.2

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2.1.3

Dateneingabe

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2.2

Eindimensionales Datenmaterial

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2.3

Umgang mit dem Datenmaterial

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2.4

Kontrolle des Datenbestandes

2.4.1

Nützliche Auskunftsfunktionen

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2.4.2

Erfasste Merkmalswerte und das Filtern

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2.4.3

Prüfen von Minimum und Maximum

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3

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3.1

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= q~ÄK=PKNMW=cÉëíäÉÖìåÖ=îçå=hä~ëëÉåÖêÉåòÉå= sáÉäãÉÜê=ÉêïÉáëí=Éë=ëáÅÜ=åìå=~äë=ìåÄÉÇáåÖí=åçíïÉåÇáÖI=òìÉêëí=hä~ëëÉå=ÑÉëíòìäÉÖÉåI=ëç=ïáÉ= ëáÉ=òK=_K=ÑΩê=ÇáÉ=ÄÉíê~ÅÜíÉíÉ=dÉïáÅÜíë~å~äóëÉ=áå=q~ÄÉääÉ=PKNM=îçêÖÉëÅÜä~ÖÉå=ïÉêÇÉåK= tÉäÅÜÉ=hä~ëëÉåÖêÉåòÉå=áã=aÉí~áä=òì=ï®ÜäÉå=ëáåÇI=Ç~ë=Ü®åÖí=àÉïÉáäë=îçå=ÇÉê=ÄÉíê~ÅÜíÉíÉå= qÜÉã~íáâ=~ÄK=bÄÉåëç=áëí=Éë=åáÅÜí=òïáåÖÉåÇI=Ç~ëë=ëíÉíë=ÖäÉáÅÜÉ=hä~ëëÉåÄêÉáíÉå=ÖÉï®Üäí=ïÉêJ ÇÉå=ãΩëëÉåK== dÉåÉêÉää=ÖáäíI=Ç~ëë=åáÅÜí=òì=îáÉäÉ=ìåÇ=åáÅÜí=òì=ëÅÜã~äÉ=hä~ëëÉå=ÖÉÄáäÇÉí=ïÉêÇÉå=ëçääíÉåK== aáÉ=råíÉêJ=ìåÇ=lÄÉêÖêÉåòÉå=ÄÉëíáããí=ã~å=òïÉÅâã®≈áÖ=ãáí=eáäÑÉ=ÇÉê=cìåâíáçåÉå=MIN(...)= ìåÇ= MAX(...)K=a~å~ÅÜ=ãìëë=ÑΩê=àÉÇÉå=dÉïáÅÜíëïÉêí=ÉêãáííÉäí=ïÉêÇÉåI=òì=ïÉäÅÜÉê=hä~ëëÉ=Éê= ÖÉÜ∏êíK=a~ÑΩê=ÖáÄí=Éë=ãÉÜêÉêÉ=jÉíÜçÇÉåK== wìÉêëí=ëçää=ÇÉê=rãÖ~åÖ=ãáí=ÇÉê=cìåâíáçå=WENN(...;...;...)=îçêÖÉëíÉääí=ïÉêÇÉåK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUS=

PKO==hä~ëëÉåÄáäÇìåÖ=

QT

^åëÅÜäáÉ≈ÉåÇ= ÉêÑçäÖí= ÇáÉ= kìíòìåÖ= ÇÉê= cìåâíáçå= VERWEIS(...;...;...)I= Ç~åå= ÑçäÖí= Éáå= eáåJ ïÉáë=~ìÑ=ÇáÉ=^Äò®ÜäÑìåâíáçå= HÄUFIGKEIT(...;...)=ìåÇ=ëÅÜäáÉ≈äáÅÜ=ÇáÉ=^êÄÉáí=ãáí=ÇÉã=tÉêâJ òÉìÖ=HISTOGRAMMK=iÉíòíÉêÉë=áëí=~ã=ÄÉèìÉãëíÉå=Ó=ïÉê=Éë=ÉáäáÖ=Ü~íI=ëçääíÉ=òìÉêëí=ÇÉå=^ÄëÅÜåáíí= PKOKQ=~Ä=pÉáíÉ=RM=äÉëÉåK==

3.2.1

Klassenzuordnung mit der Funktion WENN

aáÉ=bñÅÉäJcìåâíáçå= WENN(...;...;...)=îÉêä~åÖí=ëíÉíë=ÇêÉá=^åÖ~ÄÉåI=ÇáÉ=ãáí=pÉãáâçäçå=òì= íêÉååÉå=ëáåÇW=WENN( Test ; Ja_Eintrag ; Nein_Eintrag )= ^å=ÇáÉ=ÉêëíÉ=mçëáíáçå=áëí=ÇáÉ=_ÉÇáåÖìåÖ=òì=ëÅÜêÉáÄÉåI=ÇáÉ=òì=éêΩÑÉå=áëíK=få=ÇÉê=jáííÉ=áëí=~åJ òìÖÉÄÉåI= ï~ë= áå= ÇÉê= wÉääÉI= ÇáÉ= ÇáÉëÉ= cìåâíáçå= ÉåíÜ®äíI= ÄÉá= ÉêÑΩääíÉã=qÉëí= Éáåòìíê~ÖÉå= áëíK= oÉÅÜíë=îçã=òïÉáíÉå=pÉãáâçäçå=áëí=~åòìÖÉÄÉåI=ïÉäÅÜÉå=fåÜ~äí=ÇáÉ=wÉääÉ=ÄÉá=åáÅÜí=ÉêÑΩääíÉã= qÉëí=ÄÉâçããÉå=ëçääK=aáÉ=q~ÄÉääÉå=PKNN=òÉáÖÉå=ÉáåÉ=ÉêëíÉ=^åïÉåÇìåÖ=ìåÇ=ÇáÉ=ÉêëÅÜÉáåÉåJ ÇÉå=báåíê®ÖÉK=

=

=

q~ÄK=PKNNW=bêëíÉê=sÉêëìÅÜ=ãáí=ÇÉê=WENNJcìåâíáçå=

Verschachtelung von WENN-Funktionen lÑÑÉåÄ~ê= áëí= ÇáÉ= wìçêÇåìåÖ= ~ääÉê= tÉêíÉ= ìåíÉêÜ~äÄ= îçå= SM= âÖ= âçêêÉâíI= ~ÄÉê= ÇáÉ= Öê∏≈ÉêÉå= dÉïáÅÜíëïÉêíÉ=ïÉêÇÉå=åçÅÜ=åáÅÜí=ÇáÑÑÉêÉåòáÉêíK== aÉëÜ~äÄ=ãìëë=áã=kÉáåJbáåíê~Ö=ÇáÑÑÉêÉåòáÉêí=ïÉêÇÉåI=ï~ë=ÇìêÅÜ=ÉáåÉ=ÉêåÉìíÉI=áåíÉêåÉ=sÉêJ ïÉåÇìåÖ=ÇÉê=WENNJcìåâíáçå=ã∏ÖäáÅÜ=áëíK== aáÉ=q~ÄÉääÉ=PKNO~LÄ=òÉáÖÉå=cìåâíáçå=ìåÇ=bêÖÉÄåáëK=

=

=

q~ÄK=PKNOW=sÉêëÅÜ~ÅÜíÉäíÉ=WENNJcìåâíáçåÉåW=cçêãÉä=ìåÇ=bêÖÉÄåáë= fëí=ÇÉê=ÉêëíÉ=qÉëí=ÉêÑΩääí=EdÉïáÅÜí=ìåíÉê=SM=âÖFI=Ç~åå=ïáêÇ=ÉáåÉ= 1=ÉáåÖÉíê~ÖÉåK=^åÇÉêåÑ~ääë= ÑçäÖí=ÇÉê=áååÉêÉ=qÉëí=EdÉïáÅÜí=ìåíÉê=UM=âÖ=\FK=fëí=ÇáÉëÉê=ÉêÑΩääíI=Ç~åå=ïáêÇ=ÉáåÉ= 2=ÉáåÖÉíê~J ÖÉåK=aÉê=kÉáåJc~ää=ÇÉë=áååÉêÉå=qÉëíë=ÑΩÜêí=ëÅÜäáÉ≈äáÅÜ=òìã=báåíê~Ö=3K==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT==

P==^ÄëçäìíÉ=e®ìÑáÖâÉáíÉå=

QU

kìå=ïáêÇ=òïáëÅÜÉå=QM=ìåÇ=UM=âÖ=ÄÉêÉáíë=êáÅÜíáÖ=áå=ÇáÉ=hä~ëëÉå=ÉáåÖÉçêÇåÉíI=~ääÉêÇáåÖë=ïáêÇI= ïáÉ=òì=ÉêâÉååÉåI=ÇÉê=ΩÄÉêJNMMJtÉêí=115,76=åçÅÜ=Ñ~äëÅÜ=òìÖÉçêÇåÉíK== cçäÖäáÅÜ=ãìëë=áã=kÉáåJbáåíê~Ö=ÇÉê=áååÉêÉå=WENNJcìåâíáçå=ïÉáíÉê=ÇáÑÑÉêÉåòáÉêí=ïÉêÇÉåK== j~å= ΩÄÉêäÉÖí= ëáÅÜI= Ç~ëë= òìê= ÇáÑÑÉêÉåòáÉêíÉå= báåçêÇåìåÖ= ÇÉê= tÉêíÉ= ΩÄÉê= NOM= âÖ= ìåÇ= ΩÄÉê= NQM=âÖ=ëÅÜäáÉ≈äáÅÜ=åçÅÜ=òïÉá=ïÉáíÉêÉ=áååÉêÉ=WENNJcìåâíáçåÉå=îÉêïÉåÇÉí=ïÉêÇÉå=ãΩëëÉåK== pÉÜÉå=ïáê=ìåë=ÇáÉ=ÉåÇÖΩäíáÖÉI=òáÉãäáÅÜ=îÉêëÅÜ~ÅÜíÉäíÉ= WENNJcìåâíáçå=~åI=ÇáÉ=~ÄÉê=~ääÉ=dÉJ ïáÅÜíëïÉêíÉ=êáÅÜíáÖ=áå=ÇáÉ=òìÖÉÜ∏êáÖÉ=hä~ëëÉ=ÉáåçêÇåÉíK== =WENN(B2<60;1;WENN(B2<80;2;WENN(B2<100;3;WENN(B2<120;4;5))))

kìå=â~åå=ÇáÉ=ÄÉêÉáíë=ÄÉâ~ååíÉ=^åïÉåÇìåÖ=ÇÉê=cìåâíáçå= ZÄHLENWENN(...;...)=ÑçäÖÉåI=ãáí= ÇÉêÉå= eáäÑÉ= ëÅÜäáÉ≈äáÅÜ= ÑÉëíÖÉëíÉääí= ïáêÇI= ïáÉ= îáÉäÉ= jÉêâã~äëïÉêíÉ= ÇÉë= a~íÉåÄÉëí~åÇÉë= áå= ÇáÉ=àÉïÉáäáÖÉ=hä~ëëÉ=Ñ~ääÉåK== bë=ï®êÉ=ΩÄêáÖÉåë=~ìÅÜ=ã∏ÖäáÅÜ=ÖÉïÉëÉåI=ÇáÉ=hä~ëëÉå=~åëíÉääÉ=ãáí=ÇÉå=w~ÜäÉå=N=Äáë=S=~ìÅÜ= åáÅÜíåìãÉêáëÅÜ=òì=ÄÉòÉáÅÜåÉåK=báåÉ=ëçäÅÜÉ=s~êá~åíÉI=ÇáÉ=~ääÉêÇáåÖë=ïÉÖÉå=ÇÉê=ÖÉï®ÜäíÉå= sçâ~ÄÉäå=åáÅÜí= ìåéêçÄäÉã~íáëÅÜ= áëíI= ëçää= ãáí= ÑçäÖÉåÇÉê= cçêãÉä= ~åÖÉÖÉÄÉå= ïÉêÇÉåI= ïçÄÉá= ÇáÉ=pÅÜêÉáÄïÉáëÉ=ÇáÉ=sÉêëÅÜ~ÅÜíÉäìåÖ=Éíï~ë=ÇÉìíäáÅÜÉê=ã~ÅÜÉå=ëçääW== =WENN(B2<60; "dünn"; WENN(B2<80; "normal"; WENN(B2<100; "kräftig"; WENN(B2<120; "korpulent";"Jumbo"))))

cΩê=~ääÉ=iÉëÉêáååÉå=ìåÇ=iÉëÉêI=ÇÉåÉå=ÇÉê=rãÖ~åÖ=ãáí=ÇÉê= WENNJcìåâíáçå=áå=ÇáÉëÉê=âçãéäáJ òáÉêíÉå=cçêã=ìåëóãé~íÜáëÅÜ=ëÉáå=ëçääíÉ=Eï~ë=ÇìêÅÜ~ìë=îÉêëí®åÇäáÅÜ=áëíFI=ëÉá=ÜáÉê=ÄÉêÉáíë=Ç~êJ ~ìÑ=ÜáåÖÉïáÉëÉåI=Ç~ëë=ÇáÉ=hä~ëëÉåòìçêÇåìåÖ=çÑí=~ìÅÜ=ïÉëÉåíäáÅÜ=ÉáåÑ~ÅÜÉê=îçêÖÉåçããÉå= ïÉêÇÉå=â~ååK=a~òì=ëíÉääí=bñÅÉä=Ç~ë=tÉêâòÉìÖ= HISTOGRAMM=òìê=sÉêÑΩÖìåÖI=Ç~ë=áå=^ÄëÅÜåáíí= PKOKQ=~ìÑ=pÉáíÉ=RM=ÄÉëÅÜêáÉÄÉå=ïáêÇK== qêçíòÇÉã= ëçää= Éêëí= åçÅÜ= Éáå= ïÉáíÉêÉê= âäÉáåÉê= ^ÄëÅÜåáíí= ÇÉê= äÉáëíìåÖëÑ®ÜáÖÉå= WENNJcìåâíáçå= ÖÉïáÇãÉí=ïÉêÇÉåK=

Die Funktion WENN und die Kodierung von nichtnumerischen Daten táÉ= ëÅÜçå= ãÉÜêÑ~ÅÜ= Éêï®ÜåíI= ÄáÉíÉí= bñÅÉä= áã= dÉÖÉåë~íò= òì= ÉáåáÖÉå= êÉáåÉå= pí~íáëíáâJmêçJ Öê~ããÉå= ÇáÉ= ìåÉáåÖÉëÅÜê®åâíÉ= j∏ÖäáÅÜâÉáíI= a~íÉå= áå= áÜêÉê= ìêëéêΩåÖäáÅÜÉå= åìãÉêáëÅÜÉå= çÇÉê=åáÅÜíåìãÉêáëÅÜÉå=cçêã=áå=ÉáåÉê=q~ÄÉääÉ=òì=ëéÉáÅÜÉêåK== jáí=ÇÉê=ZÄHLENWENNJcìåâíáçå=â~åå=ã~å=éêçÄäÉãäçë=~ìÅÜ=áÜêÉ=e®ìÑáÖâÉáíÉå=~å~äóëáÉêÉåK== bë= Ü~í= ~ääÉêÇáåÖë= qê~ÇáíáçåI= Ç~ëë= áåëÄÉëçåÇÉêÉ=^ìëïÉêíìåÖÉå=îçå=_ÉÑê~ÖìåÖÉå= ÖêìåÇë®íòJ äáÅÜ=âçÇáÉêí=ÉêÑ~ëëí=ïÉêÇÉåI=ÇK=ÜK=àÉÇÉê=^åíïçêí=ïáêÇ=ÉáåÉ=w~Üä=òìÖÉçêÇåÉíI=ÇáÉ=Ç~åå=ÉáåÖÉJ ÖÉÄÉå=ïáêÇK=káÅÜí=ïÉåáÖÉ=_ΩÅÜÉê=òìê=j~êâíÑçêëÅÜìåÖ=ìåÇ=a~íÉå~å~äóëÉ=ïáÇãÉå=ëáÅÜ=~ìëJ ÑΩÜêäáÅÜ=ÇÉå=cê~ÖÉå=ÉáåÉê=ëáååîçääÉå=hçÇáÉêìåÖK== fã= ^ÄëÅÜåáíí= NKQ= ÇáÉëÉë= _ìÅÜÉë= ~ìÑ= pÉáíÉ= ON= ïìêÇÉ= ~ÄÉê= ëÅÜçå= ~ìÑ= ÇáÉ= Ç~ÄÉá= ã∏ÖäáÅÜÉå= cÉÜäáåíÉêéêÉí~íáçåÉå= ìåÇ= ëÅÜÉáåÄ~êÉå= sÉê®åÇÉêìåÖÉå= ÇÉë= a~íÉååáîÉ~ìë= ÜáåÖÉïáÉëÉå= ìåÇ= ÇÉëÜ~äÄ= ~ääÉå= bñÅÉäJkìíòÉêå= ÉãéÑçÜäÉåI= åáÅÜíåìãÉêáëÅÜÉ= a~íÉå= ~ìÅÜ= åáÅÜíåìãÉêáëÅÜ= áå= ÇáÉ=bñÅÉäJq~ÄÉääÉ=òì=ΩÄÉêåÉÜãÉåI=òK=_K=Ç~ë=dÉëÅÜäÉÅÜí=ãáí=w=ìåÇ=mI=Ç~ãáí=åáÉã~åÇ=~ìÑ=ÇáÉ= ÉáÖÉå~êíáÖÉ=fÇÉÉ=âçããíI=ÑΩê=ÇáÉëÉ=^åÖ~ÄÉ=ïçã∏ÖäáÅÜ=ÉáåÉå=łjáííÉäïÉêí=~ìëòìïÉáëÉåKKK= bë=ÖáÄí=àÉÇçÅÜ=dêÉåòÉå=ÇÉê=sÉê~êÄÉáíìåÖ=åáÅÜíåìãÉêáëÅÜÉê=a~íÉåK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT=

PKO==hä~ëëÉåÄáäÇìåÖ=

QV

wìã= _ÉáëéáÉä= ÄÉå∏íáÖí= ÇáÉ= cìåâíáçå= MODALWERT(...)I= ÇáÉ= ÇÉå= ~ã= Ü®ìÑáÖëíÉå= ~ìÑíêÉíÉåÇÉå= jÉêâã~äëïÉêí= ÜÉê~ìëëìÅÜí= ìåÇ= áã= ^ÄëÅÜåáíí= PKP= ~ìÑ= pÉáíÉ= RO= å®ÜÉê= îçêÖÉëíÉääí= ïáêÇI= ìåÄÉJ ÇáåÖí=åìãÉêáëÅÜÉ=a~íÉåK== cΩê= ÇÉå= c~ääI= Ç~ëë= åáÅÜíåìãÉêáëÅÜÉå= jÉêâã~äë~ìëéê®ÖìåÖÉå= å~ÅÜíê®ÖäáÅÜ= åìãÉêáëÅÜÉ= jÉêâã~äëïÉêíÉ= òìÖÉçêÇåÉí= ïÉêÇÉå= ãΩëëÉåI= â~åå= ã~å= ÇáÉ= cìåâíáçå= WENN(...;...;...)= ëÉÜê=Öìí=îÉêïÉåÇÉåK== q~ÄÉääÉ=PKNP=Éêâä®êí=ÄÉáëéáÉäÜ~ÑíI=ïáÉ=ÇáÉ=wìçêÇåìåÖ=w1=ìåÇ=m0=êÉ~äáëáÉêí=ïáêÇK=====

=

=

q~ÄK=PKNPW=hçÇáÉêìåÖ=ãáí=ÇÉê=WENNJcìåâíáçå=

3.2.2

Die Funktion VERWEIS

jáí= ÇÉê= bñÅÉäJcìåâíáçå= VERWEIS(...;...;...)= ä~ëëÉå= ëáÅÜ= ÉÄÉåÑ~ääë= hä~ëëÉåòìçêÇåìåÖÉå= êÉ~äáëáÉêÉåK== aáÉëÉ=cìåâíáçå=îÉêä~åÖí=ÇêÉá=^åÖ~ÄÉåK=wìÉêëí=áëí=ÇáÉ=wÉääÉ=Éáåòìíê~ÖÉåI=ÇÉêÉå=fåÜ~äí=âä~ëëáJ ÑáòáÉêí= ïÉêÇÉå= ëçääK= ^åëÅÜäáÉ≈ÉåÇ= áëí= Éáå= pé~äíÉåÄÉêÉáÅÜ= Éáåòìíê~ÖÉåI= áå= ÇÉã= ëáÅÜ= ÇáÉ= ëçêJ íáÉêíÉå=hä~ëëÉåÖêÉåòÉå=ÄÉÑáåÇÉåK=pÅÜäáÉ≈äáÅÜ=ïáêÇ=åçÅÜ=Éáå=ÖäÉáÅÜä~åÖÉê=pé~äíÉåÄÉêÉáÅÜ=îÉêJ ä~åÖíI=áå=ÇÉã=ëáÅÜ=ÇáÉ=àÉïÉáäáÖÉå=hä~ëëÉåÄÉòÉáÅÜåìåÖÉå=ÄÉÑáåÇÉåK==

= q~ÄK=PKNQ~W=^åïÉåÇìåÖ=ÇÉê=VERWEISJcìåâíáçå=W=cçêãÉäå=

= q~ÄK=PKNQÄW=^åïÉåÇìåÖ=ÇÉê=VERWEISJcìåâíáçåW=tÉêíÉ== cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT==

P==^ÄëçäìíÉ=e®ìÑáÖâÉáíÉå=

RM

aáÉ= cìåâíáçå= VERWEIS(...;...;...) ÇìêÅÜëìÅÜí= ÑΩê= àÉÇÉå= jÉêâã~äëïÉêí= ÇÉå= _ÉêÉáÅÜ= ÇÉê= hä~ëëÉåÖêÉåòÉåI= îçå= çÄÉå= ÄÉÖáååÉåÇK= fëí= ÇáÉ= å~ÅÜÑçäÖÉåÇÉ= hä~ëëÉåÖêÉåòÉ= òì= Öêç≈I= Ç~åå= ïáêÇ=ÇÉê=åÉÄÉåëíÉÜÉåÇÉ=tÉêí=~äë=hä~ëëÉåÄÉòÉáÅÜåìåÖ=ÉáåÖÉíê~ÖÉåK== eáÉê=ïìêÇÉå=ÇáÉëã~ä=ÇáÉ=sÉêÄ~äÄÉòÉáÅÜåìåÖÉå=ÄÉåìíòíI=ìã=òì=òÉáÖÉåI=Ç~ëë=Éë=âÉáåÉëÑ~ääë= áããÉê=w~ÜäÉå=ëÉáå=ãΩëëÉåI=ãáí=ÇÉåÉå=ã~å=ÉáåÉ=hä~ëëÉ=ÄÉòÉáÅÜåÉíK=aÉåå=ëÅÜäáÉ≈äáÅÜ=â∏ååJ íÉ= ÇáÉ= cìåâíáçå= ZÄHLENWENN(...;...;...)= ~åëÅÜäáÉ≈ÉåÇ= éêçÄäÉãäçë= ~Äò®ÜäÉåI= ïáÉ= çÑí= ÇáÉ= hä~ëëÉ=korpulent=~ìÑÖÉíêÉíÉå=áëíK==

3.2.3

Die Funktion HÄUFIGKEIT

aáÉ=cìåâíáçå= HÄUFIGKEIT(...;...)=áëí=ÉáåÉ=ëç=ÖÉå~ååíÉ=j~íêáñJ=çÇÉê=sÉâíçêÑìåâíáçåK=páÉ= äáÉÑÉêí=åáÅÜí=åìê=ÉáåÉå=bêÖÉÄåáëïÉêíI=ïáÉ=ïáê=Éë=ÄÉá=ÇÉå=ÄáëÜÉê=îçêÖÉëíÉääíÉå=cìåâíáçåÉå= ÇìêÅÜïÉÖ=ÉêäÉÄíÉåI=ëçåÇÉêå=ÑΩääí=ëáãìäí~å=ÉáåÉå=Ö~åòÉå=îçêÖÉÖÉÄÉåÉå=_ÉêÉáÅÜK== báåÉ= ÉêëíÉ= ^åïÉåÇìåÖ= ÉáåÉê= ëçäÅÜÉå= j~íêáñÑìåâíáçå= áëí= áã= ^ÄëÅÜåáíí= TKP= ~ìÑ= pÉáíÉ=NOV= òì= ÉêäÉÄÉåX=áåíÉêÉëëáÉêíÉ=iÉëÉê=ëÉáÉå=òìë®íòäáÅÜ=~ìÑ=ïÉáíÉêÑΩÜêÉåÇÉ=iáíÉê~íìêI=òK=_K=xNRz=îÉêïáÉJ ëÉåK==

3.2.4

Das Werkzeug HISTOGRAMM

a~ë=tÉêâòÉìÖ=HISTOGRAMM=âçãÄáåáÉêí=ÇáÉ=iÉáëíìåÖÉå=ÇÉê=ÄÉáÇÉå=ÄÉêÉáíë=îçêÖÉëíÉääíÉå=cìåâJ íáçåÉå=WENN(...;...;...)=ìåÇ=ZÄHLENWENN(...;...)K== jáí=eáäÑÉ=ÇÉë=tÉêâòÉìÖë=HISTOGRAMM=â~åå=å~ÅÜ=cÉëíäÉÖìåÖ=ÇÉê=hä~ëëÉåÖêÉåòÉå=ëçÑçêí=Ç~ë= bêÖÉÄåáë=ÇÉê=^ìëò®ÜäìåÖ=ÉêÜ~äíÉå=ïÉêÇÉåK== bë= ëçää= ÇÉêëÉäÄÉ= a~íÉåÄÉëí~åÇ= ïáÉ= áã= îçêáÖÉå= ^ÄëÅÜåáíí= îÉêïÉåÇÉí= ïÉêÇÉåK= q~ÄÉääÉ= PKNR= ÉåíÜ®äí=ÇáÉëÉå=a~íÉåÄÉëí~åÇ=ìåÇ=Ç~òì=áã=_ÉêÉáÅÜ=D2:D5=ÇáÉ=hä~ëëÉåÖêÉåòÉåK==

= q~ÄK=PKNRW=a~íÉåÄÉëí~åÇ=ìåÇ=hä~ëëÉåÖêÉåòÉå= kìå=ãìëë=Ç~ë=tÉêâòÉìÖ= HISTOGRAMM=~åÖÉÑçêÇÉêí=ïÉêÇÉåK=aáÉ=^åÑçêÇÉêìåÖ=ÇÉë=tÉêâòÉìÖë= ÉêÑçäÖí=ΩÄÉê=buqo^p^k^ivpbJcrkhqflkbk=EëáÉÜÉ=_áäÇ=PKQFK= pçääíÉå= ÇáÉ= ^å~äóëÉJcìåâíáçåÉå= åáÅÜí= áã= jÉåΩ= buqo^p= ~åÖÉÄçíÉå= ïÉêÇÉåI= Ç~åå= ëáåÇ= ëáÉ= ãáííÉäë= buqo^p^aaJfkp= ìåÇ= ÇìêÅÜ= pÉíòÉå= ÉáåÉë= e~âÉåë= áå= ÇÉå= ÄÉáÇÉå= ÉåíëéêÉÅÜÉåÇÉå= wÉáäÉå=EëáÉÜÉ=_áäÇ=PKRF=~åòìÑçêÇÉêåK== aáÉ=e~åÇÜ~ÄìåÖ=ÇÉë=tÉêâòÉìÖë=HISTOGRAMM=áëí=êÉÅÜí=ÉáåÑ~ÅÜK=j~å=Äê~ìÅÜí=åìêI=ïáÉ=áå=_áäÇ= PKS=òì=ëÉÜÉåI=òïÉá=^åÖ~ÄÉå=áå=ÇáÉ=òïÉá=báåÖ~ÄÉÑÉåëíÉê=Éáåòìíê~ÖÉåK== a~ë=cÉåëíÉê=EINGABEBEREICH=ÉêÜ®äí=ÇáÉ=òì=ìåíÉêëìÅÜÉåÇÉå=a~íÉå=Ó=ÜáÉê=áëí=~äëç=ÇáÉ=pé~äíÉ= ãáí=ÇÉå=dÉïáÅÜíë~åÖ~ÄÉå=ÉáåÖÉíê~ÖÉåK=få=Ç~ë=cÉåëíÉê=KLASSENBEREICH=áëí=Éáåòìíê~ÖÉåI=ïç= ëáÅÜ=ÇáÉ=ÑÉëíÖÉäÉÖíÉå=hä~ëëÉåÖêÉåòÉå=ÄÉÑáåÇÉåK===

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT=

PKO==hä~ëëÉåÄáäÇìåÖ=

RN

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cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT==

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RO

^å= ÇáÉëÉê= píÉääÉ= òÉáÖí= ëáÅÜI= ïÉëÜ~äÄ= áã= îçêáÖÉå= ^ÄëÅÜåáíí= ÇáÉ= WENNJcìåâíáçå= ÄÉëÅÜêáÉÄÉå= ïìêÇÉK=páÉ=ãìëë=ã~å=ÄÉåìíòÉåI=ïÉåå=ã~å=ëéÉòáÉääÉ=tΩåëÅÜÉ=Ü~íI=ÄÉáëéáÉäëïÉáëÉI=Ç~ëë=ÇáÉ= ~åÖÉÖÉÄÉåÉå=hä~ëëÉåÖêÉåòÉå=àÉïÉáäë=ÇáÉ=ìåíÉêÉå=hä~ëëÉåê®åÇÉê=ÄÉëÅÜêÉáÄÉå=ëçääÉåK==

= q~ÄK=PKNSW=bêÖÉÄåáë=ÇÉë=tÉêâòÉìÖë=HISTOGRAMM= _Éåìíòí= ã~å= Ç~ÖÉÖÉå= Ç~ë= ÄÉèìÉãÉ= tÉêâòÉìÖ= HISTOGRAMMI= ò~Üäí= ã~å= ÑΩê= ÇáÉëÉ= _ÉèìÉãJ äáÅÜâÉáí=å~íΩêäáÅÜ=ÉáåÉå=mêÉáëW== HISTOGRAMM=ÄÉíê~ÅÜíÉí=ÇáÉ=~åÖÉÖÉÄÉåÉå=tÉêíÉ=áã=hä~ëëÉåÄÉêÉáÅÜ=ëíÉíë=~äë=çÄÉêÉ=hä~ëëÉåJ

ÖêÉåòÉåK== q~ÄÉääÉ=PKNT=Éêâä®êí=ÇÉëÜ~äÄ=ÖÉå~ìI=ïáÉ=ã~å=ÇáÉ=^ìëÖ~ÄÉ=äÉëÉå=ãìëëK==

= q~ÄK=PKNTW=bêä®ìíÉêìåÖ=ÇÉê=^ìëÖ~ÄÉ=ÇÉë=tÉêâòÉìÖë=efpqldo^jj= táÉ=ÖÉë~ÖíI=Ç~ãáí=ãìëë=ã~å=äÉÄÉåK=j~å=â~åå=äÉáÇÉê=âÉáåÉ=báåëíÉääìåÖ=áå=ÇÉã=tÉêâòÉìÖ= HISTOGRAMM= îçêåÉÜãÉåI= ëç= Ç~ëë= ÇáÉ= ~åÖÉÖÉÄÉåÉå= dêÉåòÉå= ~äë= ìåíÉêÉ= o®åÇÉê= ÇÉê= hä~ëëÉå= ~åÖÉëÉÜÉå=ïÉêÇÉåK== fåÇáîáÇìÉääÉ=tΩåëÅÜÉ=ãΩëëÉå=~äëç=ãáí=ÇÉê= WENNJcìåâíáçå=ìãÖÉëÉíòí=ïÉêÇÉåK=a~ë=áëí=òï~ê= ~ìÑïÉåÇáÖÉêI=Ü~í=~ÄÉê=òìë®íòäáÅÜ=ÇÉå=Öêç≈Éå=sçêíÉáäI=Ç~ëë=ÄÉá=ûåÇÉêìåÖ=ÇÉê=a~íÉå=~ìíçã~J íáëÅÜ=~ääÉ=bêÖÉÄåáëëÉ=åÉì=ÄÉêÉÅÜåÉí=ïÉêÇÉåK== ^ääÉ=bñÅÉäJtÉêâòÉìÖÉ=äáÉÑÉêå=Ç~ÖÉÖÉå=ëí~êêÉ=Eëí~íáëÅÜÉF=bêÖÉÄåáëëÉX=ÇK=ÜK=ïÉêÇÉå=ÇáÉ=a~J íÉå=ÖÉ®åÇÉêíI=Ç~åå=ãìëë=Ç~ë=tÉêâòÉìÖ=ïáÉÇÉê=åÉì=~åÖÉï~åÇí=ïÉêÇÉåK==

3.3

Modalwert

táêÇ= ãáí= ÇÉê= cìåâíáçå= ZÄHLENWENN(...;...)= ÑΩê= ~ääÉ= îçêâçããÉåÇÉå= jÉêâã~äëïÉêíÉ= ÇÉêÉå= ~ÄëçäìíÉ=e®ìÑáÖâÉáí=~ìëÖÉò®Üäí=EëáÉÜÉ=q~ÄÉääÉ=PKNUFI=Ç~åå=ÉêÖáÄí=ëáÅÜ=òï~åÖëä®ìÑáÖ=ÇáÉ=cê~J ÖÉI= çÄ= Éáå= ÉáåòÉäåÉê= jÉêâã~äëïÉêí= ~ã= Ü®ìÑáÖëíÉå= ~ìÑíêáíí= Ó= çÇÉê= çÄ= Éë= ãÉÜêÉêÉ= jÉêâJ ã~äëïÉêíÉ= ãáí= ÇÉêëÉäÄÉå= e®ìÑáÖâÉáí= ÖáÄíK= a~êΩÄÉê= Üáå~ìë= ÉêÑ®Üêí= ã~å= ãáí= ZÄHLENWENN(...;...)=ÇáÉ=àÉïÉáäáÖÉå=^åò~ÜäÉåK== bë=ÉêÖáÄí=ëáÅÜ=ÇáÉ=cê~ÖÉI=çÄ=ã~å=ÇáÉëÉ=^ìëâΩåÑíÉ=åáÅÜí=ÉáåÑ~ÅÜÉê=ÉêÜ~äíÉå=â~ååK=pÉÜÉå=ïáê= ìåë=Ç~òì=áå=q~ÄÉääÉ=PKNVLPKOM=ÇáÉ=táêâìåÖ=ÇÉê=cìåâíáçå=MODALWERT(...)=~åK= táÉ=òì=ÉêâÉååÉåI=äáÉÑÉêí=ÇáÉëÉ=cìåâíáçå=òì=ÄÉáÇÉå=ÄÉíê~ÅÜíÉíÉå=a~íÉåÄÉëí®åÇÉå=ÇÉå=jÉêâJ ã~äëïÉêí=30K==

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3.4

Häufigkeiten von Paaren: Pivot-Tabellen

3.4.1

Aufgabenstellung und Bezeichnungen

q~ÄÉääÉ= PKOP= òÉáÖí= ÉáåÉ= EÇÉåâÄ~êÉF= §ÄÉêëáÅÜí= ΩÄÉê= rãë~íòãáííÉáäìåÖÉå= îçå= îáÉê= jáí~êÄÉáJ íÉêåX= Ç~ÄÉá= ïáêÇ= ~åÖÉåçããÉåI= Ç~ëë= ëáÉ= áã= bêÑçäÖëÑ~ääÉ= ìåîÉêòΩÖäáÅÜ= ÇÉå= jçå~í= ìåÇ= ÇÉå= tÉêí=ÇÉë=ÉêòáÉäíÉå=bêÖÉÄåáëëÉë=ãÉäÇÉåK== a~ÄÉá=ÉåíëíÉÜí=~äëç=Éáå=ìåΩÄÉêíêçÑÑÉå=åáÅÜíë=ë~ÖÉåÇÉê=a~íÉåÄÉëí~åÇK= aÉê= a~íÉåÄÉëí~åÇ= áëí= áå= ÇáÉëÉê= cçêã= ÑΩê= ^ìëïÉêíìåÖÉå= î∏ääáÖ= ìåÄê~ìÅÜÄ~êW= tÉÇÉê= áëí= òì= ÉêâÉååÉåI=ïáÉ=îáÉäÉ=jÉäÇìåÖÉå=ΩÄÉêÜ~ìéí=îçêäáÉÖÉåI=åçÅÜ=ä®ëëí=ëáÅÜ=~ÄäÉëÉåI=ïÉäÅÜÉå=rãJ ë~íò=ïÉäÅÜÉê=jáí~êÄÉáíÉê=áå=ïÉäÅÜÉã=jçå~í=í~íë®ÅÜäáÅÜ=ÉêòáÉäí=Ü~íK== a~ÖÉÖÉå=ÄÉ~åíïçêíÉí=ÇáÉ=áå=q~ÄÉääÉ=PKOQ=Ç~êÖÉëíÉääíÉ=máîçíJq~ÄÉääÉ=EÑêΩÜÉê=~ìÅÜ=~äë=hêÉìòJ í~ÄÉääÉ=ÄÉòÉáÅÜåÉíF=ÖÉå~ì=ÇáÉëÉ=cê~ÖÉåK== páÉ=áåíÉêéêÉíáÉêí=ëáÅÜ=ÖÉïáëëÉêã~≈Éå=îçå=ëÉäÄëíX=äÉáÅÜí=òì=ÉêâÉååÉå=ëáåÇ=ÇáÉ=jçå~íÉ=çÜåÉ= jÉäÇìåÖÉåI=ÇáÉ=g~ÜêÉëJpìããÉå=ÇÉê=jáí~êÄÉáíÉêI=ÇáÉ=jçå~íëìãë®íòÉI=ÇÉê=dÉë~ãíJg~ÜêÉëìãJ ë~íò=îçå=QQMURISM=AK==

3.4.2

Herstellung einer einfachen Pivot-Tabelle

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3.4.3

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3.4.5

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3.4.6

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4

Grafische Darstellungen

4.1

Histogramme: Werkzeug HISTOGRAMM

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= q~ÄK=PKNRW=a~íÉåÄÉëí~åÇ=ìåÇ=hä~ëëÉåÖêÉåòÉå= a~ë= tÉêâòÉìÖ= HISTOGRAMM= äáÉÑÉêíI= ïÉåå= áã= báåÖ~ÄÉÑÉåëíÉê= Éáå= e~âÉå= ÄÉá= DIAGRAMMDARSTELLUNG= ~åÖÉÄê~ÅÜí= ïìêÇÉ= E_áäÇ= QKNFI= òìë®íòäáÅÜ= ëçÑçêí= ÉáåÉ= ÉêëíÉ=Öê~ÑáëÅÜÉ=a~êëíÉääìåÖ= ÇÉê=e®ìÑáÖâÉáí=áå=cçêã=ÉáåÉë=ÉáåÑ~ÅÜÉå=p®ìäÉåÇá~Öê~ããëK==

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TO

a~ë=sçêÖÉÜÉå=Ç~òìW=jáí=ÇÉê=kÉÄÉåJj~ìëí~ëíÉ=EáK=~ääÖK=êÉÅÜíëF=ïáêÇ=ÉáåÉê=ÇÉê=_~äâÉå=~åÖÉJ âäáÅâíI= Ç~åå= âçããí= ã~å= òìã= jìëíÉê~åÖÉÄçí= ΩÄÉê= a^qbkobfebk= cloj^qfbobkjrpqbo= c§iibccbhqbjrpqboK= táêÇ=Ç~ë=tÉêâòÉìÖ= HISTOGRAMM=åáÅÜí=ÄÉåìíòíI=Ç~åå=ãìëë=ã~å=ÑΩê=Öê~ÑáëÅÜÉ=a~êëíÉääìåÖÉå= ÇÉå=aá~Öê~ããJ^ëëáëíÉåíÉå=îÉêïÉåÇÉå=çÇÉê=ãáí=ÇÉê= F11 JjÉíÜçÇÉ=~êÄÉáíÉåK== a~=ÇÉê=rãÖ~åÖ=ãáí=ÇÉã=aá~Öê~ããJ^ëëáëíÉåíÉåI=ïÉåå=åáÅÜí=ÄÉêÉáíë=ÄÉâ~ååíI=Ç~åå=ÇçÅÜ=ëÉÜê= äÉáÅÜí=òì=ÉêäÉêåÉå=áëíI=ëçää=~äíÉêå~íáî=ÜáÉê=ÇáÉ=ÉáåÑ~ÅÜÉ= F11 JjÉíÜçÇÉ=îçêÖÉëíÉääí=ïÉêÇÉåK== aáÉ= F11 JjÉíÜçÇÉ=äáÉÑÉêí=ëçÑçêí=ÉáåÉ=dê~Ñáâ=ã~ñáã~äÉê=dê∏≈É=~ìÑ=ÉáåÉã=~åÇÉêÉå=q~ÄÉäJ äÉåÄä~ííI=ÇáÉ=~åëÅÜäáÉ≈ÉåÇ=áå=áÜêÉê=dÉëí~äíìåÖ=îÉê®åÇÉêí=ïÉêÇÉå=â~ååK== aÉê= aá~Öê~ããJ^ëëáëíÉåí= Ç~ÖÉÖÉå= Ñê~Öí= îçê= ÇÉê= eÉêëíÉääìåÖ= ÇÉê= dê~Ñáâ= å~ÅÜ= ÇÉå= dÉëí~äJ íìåÖëïΩåëÅÜÉåI=ìåÇ=äáÉÑÉêíI=ïÉåå=åáÅÜí=áã=äÉíòíÉå=pÅÜêáíí=~åÇÉêë=ÖÉÑçêÇÉêíI=Éêëí=Éáåã~ä=ÉáåÉ= âäÉáåÉ=dê~Ñáâ=~ìÑ=ÇÉã=q~ÄÉääÉåÄä~íí=ãáí=ÇÉã=a~íÉåÄÉëí~åÇK== _ÉáÇÉå=jÉíÜçÇÉå=ÖÉãÉáåë~ã=áëí=àÉÇçÅÜ=ÇáÉ=~ì≈ÉêçêÇÉåíäáÅÜ=ïáÅÜíáÖÉ=báÖÉåëÅÜ~ÑíI=Ç~ëë=ÇáÉ= îçå=áÜåÉå=ÉêòÉìÖíÉå=dê~ÑáâÉå=åáÅÜí=ëí~íáëÅÜ=ëáåÇW= _Éá=ûåÇÉêìåÖÉå=áã=a~íÉåÄÉëí~åÇ=é~ëëÉå=ëáÅÜ=ÇáÉ=dê~ÑáâÉå=ëçÑçêí=ìåÇ=~ìíçã~íáëÅÜ=ÇÉê= åÉìÉå=páíì~íáçå=~åK===

4.2

Die F11 -Methode zur Herstellung von Grafiken

4.2.1

Zusammenhängende Daten

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4.4

Skalierung

4.4.1

Bedeutung

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4.4.2

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4.5

Grafische Darstellung von Pivot-Tabellen

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4.6

Darstellung von absoluten Summenhäufigkeiten

4.6.1

Bereits berechnete Summenhäufigkeiten

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4.6.2

100-Prozent-Diagramme

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4.6.3

100-Prozent-Diagramme im Zeitablauf

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5

Relative Häufigkeiten, empirische Verteilung

5.1

Berechnung relativer Häufigkeiten

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5.2

Excel rechnet falsch !?

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6

Statistische Maßzahlen

6.1

Mittelwerte

6.1.1

Median und arithmetisches Mittel (Durchschnitt)

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1000

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6.2.3

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SKO==píêÉììåÖëã~≈É=

NMV

=

= q~ÄK=SKTÄW=bãéáêáëÅÜÉ=s~êá~åò=ìåÇ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=ÉäÉãÉåí~êW=cçêãÉäå=

= q~ÄK=SKTÅW=bãéáêáëÅÜÉ=s~êá~åò=ìåÇ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=ÉäÉãÉåí~êW=tÉêíÉ= få=q~ÄÉääÉ=SKT~=ïáêÇ=ÇÉê=rãÖ~åÖ=ãáí=ÄÉáÇÉå=bñÅÉäJcìåâíáçåÉå=ÇÉãçåëíêáÉêíK== få= ÇÉå= q~ÄÉääÉå= SKTÄ= ìåÇ= SKTÅ= ïáêÇ= ÇáÉ= ÉäÉãÉåí~êÉ= _ÉêÉÅÜåìåÖ= îçå= ÉãéáêáëÅÜÉê= s~êá~åò= ìåÇ=ÉãéáêáëÅÜÉê=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=å~ÅÜîçääòáÉÜÄ~ê=îçêÖÉÑΩÜêíK==

6.2.4

Einschub: Normalverteilung

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cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVR=

S==pí~íáëíáëÅÜÉ=j~≈ò~ÜäÉå=

NNM

NK=^ääÉ=tÉêíÉ=âçåòÉåíêáÉêÉå=ëáÅÜ=ëí~êâ=ìã=Ç~ë=~êáíÜãÉíáëÅÜÉ=jáííÉäK= OK=aáÉ=tÉêíÉ=ÄÉÑáåÇÉå=ëáÅÜ=ìåÖÉÑ®Üê=òì=ÖäÉáÅÜÉå=qÉáäÉå=äáåâë=ìåÇ=êÉÅÜíë=îçã=~êáíÜãÉJ= ====íáëÅÜÉå=jáííÉäK= PK=^ì≈ÉêÜ~äÄ=ÇÉê=ëç=ÖÉå~ååíÉå=aêÉáJpáÖã~JdêÉåòÉå=ÖáÄí=Éë=ëç=Öìí=ïáÉ=âÉáåÉ=tÉêíÉ=ãÉÜêK== aáÉ=pí~íáëíáâ=~êÄÉáíÉí=éêáåòáéáÉää=åáÅÜí=ãáí=ÇÉê=sçâ~ÄÉä=łà~K=^äëç=òáÉÜí=ã~å=~ìë=ÇÉã=bêÑΩääíJ ëÉáå=~ääÉê=ÇêÉá=hêáíÉêáÉå=åáÉã~äë=ÇÉå=pÅÜäìëëI=Ç~ëë=kçêã~äîÉêíÉáäìåÖ=îçêäáÉÖÉK=pçåÇÉêå=ã~å= ÑçêãìäáÉêí=ëíÉíë=łåÉáå=çÇÉê=łåáÅÜí=åÉáåW==

=

páåÇ= ÇáÉ= ÇêÉá= oÉÖÉäå= ÉêÑΩääíI= Ç~åå= ëéêáÅÜí=Éêëí=Éáåã~ä=åáÅÜíë=ÖÉÖÉå=ÇáÉ=^åå~ÜãÉI= Ç~ëë= kçêã~äîÉêíÉáäìåÖ=îçêäáÉÖÉå=â~ååK== píÉääí= ã~å= ÑΩê= ÉáåÉå= a~íÉåÄÉëí~åÇ= àÉÇçÅÜ= ÇÉå= sÉêëíç≈= ÖÉÖÉå= ÉáåÉ= ÇáÉëÉê= ÇêÉá= oÉÖÉäå= ÑÉëíI=Ç~åå=áëí=ÇáÉ=^åå~ÜãÉI=Éê=Éåíëí~ããÉ=ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáíI=åáÅÜí= ÖÉêÉÅÜíÑÉêíáÖíK==

tçÄÉá= ÇáÉëÉ= pÅÜäìëëÑçäÖÉêìåÖÉå= ÉáåÉå= ëí~íáëíáëÅÜÉå= qÉëí= ÖÉã®≈= ÇÉå= ëíêÉåÖÉå= oÉÖÉäå= ÇÉê= ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=íêçíòÇÉã=åáÅÜí=ÉêëÉíòÉå=â∏ååÉå=Ó=~ÄÉê=ÜáÉê=ëçää=à~=åìê=Éáå=ëÅÜåÉääÉê= ìåÇ=ÉáåÑ~ÅÜÉê=tÉÖ=òì=ÉáåÉê=îáëìÉääÉå=sÉêãìíìåÖ=ÖÉòÉáÖí=ïÉêÇÉåK==

= q~ÄK=SKU~W=cçêãÉäå=

= q~ÄK=SKUÄW=tÉêíÉ= aáÉ= q~ÄÉääÉå= SKU~LÄ= òÉáÖÉå= ÉáåÉå= a~íÉåÄÉëí~åÇI= ÇÉê= òïÉÅâë= k~ÅÜîçääòáÉÜÄ~êâÉáí= ÇáÉëã~ä= åáÅÜí=áå=ÉáåÉ=wÉáäÉ=çÇÉê=pé~äíÉI=ëçåÇÉêå=áå=ÇÉå=oÉÅÜíÉÅâÄÉêÉáÅÜ=A3:E12=ÉáåÖÉíê~ÖÉå=ïìêÇÉK===== pÉÜÉå=ïáê=ìåë=Ç~òì=Éáå=_ÉáëéáÉä=òìê=fääìëíê~íáçå=ÇÉë=sçêÖÉÜÉåë=~åK== cΩê= ÉáåÉ= pÅÜ®íòìåÖ=ÇÉê=aêÉáJpáÖã~JdêÉåòÉå= îÉêïÉåÇÉí= ã~å= Ç~ÄÉá= Ç~ë= äÉáÅÜí= îÉêÑΩÖÄ~êÉ= fåíÉêî~ää== [arithm.Mittel – 3*emp.Standardabweichung , arithm.Mittel + 3*emp.Standardabweichung]

j~å=äáÉëí=áå=ÇÉê=q~ÄÉääÉ=SKUÄ=~ÄW=a~ë=~êáíÜãÉíáëÅÜÉ=jáííÉä=áëí=ÖäÉáÅÜ=29,8=ìåÇ=ÇáÉ=ÉãéáêáëÅÜÉ= pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=áëí=ÖäÉáÅÜ=4,7K==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVR=

SKO==píêÉììåÖëã~≈É=

NNN

a~ãáí=ÉêÜ®äí=ã~å=ëçÑçêí=pÅÜ®íòìåÖÉå=ÑΩê=ÇáÉ=ÄÉáÇÉå=aêÉáJpáÖã~JdêÉåòÉåW== pÅÜ®íòìåÖ=ÇÉê=äáåâÉå=PJpáÖã~JdêÉåòÉ=W==

29,8 - 3*4,7 = 15,7==

pÅÜ®íòìåÖ=ÇÉê=êÉÅÜíÉå=PJpáÖã~JdêÉåòÉW=

29,8 + 3*4,7 = 43,9=

a~ë=ÜÉá≈í=~äëçW=tÉåå=ëáÅÜ=åáÅÜí=å~ÜÉòì=~ääÉ=a~íÉå=áã=_ÉêÉáÅÜ=îçå= 15,7=Äáë= 43,9=ÄÉÑáåÇÉåI= ïáêÇ=ã~å=ÄÉêÉáíë=ÇÉê=sÉêãìíìåÖ=~ìÑ=kçêã~äîÉêíÉáäìåÖ=ïáÇÉêëéêÉÅÜÉå=ãΩëëÉåK=eáåòì=âçãJ ãÉå=Ç~åå=~ÄÉê=åçÅÜ=ÇáÉ=_ÉÇáåÖìåÖÉå=N=ìåÇ=OK== ^ääÉ=ÇêÉá=_ÉÇáåÖìåÖÉå=òìë~ããÉå=â~åå=ã~å=îáëìÉää=ãáí=eáäÑÉ=ÇÉë=tÉêâòÉìÖë= HISTOGRAMM= ΩÄÉêéêΩÑÉåK== a~òì=íÉáäí=ã~å=òìÉêëí=ÇÉå=ìåíÉê=sÉêïÉåÇìåÖ=îçå=jáííÉäïÉêí=ìåÇ=ÉãéáêáëÅÜÉê=pí~åÇ~êÇ~ÄJ ïÉáÅÜìåÖ= ÖÉëÅÜ®íòíÉå= aêÉáJpáÖã~J_ÉêÉáÅÜ= áå= ãáåÇÉëíÉåë=OM=ÖäÉáÅÜÉ=qÉáäÉ= ÉáåX= áå= ìåëÉêÉã= _ÉáëéáÉä=ÉêïÉáëí=Éë=ëáÅÜ=~äë=ÖΩåëíáÖI=~äë=ÉêëíÉ=hä~ëëÉåÖêÉåòÉ= 15=òì=ï®ÜäÉåI=Ç~åå= 16,5I=Ç~åå= 18,0=ìëïK=Äáë=45K==

=

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cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVR=

S==pí~íáëíáëÅÜÉ=j~≈ò~ÜäÉå=

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6.3

Schiefe und Wölbung

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7

Korrelation und Regression

7.1

Der Korrelationskoeffizient von Bravais-Pearson

7.1.1

Begriff, Bedeutung, Berechnung

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7.1.2

Herstellung der Punktwolke

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7.2

Regression

7.2.1

Berechnung der Regressionskonstanten

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7.2.2

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NOU

bêáååÉêå=ïáê=ìåë=Ó=ïáê=ëìÅÜíÉå=åìê=òïÉá=w~ÜäÉåI=å®ãäáÅÜ=ÇáÉ=píÉáÖìåÖ=ìåÇ=ÇÉå=^ÅÜëÉå~ÄJ ëÅÜåáííK=kìå=ÖìíI=Ç~ëë=ÉáåÉ=ÇêáííÉ=w~ÜäI=å®ãäáÅÜ=ÇÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=Eáå=wÉääÉ= B4F=ìåJ ~ìÑÖÉÑçêÇÉêí=ãáíÖÉäáÉÑÉêí=ïáêÇI=Ç~ë=áëí=åçÅÜ=~åòìÉêâÉååÉåK== aáÉ= ~åÖÉÇÉìíÉíÉ= iìéÉ= òÉáÖíI= ïç= ïáê= ìåëÉêÉ= bêÖÉÄåáëëÉ= òì= ëìÅÜÉå= Ü~ÄÉå= Ó= áå= ÇÉå= wÉääÉå= B17=ìåÇ=B18K==

sÉêÖê∏≈Éêå=ïáê=ÇáÉëÉå=_ÉêÉáÅÜI=ëç=ÉêâÉååÉå=ïáê=áå=q~ÄÉääÉ=TKT=Ççêí=áå=ÇÉê=q~í=ÇáÉ=ÖÉëìÅÜJ íÉå= ÄÉáÇÉå= tÉêíÉ= Ó= ÇÉå= ^ÅÜëÉå~ÄëÅÜåáíí= EÜáÉê= ~äë= Schnittpunkt= ÄÉòÉáÅÜåÉíF= ìåÇ= ÇáÉ= píÉáJ ÖìåÖ=EÜáÉê=ÄÉòÉáÅÜåÉí=~äë=X Variable 1FK==

== _áäÇ=TKNPW=bêÖÉÄåáëëÉ=ÇÉë=tÉêâòÉìÖë=REGRESSION=

= q~ÄK=TKTW=dÉëìÅÜíÉ=tÉêíÉ=áã=bêÖÉÄåáëÄä~íí=ÇÉë=tÉêâòÉìÖë=REGRESSION== råÇ= ÇáÉ= êÉëíäáÅÜÉå= OU= ^åÖ~ÄÉå\= eáÉê= Ü~í= ã~å= ÇÉë= dìíÉå= ïçÜä= òìîáÉä= ÖÉí~åX= áã= píêÉÄÉå= å~ÅÜ=ìãÑ~ëëÉåÇÉê=^ìëâìåÑí=ÑΩê=~ääÉ=ÇÉåâÄ~êÉå=mêçÑáë=ïìêÇÉ=ëçîáÉä=~å=iÉáëíìåÖëÑ®ÜáÖâÉáí=áå= Ç~ë=tÉêâòÉìÖ=REGRESSION=ÜáåÉáåÖÉé~ÅâíI=Ç~ëë=ÇÉê=^åÑ®åÖÉê=ÄÉá=ëÉáåÉê=pìÅÜÉ=å~ÅÜ=ÇÉå=ÄÉáJ ÇÉå=w~ÜäÉåïÉêíÉå= ÑΩê= píÉáÖìåÖ= ìåÇ= ^ÅÜëÉå~ÄëÅÜåáíí= îçê= ÇÉê= §ÄÉêÑΩääÉ= ~å= fåÑçêã~íáçåÉå= â~éáíìäáÉêÉå=ãìëëK== aÉã=^åÑ®åÖÉê=ëÅÜÉáåí=~äëç=ãÉÜê=Ç~ãáí=ÖÉÇáÉåí=òì=ëÉáåI=ïÉåå=Éê=~åëíÉääÉ=ÇÉë=tÉêâòÉìJ ÖÉë= REGRESSION= ÇáÉ= ÄÉáÇÉå= äÉáÅÜí= òì= åìíòÉåÇÉå= cìåâíáçåÉå= STEIGUNG(...;...)= ìåÇ= ACHSENABSCHNITT(...;...) ~åïÉåÇÉíK== a~åå=áëí=Éë=ΩÄêáÖÉåë=~ìÅÜ=î∏ääáÖ=ÖäÉáÅÜÖΩäíáÖI=çÄ=ÇÉê=a~íÉåÄÉëí~åÇ=áå=pé~äíÉå=çÇÉê=wÉáäÉå= çêÖ~åáëáÉêí=áëíK== råÇ=ÄÉá=àÉÇÉê=ûåÇÉêìåÖ=áã=a~íÉåÄÉëí~åÇ=é~ëëÉå=ëáÅÜ=ÇáÉ=ãáí=eáäÑÉ=ÇÉê=ÄÉáÇÉå=cìåâíáçJ åÉå= ÉêãáííÉäíÉå= oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå= ëíÉíë= òìë®íòäáÅÜ= ~ìíçã~íáëÅÜ= ëçÑçêí= ~å= Ó= ï®ÜJ êÉåÇ= Ç~ë= ëí~íáëÅÜÉ= tÉêâòÉìÖ= REGRESSION= Ç~ÖÉÖÉå= å~ÅÜ= àÉÇÉê= ûåÇÉêìåÖ= âçãéäÉíí= åÉì= ~ìÑÖÉêìÑÉå=ïÉêÇÉå=ãΩëëíÉK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

TKP==jìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=

7.3

NOV

Multiple lineare Regression

få=ÇÉê=q~ÄÉääÉ=TKU=ÄÉÑáåÇÉå=ëáÅÜ=áå=ÇÉå=pé~äíÉå=AI=B=ìåÇ=C=ÇêÉá=ÖäÉáÅÜä~åÖÉ=a~íÉåêÉáÜÉåK== fÜêÉ= pé~äíÉåΩÄÉêëÅÜêáÑíÉå= ÄêáåÖÉå= Éë= ÄÉêÉáíë= òìã= ^ìëÇêìÅâW= aáÉ= tÉêíÉ= ÇÉê= ÄÉáÇÉå= ÉêëíÉå= pé~äíÉå=ëçääÉå=åìå=~åÖÉëÉÜÉå=ïÉêÇÉå=~äë=òïÉá=báåÑäìëëÖê∏≈ÉåI=ï®ÜêÉåÇ=ÇáÉ=tÉêíÉ=áå=ÇÉê= pé~äíÉ=C=ÇáÉ=wáÉäÖê∏≈É=ÄÉëÅÜêÉáÄÉå=ëçääÉåK==

= q~ÄK=TKUW=wïÉá=báåÑäìëëÖê∏≈ÉåI=ÉáåÉ=wáÉäÖê∏≈É== ^ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ëÉá= ÄÉâ~ååíI= Ç~ëë= Éë= ëáååîçää= áëíI= ÉáåÉ= äáåÉ~êÉ=wìë~ããÉåÜ~åÖëJ ÑçêãÉä=ÇÉê=cçêã== ETKMTF=

=y

= a1 x1 + a 2 x2 + b

~åòìëíêÉÄÉåI=ãáí=ÇÉêÉå=eáäÑÉ=Ç~åå=ëé®íÉê=ÑΩê=àÉÇÉ=x1-x2JhçãÄáå~íáçå=Éáå=òìÖÉÜ∏êáÖÉê=yJtÉêí= éêçÖåçëíáòáÉêí=ïÉêÇÉå=â~ååK== a~ÄÉá=ïÉêÇÉå== y=~äë=oÉÖêÉëë~åÇ=E~ÄÜ®åÖáÖÉ=s~êá~ÄäÉFI== x1=ìåÇ=x2=~äë=oÉÖêÉëëçêÉå=Eìå~ÄÜ®åÖáÖÉ=s~êá~ÄäÉåFI== a1=ìåÇ=a2=~äë=oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå=îçå=x1=ìåÇ=x2=ìåÇ== b=~äë=âçåëí~åíÉë=däáÉÇ== ÄÉòÉáÅÜåÉíK=== aáÉ=rãëÉíòìåÖ=ÇÉë=ëÅÜçå=~ìÑ=pÉáíÉ=NOQ=Éêï®ÜåíÉ=d~ì≈ÛëÅÜÉå=sçêëÅÜä~Öë=ÇÉê=jáåáãáÉêìåÖ= ÇÉê=cÉÜäÉêèì~Çê~íÉ=ÑΩÜêí=òì=ÉáåÉã=oÉÅÜÉåîÉêÑ~ÜêÉåI=Ç~ë=~äë=ãìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=ÄÉJ òÉáÅÜåÉí=ïáêÇK=== cΩê= ÇáÉ= ãìäíáéäÉ= äáåÉ~êÉ= oÉÖêÉëëáçå= ëíÉääí= bu`bi= âÉáå= tÉêâòÉìÖ= ÄÉêÉáíI= ëçåÇÉêå= åìê= ÉáåÉ= cìåâíáçåK== aáÉëÉ=cìåâíáçå=ÜÉá≈í= RGP=ìåÇ=áëí=ÉáåÉ=ëç=ÖÉå~ååíÉ=j~íêáñÑìåâíáçå=J=ÇÉåå=ëáÉ=ÖáÄí=åáÅÜí= åìê=ÉáåÉå=ÉáåòáÖÉå=w~ÜäÉåïÉêíI=ëçåÇÉêå=ãÉÜêÉêÉ=w~ÜäÉå=òìêΩÅâK== tÉåå= ïáê= ÑΩê= ìåëÉê= mêçÄäÉã= ÇêÉá= pé~äíÉå= ÄÉåìíòÉå= EòïÉá= pé~äíÉå= ÑΩê= ÇáÉ= ìå~ÄÜ®åÖáÖÉå= s~êá~ÄäÉå=ìåÇ=ÉáåÉ=pé~äíÉ=ÑΩê=ÇáÉ=~ÄÜ®åÖáÖÉ=s~êá~ÄäÉFI=Ç~åå=äáÉÑÉêí= RGP=áåëÖÉë~ãí= 3=ã~ä= 5I= ~äëç=ÑΩåÑòÉÜå=tÉêíÉK== aÉëÜ~äÄ=ãìëë=òìê=sçêÄÉêÉáíìåÖ=ÇÉê=^ìëÖ~ÄÉ=ÇÉê=j~íêáñÑìåâíáçå=òìÉêëí=ÑΩê=~ääÉ=òì=Éêï~êJ íÉåÇÉå=NR=^ìëÖ~ÄÉïÉêíÉ=ÇÉê= RGPJcìåâíáçå=Éáå=_ÉêÉáÅÜ=îçå=ÇêÉá=pé~äíÉå=ìåÇ=ÑΩåÑ=wÉáäÉå= ã~êâáÉêí=ïÉêÇÉåK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=

NPM ===

= q~ÄÉääÉ=TKV~W=j~êâáÉêìåÖ=ÇÉë=^ìëÖ~ÄÉÄÉêÉáÅÜÉë=ÑΩê=ÇáÉ=RGPJcìåâíáçå= få=q~ÄÉääÉ=TKV~=áëí=Ç~ÑΩê=ÄÉêÉáíë=ÇÉê=_ÉêÉáÅÜ= A11:C15=ã~êâáÉêí=ïçêÇÉåK=råãáííÉäÄ~ê=áã=^åJ ëÅÜäìëë=ÇÉê=j~êâáÉêìåÖ=ãìëë=Ó=çÜåÉ=Ç~å~ÅÜ=ÉáåÉ=ÄÉëíáããíÉ=wÉääÉ=~ìëòìï®ÜäÉå=Ó=ëçÑçêí=áå= ÇáÉ=q~ëí~íìê=ÖÉÖêáÑÑÉå=ìåÇ=ÇáÉ=cìåâíáçåëÑçêãÉä=ÉáåÖÉíáééí=ïÉêÇÉåW== =RGP(C2:C9;A2:B9;WAHR;WAHR)

t®ÜêÉåÇ=ÇÉë=báåíáééÉåë=ÉêëÅÜÉáåí=ÇáÉëÉ=cçêãÉä=áå=ÇÉê=ΩÄäáÅÜÉå=báåÖ~ÄÉòÉáäÉ=çÄÉêÜ~äÄ=ÇÉê= wÉáäÉåâ∏éÑÉ=ìåÇ=ÖäÉáÅÜòÉáíáÖ=áå=ÇÉê=äáåâÉå=çÄÉêÉå=wÉääÉ=ÇÉë=ã~êâáÉêíÉå=_ÉêÉáÅÜÉëI=~äëç=áå= ÇÉê=wÉääÉ=A11=EëáÉÜÉ=q~ÄÉääÉ=TKVÄFK====

= q~ÄÉääÉ=TKVÄW=cìåâíáçåëÑçêãÉä=ÉêëÅÜÉáåí=áã=ã~êâáÉêíÉå=_ÉêÉáÅÜ=äáåâë=çÄÉå= aáÉëÉ= cçêãÉä= íÉáäí= òìÉêëí= ÇÉå= _ÉêÉáÅÜ=ÇÉê=~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= C2:C9 ãáíI= Ç~òì= ÇÉå= ÖÉJ ë~ãíÉå=_ÉêÉáÅÜ=ÇÉê=ÄÉáÇÉå=ìå~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= A2:B9=ãáíI=ìåÇ=ëáÉ=îÉêä~åÖí=ïÉáíÉê=ÄÉJ ëíáããíÉ=ëí~íáëíáëÅÜÉ=hÉååÖê∏≈ÉåI=~ìÑ=ÇáÉ=ÜáÉê=åáÅÜí=ïÉáíÉê=ÉáåÖÉÖ~åÖÉå=ïÉêÇÉå=â~ååK== ^ÅÜíìåÖW=a~ãáí=ÇáÉ=cìåâíáçå=RGP=áÜêÉ=ÑΩåÑòÉÜå=tÉêíÉ=~ìÑ=~ääÉ=ã~êâáÉêíÉå=wÉääÉå=îÉêíÉáäÉå= â~ååI=ãìëë=ÇáÉ=báåÖ~ÄÉ=ÇÉê=cìåâíáçåëÑçêãÉä=~ÄÖÉëÅÜäçëëÉå=ïÉêÇÉå=ÇìêÅÜ=ÖäÉáÅÜòÉáíáÖÉë= aêΩÅâÉå=îçå==E==Strg==H ⇑ =F=ìåÇ= i↵ ↵i ==K== aÉê=ÉáåÑ~ÅÜÉ=aêìÅâ=~ìÑ=ÇáÉ=bkqboJq~ëíÉ= i↵ ↵i =äáÉÑÉêí=åìê=ÉáåÉå=ÉáåòáÖÉå=tÉêí=å~ÅÜ=A11K= táêÇ=ÇáÉëÉê=eáåïÉáë=ÄÉêΩÅâëáÅÜíáÖíI=Ç~åå=ÉêëÅÜÉáåÉå=í~íë®ÅÜäáÅÜ=áã=ã~êâáÉêíÉå=_ÉêÉáÅÜ=ÇáÉ= ÑΩåÑòÉÜå=bêÖÉÄåáëïÉêíÉ=ÇÉê=j~íêáñÑìåâíáçå=RGP=EëáÉÜÉ=q~ÄÉääÉ=TKVÅFK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

TKQ==káÅÜíäáåÉ~êÉ=wìë~ããÉåÜ®åÖÉ=

=

NPN

==

= q~ÄK=TKVÅW=bêÖÉÄåáëïÉêíÉ=ÇÉê=j~íêáñÑìåâíáçå=RGP= kìå=â∏ååÉå=áå=ÇÉê=ÉêëíÉå=wÉáäÉ=ÇÉë=bêÖÉÄåáëÄÉêÉáÅÜÉë=îçå=êÉÅÜíë=å~ÅÜ=äáåâë=ÇáÉ=hçÉÑÑáòáÉåJ íÉå=bI=a1=ìåÇ=a2=~ÄÖÉäÉëÉå=ïÉêÇÉåW== b = 78750,27 , a1 = 189,03, a2 = 1390,79

wì=ÄÉ~ÅÜíÉå=áëí=ÜáÉêÄÉáI=Ç~ëë=ÇÉê=oÉÖêÉëëáçåëâçÉÑÑáòáÉåí=a1=åáÅÜí=ìåíÉê=x1=ìåÇ=ÇÉê=oÉÖêÉëJ ëáçåëâçÉÑÑáòáÉåí=a2=åáÅÜí=ìåíÉê=x2=ëíÉÜíK== aáÉ= wìçêÇåìåÖ= òì= ÇÉå= ÄÉáÇÉå= ìå~ÄÜ®åÖáÖÉå= s~êá~ÄäÉå= äáÉÑÉêí= Ç~åå= ÇáÉ= ÖÉëìÅÜíÉ= oÉÖêÉëëáJ çåëÑìåâíáçåW=== ETKMUF=

=y

= 189,03 ⋅ x1 + 1391,79 ⋅ x2 + 78750, 27

jáí=ÇÉê=ëç=ÖÉÑìåÇÉåÉå=cìåâíáçå=â~åå=åìå=ÑΩê=àÉÇÉ=ÇÉåâÄ~êÉ=ìåÇ=ëáååîçääÉ=x1-x2JhçãÄáå~J íáçå=Éáå=êÉëìäíáÉêÉåÇÉê=mêçÖåçëÉïÉêí= y=ëÅÜåÉää=~ìëÖÉêÉÅÜåÉí=ïÉêÇÉåK=q~ÄÉääÉ=TKNM=òÉáÖí=ÉáJ åáÖÉ=ëçäÅÜÉ=oÉÅÜåìåÖÉåK==

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7.4

Nichtlineare Zusammenhänge

7.4.1

Grundlagen

bë=áëí=ÇÉã=jÉåëÅÜÉå=òï~ê=ÖÉÖÉÄÉåI=ÉáåÉ=dê~Ñáâ=~äë=hêÉáë=òì=áÇÉåíáÑáòáÉêÉå=ìåÇ=ÇáÉëÉå=~ìÅÜ= ãΩÜÉäçë= áå= ëÉÅÜòáÖ= ÖäÉáÅÜÉ= qÉáäÉ= òì= ìåíÉêíÉáäÉå= Eëçåëí= â∏ååíÉ= åáÉã~åÇ= ÇáÉ= rÜê= ~ÄäÉëÉåFI= ~ÄÉê=~ì≈Éê=ÇáÉëÉê=c®ÜáÖâÉáí=ÖÉäáåÖí=Éë=åìê=åçÅÜI=ÉáåÉ=dÉê~ÇÉ=ÑÉëíòìëíÉääÉåK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=

NPO

lÄ=ÄÉáëéáÉäëïÉáëÉ=ÉáåÉ=łÖÉÄçÖÉåÉ=mìåâíïçäâÉ=ïáÉ=áå=_áäÇ=TKNQ=~ìÑ=ÉáåÉå=èì~Çê~íáëÅÜÉå= çÇÉê= ÜóéÉêÄçäáëÅÜÉå= çÇÉê= äçÖ~êáíÜãáëÅÜÉå= çÇÉê= ÉñéçåÉåíáÉääÉå= wìë~ããÉåÜ~åÖ= òïáëÅÜÉå= báåÑäìëëJ=ìåÇ=wáÉäÖê∏≈É=ëÅÜäáÉ≈Éå=ä®ëëí=Ó=ïÉê=ïáää=Ç~ë=ãáí=ëÉáåÉå=^ìÖÉå=ÉêâÉååÉå\== råÇ=ïÉê=ïáää=Ç~åå=åçÅÜ=ÉáåÉ=cçêãÉä=EÉêFÑáåÇÉåI=ãáí=ÇÉê=ÇÉê=rêë~ÅÜÉJtáêâìåÖëJwìë~ãJ ãÉåÜ~åÖ=ã~íÜÉã~íáëÅÜ=ÄÉëÅÜêáÉÄÉå=ïÉêÇÉå=â~åå\==

= _áäÇ=TKNQW=råÄÉâ~ååíÉê=åáÅÜíäáåÉ~êÉê=wìë~ããÉåÜ~åÖ= açÅÜ=ã~åÅÜã~ä=ÖáÄí=Éë=ëÉäÄëí=áå=ëçäÅÜÉå=c®ääÉå=ÉáåÉå=tÉÖK=pÉÜÉå=ïáê=ìåë=áå=ÇÉê=q~ÄÉääÉ= TKNN=áå=ÇÉå=wÉáäÉå=1=ìåÇ=2=ÇÉå=a~íÉåÄÉëí~åÇ=ÑΩê=ÇáÉ=mìåâíïçäâÉ=îçå=_áäÇ=TKNQ=~åK= aáÉëã~ä=ëçää=~ìë=ë~ÅÜäáÅÜÉå=dêΩåÇÉå=ÄÉêÉáíë=ÖÉâä®êí=ëÉáåI=Ç~ëë=ÇáÉ=wÉáäÉ= 1=ÇáÉ=ìå~ÄÜ®åÖáÖÉ= sÉê®åÇÉêäáÅÜÉ=E~äë=x=ÄÉòÉáÅÜåÉíF=ìåÇ=ÇáÉ=wÉáäÉ=2=ÇáÉ=~ÄÜ®åÖáÖÉ=sÉê®åÇÉêäáÅÜÉ=y=ÉåíÜ®äíK==

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cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

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NPP

få=wÉääÉ=B6=ÉêëÅÜÉáåí=å®ãäáÅÜ=Éáå=ëíçäòÉê=tÉêí=îçå=Ñ~ëí=1,0=ÑΩê=ÇÉå=hçêêÉä~íáçåëâçÉÑÑáòáÉåíÉå= ÑΩê=ÇáÉ=åÉì=ÄÉêÉÅÜåÉíÉå=wÉáäÉå=ÑΩê=X=ìåÇ=Y=Ó=ïÉê=ëáÅÜ=ãÉÜê=píÉääÉå=~åòÉáÖÉå=ä®ëëíI=ïáêÇ=ÉñJ ~âí==0,995596856=ÑÉëíëíÉääÉåK==

= q~ÄK=TKNO~W=bêÖÉÄåáëëÉ=ÇÉê=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå== t®ÜêÉåÇ= ÇáÉ= mìåâíïçäâÉ= áå= _áäÇ= TKNR= ìåë= ÇÉìíäáÅÜ= îçê= ^ìÖÉå= ÑΩÜêíÉI= Ç~ëë= òïáëÅÜÉå= ÇÉå= ÄÉáÇÉå=ìêëéêΩåÖäáÅÜÉå=a~íÉåêÉáÜÉå= x=ìåÇ= y=âÉáåÉëÑ~ääë=Éáå=äáåÉ~êÉê=wìë~ããÉåÜ~åÖ=ÄÉëíÉJ ÜÉå= â~ååI= ë~Öí= ìåë= ÇÉê= X-Y-hçêêÉä~íáçåëâçÉÑÑáòáÉåí= Ç~ÖÉÖÉå= ÑΩê= ÇáÉ= ÄÉáÇÉå= ÇìêÅÜ=ÇçééÉäí= äçÖ~êáíÜãáëÅÜÉ=qê~åëÑçêã~íáçå=ÉêÜ~äíÉåÉå=a~íÉåêÉáÜÉå= X=ìåÇ= Y=ÉáåÉ=ëí~êâÉ=äáåÉ~êÉ=^ÄÜ®åJ ÖáÖâÉáí=îçê~ìëW= t®ÜêÉåÇ= x=ìåÇ= y=çÑÑÉåëáÅÜíäáÅÜ=åáÅÜí=âçêêÉäáÉêí=ëáåÇI=ëáåÇ=ÇáÉ=ãáí=eáäÑÉ=ÇÉë=içÖ~êáíÜãìë= ~ìë=áÜåÉå=ÉêÜ~äíÉåÉå=íê~åëÑçêãáÉêíÉå=tÉêíÉ=X=ìåÇ=Y=Ç~ÖÉÖÉå=ÜçÅÜ=âçêêÉäáÉêíK= ^äëç=â~åå=ã~å=ÑΩê=ÇÉå=îçê~ìëëáÅÜíäáÅÜÉå=äáåÉ~êÉå=X-YJwìë~ããÉåÜ~åÖ=ëçÑçêí=ÇáÉ=òìÖÉÜ∏êáJ ÖÉå=oÉÖêÉëëáçåëé~ê~ãÉíÉê=ãáí=ÇÉå=ÄÉáÇÉå=bñÅÉäJcìåâíáçåÉå=~ìëêÉÅÜåÉå=ä~ëëÉåW=

= q~ÄK=TKNOÄW=píÉáÖìåÖ=ìåÇ=^ÅÜëÉå~ÄëÅÜåáíí=ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉå=a~íÉåêÉáÜÉå=

= q~ÄK=TKNOÅW=píÉáÖìåÖ=ìåÇ=^ÅÜëÉå~ÄëÅÜåáííW=tÉêíÉ= j~å=ÉêÜ®äí=ÑΩê=ÇáÉ=píÉáÖìåÖ=ÇÉå=tÉêí=a=5,72 ìåÇ=ÑΩê=ÇÉå=^ÅÜëÉå~ÄëÅÜåáíí=b=0,77.== a~ãáí= ÉêÖáÄí= ëáÅÜ= ÑΩê= ÇÉå= ÖÉÑìåÇÉåÉå= ÉãéáêáëÅÜÉå= äáåÉ~êÉå= wìë~ããÉåÜ~åÖ= òïáëÅÜÉå= X= ìåÇ=Y=ëçÑçêí=ÇáÉ=cçêãÉäW== ETKMVF=

=Y

= 5,72 ⋅ X + 0,77

açÅÜ=ïÉäÅÜÉê=wìë~ããÉåÜ~åÖ=ä®ëëí=ëáÅÜ=Ç~ê~ìë=ÑΩê= x=ìåÇ=ó=~ÄäÉáíÉå=Ó=ïáÉ=Ü®åÖí= y=îçå= x= ~ÄI= ïÉäÅÜÉ= wìë~ããÉåÜ~åÖëÑçêãÉä= Öáäí= Ç~åå\= dáÄí= Éë= ΩÄÉêÜ~ìéí= ÉáåÉ= ëçäÅÜÉ= ñJóJwìJ ë~ããÉåÜ~åÖëÑçêãÉä=\= aÉåå=y=Ü®åÖí=ÇçÅÜ=Ö~åò=çÑÑÉåëáÅÜíäáÅÜ=åáÅÜíäáåÉ~ê=îçå=x=~ÄK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=

NPQ a~=ÜáäÑí=ÇáÉ=j~íÜÉã~íáâW==

p~íò=TKNW=táêÇ=ÑΩê=ÇáÉ=ÄÉáÇÉå=a~íÉåêÉáÜÉå=ãáí=ÇÉê=Eíê~åëÑçêãáÉêíÉåF=báåÑäìëëÖê∏≈É= X= ìåÇ=ÇÉê=Eíê~åëÑçêãáÉêíÉåF=wáÉäÖê∏ëëÉ=Y=ÇÉê=äáåÉ~êÉ=X-Y-wìë~ããÉåÜ~åÖ== ETKNMF==

=Y = aX += b

ÑÉëíÖÉëíÉääíI= ìåÇ= ëáåÇ= X= ìåÇ= Y= ~ìë= ÇÉå= ìêëéêΩåÖäáÅÜÉå= a~íÉåêÉáÜÉå= x= ìåÇ= y= ÇìêÅÜ= ÇçééÉäí=äçÖ~êáíÜãáëÅÜÉ=qê~åëÑçêã~íáçå= ETKNNF==

=X

= ln x

Y = ln y

Éåíëí~åÇÉåI= Ç~åå= Öáäí= ÑΩê= ÇáÉ= ^ÄÜ®åÖáÖâÉáí= ÇÉê= ìêëéêΩåÖäáÅÜÉå= wáÉäÖê∏≈É= y= îçå= ÇÉê= ìêëéêΩåÖäáÅÜÉå=báåÑäìëëÖê∏≈É=x=ÇáÉ=ÉãéáêáëÅÜÉ=cçêãÉä= ETKNOF==

=y

= eb ⋅ x a

a~ÄÉá=áëí=e=ÇáÉ=ÄÉâ~ååíÉ=bìäÉêëÅÜÉ=w~ÜäW=e= 2,71828182845905…= aáÉëÉå=p~íò=â∏ååÉå=ïáê=àÉíòí=~åïÉåÇÉåW== a~ë=báåëÉíòÉå=îçå=a=ìåÇ=b=äáÉÑÉêí=Ç~ë=bêÖÉÄåáëW=wïáëÅÜÉå=ÇÉê=báåÑäìëëÖê∏≈É=x=ìåÇ=ÇÉê=wáÉäJ Öê∏≈É=y =ÄÉëíÉÜí=ÇÉê=ÉãéáêáëÅÜÉ=wìë~ããÉåÜ~åÖW== ETKNPF=

y = e 0, 774 ⋅ x 5,72 = 2,7180 , 77 ⋅ x 5, 72 = 2,17 ⋅ x 5, 72

eáåïÉáëW=wìê=_ÉêÉÅÜåìåÖ=ÇÉê=mçíÉåò==2,7180,77=ãáí=eáäÑÉ=îçå=bñÅÉä=áëí==2,718^0,77=ÉáåòìJ íáééÉåI=ïçÄÉá=Ç~ë=wÉáÅÜÉå=^=EãÉáëí=äáåâë=åÉÄÉå=ÇÉê=q~ëíÉ= 1 =F=~ÄÉê=Éêëí=~åÖÉòÉáÖí=ïáêÇI= ïÉåå=ÇáÉ=ÑçäÖÉåÇÉ=kìää=ÉáåÖÉÖÉÄÉå=ïáêÇK== tÉê= Öê∏≈ÉêÉ= dÉå~ìáÖâÉáí= ~åëíêÉÄíI= ëçääíÉ= =EXP(1)^0,77= ÉáåÖÉÄÉåI= Ç~åå= ïáêÇ= ÇáÉ= bìäÉêJ ëÅÜÉ=w~Üä=e=~ìÑ=NR=aÉòáã~äëíÉääÉå=ÖÉå~ì=ÄÉêÉÅÜåÉíK==

= _áäÇ=TKNRW=mìåâíïçäâÉ=ÇÉê=içÖ~êáíÜãÉå=îçå=ñ=ìåÇ=ó=

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

TKQ==káÅÜíäáåÉ~êÉ=wìë~ããÉåÜ®åÖÉ=

=

NPR

t®ÜêÉåÇ=_áäÇ=TKNR=ÇáÉ=mìåâíïçäâÉ=ÇÉê=ÇçééÉäí=äçÖ~êáíÜãáëÅÜ=íê~åëÑçêãáÉêíÉå=a~íÉåêÉáÜÉå= X=ìåÇ=Y=áå=áÜêÉã=ÇÉìíäáÅÜ=ÉêâÉååÄ~êÉ=äáåÉ~êÉå=wìë~ããÉåÜ~åÖ=òÉáÖíI=áëí=áå=_áäÇ=TKNS=áå=ÇáÉ= ÄÉêÉáíë= ~ìë= _áäÇ= TKNQ=ÄÉâ~ååíÉ= mìåâíïçäâÉ= ÇáÉ= hìêîÉ= ÇÉê= ÉñéçåÉåíáÉääÉå= x-y-wìë~ããÉåJ Ü~åÖëÑìåâíáçå=ETKMQF=ÉáåÖÉòÉáÅÜåÉí=ïçêÇÉåK==

= RITO

_áäÇ=TKNSW=mìåâíïçäâÉ=îçå=ñ=ìåÇ=ó=ëçïáÉ=ÇáÉ=^ìëÖäÉáÅÜëâìêîÉ=óZOINT=G=ñ

=

j~å= â~åå= ÇÉìíäáÅÜ= ÉêâÉååÉåI= Ç~ëë= ÇÉê= ÖÉÑìåÇÉåÉ= åáÅÜíäáåÉ~êÉ= x-y-wìë~ããÉåÜ~åÖ= áå= ÇÉê=q~í=ÖÉÉáÖåÉí=áëíI=ÇáÉ=páíì~íáçå=áã=a~íÉåÄÉëí~åÇ=íêÉÑÑÉåÇ=ÑçêãÉäã®≈áÖ=òì=ÄÉëÅÜêÉáÄÉåK==

7.4.2

Transformationen

kìå= áëí= Éë= ~å= ÇÉê= wÉáíI= ÇáÉ= ~åÇÉêÉå= bêâÉååíåáëëÉ=ÇÉê= j~íÜÉã~íáâ=îçêòìëíÉääÉåI=ãáí= ÇÉåÉå= ÑΩê=ïÉáíÉêÉ=åáÅÜíäáåÉ~êÉ=rêë~ÅÜÉJtáêâìåÖëJwìë~ããÉåÜ®åÖÉ=ÉãéáêáëÅÜÉ=cçêãÉäå=ÖÉÑìåÇÉå= ïÉêÇÉå=â∏ååÉåW== p~íò= TKOW= dÉÖÉÄÉå= ëÉáÉå= òïÉá= ÖäÉáÅÜä~åÖÉ= a~íÉåêÉáÜÉå= ãáí= ÇÉå= _ÉòÉáÅÜåìåÖÉå= x= ìåÇ= yI= ïçÄÉá= ~ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ÄÉâ~ååí= ëÉáI= Ç~ëë= ÇáÉ= oÉáÜÉ= y= ~äë= oÉáÜÉ= ÇÉê= ~ÄÜ®åÖáÖÉå=tÉêíÉ= EwáÉäÖê∏≈ÉF= ìåÇ= ÇáÉ= oÉáÜÉ= x= ~äë= oÉáÜÉ= ÇÉê= ìå~ÄÜ®åÖáÖÉå=tÉêíÉ= EbáåÑäìëëÖê∏≈ÉF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååK= bêÖáÄí=ëáÅÜ=å~ÅÜ=ÇÉê=ÉáåÑ~ÅÜ=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå=îçå=y ÖÉã®≈= ETKNQF==

=X

=x

Y = ln y

ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉ=XJYJa~íÉåêÉáÜÉ=ÉáåÉ=ÉãéáêáëÅÜÉ=äáåÉ~êÉ=wìë~ããÉåÜ~åÖëÑçêãÉä= ETKNRF==

=Y = aX += b

ëç=ÄÉëíÉÜí=òïáëÅÜÉå=x=ìåÇ=y=ÇÉê=ÉãéáêáëÅÜÉ=åáÅÜíäáåÉ~êÉ=wìë~ããÉåÜ~åÖ= ETKNSF==

=y

= e b ⋅ e a⋅ x

=

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=

NPS

p~íò= TKPW= dÉÖÉÄÉå= ëÉáÉå= òïÉá= ÖäÉáÅÜä~åÖÉ= a~íÉåêÉáÜÉå= ãáí= ÇÉå= _ÉòÉáÅÜåìåÖÉå= x= ìåÇ= yI= ïçÄÉá= ~ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ÄÉâ~ååí= ëÉáI= Ç~ëë= ÇáÉ= oÉáÜÉ= y= ~äë= oÉáÜÉ= ÇÉê= ~ÄÜ®åÖáÖÉå=tÉêíÉ= EwáÉäÖê∏≈ÉF= ìåÇ= ÇáÉ= oÉáÜÉ= x= ~äë= oÉáÜÉ= ÇÉê= ìå~ÄÜ®åÖáÖÉå=tÉêíÉ= EbáåÑäìëëÖê∏≈ÉF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååK= bêÖáÄí=ëáÅÜ=å~ÅÜ=ÇÉê=ÉáåÑ~ÅÜ=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå=îçå=x=ÖÉã®≈= ETKNTF==

=X

= ln x = Y = y=

ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉ=XJYJa~íÉåêÉáÜÉ=ÉáåÉ=ÉãéáêáëÅÜÉ=äáåÉ~êÉ=wìë~ããÉåÜ~åÖëÑçêãÉä= ETKNUF==

=Y = aX += b

ëç=ÄÉëíÉÜí=òïáëÅÜÉå=x=ìåÇ=y=ÇÉê=ÉãéáêáëÅÜÉ=åáÅÜíäáåÉ~êÉ=wìë~ããÉåÜ~åÖ= ETKNVF==

=y

= b + a=⋅ ln x

a~ê~ìë=ÉêÖáÄí=ëáÅÜ=ÑçäÖÉåÇÉ=^åäÉáíìåÖ=òìã=e~åÇÉäåW== iáÉÖí=Éáå=a~íÉåÄÉëí~åÇ=îçêI=ÇÉê=~ìë=òïÉá=ÖäÉáÅÜä~åÖÉå=a~íÉåêÉáÜÉå=ÄÉëíÉÜíI=ìåÇ=ÄÉá=ÇÉJ åÉå=ÉáåÉ=a~íÉåêÉáÜÉ= ~ìë= ë~ÅÜäáÅÜÉå=dêΩåÇÉå= ~äë=báåÑäìëëÖê∏≈É= ExF= ìåÇ=ÇáÉ= ~åÇÉêÉ= a~J íÉåêÉáÜÉ=~äë=wáÉäÖê∏≈É=EyF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååI=Ç~åå=ëçääíÉå=ÖêìåÇë®íòäáÅÜ=åÉÄÉå=ÇÉå= ^ìëÖ~åÖëÇ~íÉå=ïÉáíÉêÉ=ÇêÉá=wìë~ããÉåëíÉääìåÖÉå=îçå=íê~åëÑçêãáÉêíÉå=tÉêíÉé~~êÉåI=ïáÉ= áå=ÇÉê=q~ÄÉääÉ=TKNP=Ç~êÖÉëíÉääíI=áå=Ç~ë=bñÅÉäJ_ä~íí=ÉáåÖÉíê~ÖÉå=ïÉêÇÉåK==

= q~ÄK=TKNP~W=cçêãÉäå=

= q~ÄK=TKNPÄW=tÉêíÉ= aáÉ=îáÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåíÉå=áå=ÇÉê=ÉêëíÉå=wÉáäÉ=ÖÉÄÉå=Ç~åå=Ç~êΩÄÉê=^ìëâìåÑíI=ïÉäJ ÅÜÉë= pé~äíÉåé~~ê= ÑΩê= ÇáÉ= äáåÉ~êÉ=oÉÖêÉëëáçåëêÉÅÜåìåÖ= áåÑê~ÖÉ= âçããíW= fëí= ÇÉê= hçêêÉä~íáJ çåëâçÉÑÑáòáÉåí=áå=ÇÉê=wÉääÉ= A1=å~ÜÉ=N=çÇÉê=JNI=Ç~åå=áëí=ÉáåÑ~ÅÜÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=ëáååJ îçääK= fëí= ÇÉê= tÉêí= áå= ÇÉê= wÉääÉ= D1= å~ÜÉ= N= çÇÉê= JNI= Ç~åå= â~åå= p~íò=TKP= òìê= ^åïÉåÇìåÖ= âçããÉåK=dáäí=Ç~ë=ÑΩê=ÇÉå=tÉêí=áå=ÇÉê=wÉääÉ= G1I=Ç~åå=âçããí=p~íò=TKO=òìê=^åïÉåÇìåÖK= cáåÇÉí=ëáÅÜ=áå=ÇÉê=wÉääÉ=J1=Éáå=ëçäÅÜÉê=tÉêíI=Ç~åå=â~åå=p~íò=TKN=~åÖÉï~åÇí=ïÉêÇÉåK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

=

8

Zeitreihen

8.1

Begriff und Erfassung

báåÉ=wÉáíêÉáÜÉ=áëí=ÉáåÉ=òÉáíäáÅÜ=ÖÉçêÇåÉíÉ=cçäÖÉ=îçå=jÉêâã~äëïÉêíÉåK== lÇÉê=~åÇÉêë=ÖÉëéêçÅÜÉå=Ó=ìåÇ=ìã=ÇáÉ=sÉêÄáåÇìåÖ=òìã=îçêáÖÉå=^ÄëÅÜåáíí=ÜÉêòìëíÉääÉå=Ó= ÇáÉ= ÄÉíê~ÅÜíÉíÉå= báåÑäìëëÖê∏≈Éå= ëáåÇ= ÜáÉê= ëéÉòáÉää= a~íìãëJ= çÇÉê= wÉáí~åÖ~ÄÉåI= òì= ÇÉåÉå= Ç~åå=~äë=wáÉäÖê∏≈Éå=àÉïÉáäë=ÄÉëíáããíÉ=~åÇÉêÉ=tÉêíÉ=ÖÉÜ∏êÉåK= bñÅÉä=ëíÉääí=òìê=^êÄÉáí=ãáí=wÉáíêÉáÜÉå=ÉáåÉ=ÄÉ~ÅÜíäáÅÜÉ=jÉåÖÉ=îçå=eáäÑëãáííÉäå=ÄÉêÉáíK== sçê~ìëëÉíòìåÖ= ÑΩê= ÇáÉ=kìíòÄ~êâÉáí= ÇáÉëÉê=eáäÑëãáííÉä= áëí= ~ääÉêÇáåÖë= áå= àÉÇÉã= c~ääÉI= Ç~ëë= ÇáÉ= a~íìãëJ=çÇÉê=wÉáí~åÖ~ÄÉå=~äë=åìãÉêáëÅÜÉ=tÉêíÉ=îçå=bñÅÉä=Éêâ~ååí=ïÉêÇÉå=â∏ååÉåK=== pçää= òìã= _ÉáëéáÉä= ÉáåÉ= ãçå~íäáÅÜÉ=båíïáÅâäìåÖ= Ç~êÖÉëíÉääí= ïÉêÇÉåI= Ç~åå= áëí= ÇáÉ= åáÅÜíåìJ ãÉêáëÅÜÉ=báåÖ~ÄÉ=ÇÉê=a~íìãë~åÖ~ÄÉå=EÜáÉê=ëáåÇ=Éë=ÇáÉ=jçå~íë~ÄâΩêòìåÖÉåF=ïáÉ=áå=q~ÄÉäJ äÉ=UKN~=çÑí=ìåÄê~ìÅÜÄ~ê=ÑΩê=ÇáÉ=ïÉáíÉêÉ=sÉê~êÄÉáíìåÖK==

= q~ÄK=UKN~W=jçå~íëå~ãÉå=åáÅÜíåìãÉêáëÅÜ=~äë=wÉáÅÜÉåÑçäÖÉå=ÉáåÖÉÖÉÄÉå= sáÉäãÉÜê= ëçääíÉ= ã~å= ëçI= ïáÉ= áå= q~ÄÉääÉ= UKNÄ= ÖÉòÉáÖíI= ÇáÉ= åìãÉêáëÅÜÉå= a~íìãë~åÖ~ÄÉå= łNKNKMTI=łNKOKMT=ìëïK=ãáí=ÉáåÉê=ÄÉäáÉÄáÖÉå=g~ÜêÉëò~Üä=Éáåíê~ÖÉåK==

= q~ÄK=UKNÄW=jçå~íë~åÑ®åÖÉ=åìãÉêáëÅÜ=ÉáåÖÉÖÉÄÉå==

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8.2

Experimentell-visuelle Trendermittlung

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8.3

Lineare Zeitreihen und die TREND-Funktion

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= 0,001122709 ⋅ Datumswert - 29,43253314

rã=ÇáÉ=mêçÖåçëÉïÉêíÉ=ÑΩê=kçîÉãÄÉê=ìåÇ=aÉòÉãÄÉê=ÄÉêÉÅÜåÉå=òì=â∏ååÉåI=ÄÉå∏íáÖÉå=ïáê= ÑçäÖäáÅÜ=ÇáÉ=ÄÉáÇÉå=òìÖÉÜ∏êáÖÉå=a~íìãëïÉêíÉK=páÉ=â∏ååÉå=ïáê=ÉêÜ~äíÉåI=áåÇÉã=ïáê=ÇáÉ=^åJ òÉáÖÉ=ãáííÉäë=cloj^qwbiibkw^ei=ìãëíÉääÉåE=ëK=q~ÄÉääÉ=UKTFK===

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q~ÄK=UKTW=kçîÉãÄÉê=ìåÇ=aÉòÉãÄÉêW=hìêòÑçêãI=a~íìãI=a~íìãëïÉêíÉ= jáí=ÇÉå=ÄÉáÇÉå=ÄÉâ~ååíÉå=a~íìãëïÉêíÉå=â∏ååÉå=àÉíòí=ÇáÉ=qêÉåÇïÉêíÉ=ÑΩê=kçîÉãÄÉê=ìåÇ= aÉòÉãÄÉê=ÇìêÅÜ=báåëÉíòÉå=áå=ÇáÉ=oÉÖêÉëëáçåëÑçêãÉä=ÉêãáííÉäí=ïÉêÇÉåK==

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= 0,001123 ⋅ 39387 - 29,43253314 ≈ 14,79

EUKMPF=

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= 0,001122709 ⋅ 39417 - 29,43253314 ≈ 14,82

k~íΩêäáÅÜ= Ü®ííÉ= ã~å= ~ìÅÜ= ÖäÉáÅÜ= áå= ÇÉê= bñÅÉäJq~ÄÉääÉ= êÉÅÜåÉå= ä~ëëÉå= â∏ååÉåK= açÅÜ= ~ìÅÜ= Ç~ë= áëí=åáÅÜí=å∏íáÖ=Ó=ÇáÉ= ÄÉáÇÉå= ÖÉëìÅÜíÉå=qêÉåÇïÉêíÉ= ä~ëëÉå=ëáÅÜ=ãáí=bñÅÉä= îáÉä=ëÅÜåÉääÉê= ìåÇ=ÄÉèìÉãÉê=ÉêãáííÉäåK== táêÇ=ÇáÉ=bñÅÉäJcìåâíáçå= TREND(...;...;...)=îÉêïÉåÇÉíI=Ç~åå=â~åå=ã~å=ëáÅÜ=ÇáÉ=bêãáííJ äìåÖ=ÇÉê=oÉÖêÉëëáçåëÑçêãÉä=ëé~êÉåK= ^å=ÇáÉ=ÉêëíÉ=mçëáíáçå=ÇÉê= TRENDJcìåâíáçå=áëí=Ç~ÄÉá=ÇÉê=_ÉêÉáÅÜ=ãáí=ÇÉå=~ÄÜ®åÖáÖÉå=s~êá~ÄJ äÉå= EÄÉá= ìåëÉêÉå= wÉáíêÉáÜÉå= ~äëç= ÇÉê= _ÉêÉáÅÜ= ÇÉê= jÉêâã~äëïÉêíÉF= Éáåòìíê~ÖÉåK= aáÉ= òïÉáíÉ= mçëáíáçå= ãìëë= ÇÉå= _ÉêÉáÅÜ=ÇÉê=ìå~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= ÄÉâçããÉå= Erêë~ÅÜÉåïÉêíÉW= ÄÉá= ìåë= ÇáÉ= a~íìãë~åÖ~ÄÉåFK= ^å= ÇáÉ= ÇêáííÉ= píÉääÉ= ëÅÜäáÉ≈äáÅÜ= âçããí= ÇáÉ= wÉääÉ= ãáí= ÇÉã= a~J íìãëïÉêí=ÇÉë=ÖÉëìÅÜíÉå=jçå~íëK==

= q~ÄK=UKU~W=^åïÉåÇìåÖ=ÇÉê=TRENDJcìåâíáçå=

= q~ÄK=UKUÄW=TRENDJcìåâíáçåW=tÉêíÉ få=ÇÉå=ÄÉáÇÉå=q~ÄÉääÉå=UKU~=ìåÇ=UKUÄ=áëí=Ç~ë=sçêÖÉÜÉå=Ç~êÖÉëíÉääíK=bë=ÉêÖÉÄÉå=ëáÅÜ=Ó=å~J íΩêäáÅÜ=Ó=ÇáÉëÉäÄÉå=w~ÜäÉåïÉêíÉ=ïáÉ=ÄÉá=ÇÉê=çÄáÖÉå=^ìëïÉêíìåÖ=ÇÉê=oÉÖêÉëëáçåëÑçêãÉäK== a~ë=Ç~êÑ= ~ìÅÜ= åáÅÜí=îÉêïìåÇÉêäáÅÜ= ëÉáåI= ÇÉåå=ÇáÉ=cìåâíáçå= TREND(...;...;...)= ~êÄÉáíÉí= ÖÉå~ì=ëçI=ïáÉ=ïáê=Éë=ÉáåÖ~åÖë=ÇÉãçåëíêáÉêíÉåW== páÉ=ÄÉëíáããí=ÉÄÉåÑ~ääë=òìÉêëí=ÇáÉ=oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå=ãáí=eáäÑÉ=ÇÉê=cìåâíáçåÉå=STEIGUNG(...;...)= ìåÇ= ACHSENABSCHNITT(...;...),= ìåÇ= Ç~åå= ëÉíòí= ëáÉ= ÇÉå= àÉïÉáäáÖÉå= a~J íìãëïÉêí=áå=ÇáÉ=däÉáÅÜìåÖ=ÇÉê=oÉÖêÉëëáçåëÖÉê~ÇÉå=ÉáåK=

8.4

Gleitender Durchschnitt

aÉê=ÖäÉáíÉåÇÉ=aìêÅÜëÅÜåáíí=ÉáåÉê=wÉáíêÉáÜÉ=ÉäáãáåáÉêí=pÅÜï~åâìåÖÉå=ÇÉê=wÉáíêÉáÜÉI=áåÇÉã= ~ìÑ= ÇÉã= tÉÖÉ= ÇÉê= aìêÅÜëÅÜåáííëÄáäÇìåÖ= êÉä~íáî=ÜçÜÉ=tÉêíÉ= ìåÇ= êÉä~íáî=åáÉÇêáÖÉ=tÉêíÉ= ~ìÑ=Éáå=ÇìêÅÜëÅÜåáííäáÅÜÉë=káîÉ~ì=~ÄÖÉëÉåâí=ïÉêÇÉåK== fã= dÉÖÉåë~íò= òìê= jÉíÜçÇÉ= ÇÉê= äáåÉ~êÉå= oÉÖêÉëëáçå= ÄáäÇÉí= Ç~ë= jçÇÉää= ÇÉê= ÖäÉáíÉåÇÉå= aìêÅÜëÅÜåáííÉ=ÇÉå=qêÉåÇ=åáÅÜí=~äë=dÉê~ÇÉ=~ÄI=ëçåÇÉêå=Öä®ííÉí=äÉÇáÖäáÅÜ=ÇÉå=hìêîÉåîÉêä~ìÑK== a~ÇìêÅÜ= ïÉêÇÉå= tÉåÇÉéìåâíÉ= ìåÇ= sÉê®åÇÉêìåÖÉå= áå= ÇÉê= qêÉåÇÉåíïáÅâäìåÖ= ÑΩê= ÇÉå= _Éíê~ÅÜíÉê=ÇÉìíäáÅÜÉê=ëáÅÜíÄ~êK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=

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8.5

Grundlagen der Zeitreihenanalyse

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8.5.1

Aufbau des additiven Zeitreihenmodells

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aáÉ= qêÉåÇâçãéçåÉåíÉ= T= ÅÜ~ê~âíÉêáëáÉêí= ÇáÉ= ä~åÖÑêáëíáÖÉ= båíïáÅâäìåÖ= ÇÉê= wÉáíêÉáÜÉX= ëáÉ= áëí= ÉåíïÉÇÉê=ãçåçíçå=ëíÉáÖÉåÇ=çÇÉê=Ñ~ääÉåÇK== aáÉ=qêÉåÇâçãéçåÉåíÉ=ïáêÇ=áã=~ääÖÉãÉáåÉå=ÇìêÅÜ=ÉáåÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=Eãáí=ÇÉê=wÉáí=~äë= báåÑäìëëÖê∏≈ÉF=ÄÉêÉÅÜåÉí=EëáÉÜÉ=^ÄëÅÜåáíí=TKO=~ìÑ=pÉáíÉ=NOPFK= Zyklische Komponente Z

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8.5.2

Gleitende Durchschnitte und das additive Zeitreihenmodell

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8.5.3

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8.5.5

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NRU

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j~å= â~åå= ~ìÑÖêìåÇ= ÄÉêÉáíë=îçêäáÉÖÉåÇÉê=ë~áëçåÄÉêÉáåáÖíÉê=jçå~íëïÉêíÉ= Ç~ë= g~ÜêÉëÉêÖÉÄåáë= éêçÖåçëíáòáÉêÉåK== j~å=â~åå=~ìë=ÇÉê=ë~áëçåÄÉêÉáåáÖíÉå=wÉáíêÉáÜÉ=mêçÖåçëÉå=ÑΩê=ÇáÉ=å®ÅÜëíÉå=jçå~íÉ=ìåÇ=g~ÜJ êÉ= EÇìêÅÜëÅÜåáííäáÅÜÉ= g~ÜêÉëïÉêíÉF= ãáííÉäë= qêÉåÇ~å~äóëÉ= ìåÇ= ÉñéçåÉåíáÉääÉê= dä®ííìåÖ= ÄÉJ êÉÅÜåÉåK= j~å=â~åå=Éáå=îçê~ìëÖÉëÅÜ®íòíÉë=g~ÜêÉëÉêÖÉÄåáë=ãáí=eáäÑÉ=ÇÉê=ãçå~íëíóéáëÅÜÉå=^ÄïÉáÅÜìåJ ÖÉå=~ìÑ=ÇáÉ=ÉáåòÉäåÉå=jçå~íÉ=~ìÑíÉáäÉåK== ^ìÑ=ÇáÉëÉ=tÉáëÉ=ÉêÜ®äí=ã~å=ãçå~íäáÅÜÉ=mêçÖåçëÉïÉêíÉK= pÉäÄëíîÉêëí®åÇäáÅÜ=ÖáÄí=Éë=~ÄÉê=~ìÅÜ=dêÉåòÉå=ÇÉê=^åïÉåÇÄ~êâÉáí=ÇÉê=jÉíÜçÇÉ=ÇÉê=ÖäÉáíÉåJ ÇÉå=aìêÅÜëÅÜåáííÉW= ^åÜ~åÇ=ÇÉê=çÄáÖÉå=^ìëÑΩÜêìåÖÉå=ïìêÇÉå=ÄÉêÉáíë=ÉáåáÖÉ=pÅÜï®ÅÜÉå=ÇÉê=wÉáíêÉáÜÉå~å~äóëÉ= ãáí=eáäÑÉ=ÇÉê=jÉíÜçÇÉ=ÇÉê=ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáííÉ=ëáÅÜíÄ~êK=aáÉ=^åïÉåÇìåÖëëÅÜï®ÅÜÉå= ÇÉë=jçÇÉääë=ìåÇ=ÇÉê=_ÉêÉÅÜåìåÖëãÉíÜçÇÉ=òÉáÖÉå=ëáÅÜ=áå=ÑçäÖÉåÇÉå=mìåâíÉåW== qêÉåÇÄÉêÉÅÜåìåÖW=cΩê=ÇáÉ=ÄÉáÇÉå=båÇÉå=ÇÉê=wÉáíêÉáÜÉ=E^åÑ~åÖ=ìåÇ=pÅÜäìëëF=â∏ååÉå=âÉáåÉ= ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáííÉ=ÄÉêÉÅÜåÉí=ïÉêÇÉåK=aÉëÜ~äÄ=â~åå=ÇÉê=qêÉåÇ=~ìÅÜ=åáÅÜí=ïÉáí=ΩÄÉê= ÇÉå=~âíìÉääÉå=pí~åÇ=Üáå~ìë=áåíÉêéêÉíáÉêí=ïÉêÇÉåK=eáÉêÄÉá=òÉáÖí=ëáÅÜ=Éáå=ÇÉìíäáÅÜÉê=k~ÅÜíÉáä= ÖÉÖÉåΩÄÉê= ÇÉê= qêÉåÇÄÉêÉÅÜåìåÖ= ãáííÉäë= äáåÉ~êÉê=oÉÖêÉëëáçå= çÇÉê= ÇÉê= jÉíÜçÇÉ= ÇÉë= ÉñéçJ åÉåíáÉääÉå=dä®ííÉåë=EëáÉÜÉ=òK=_K=áå=xNzFI=ÇáÉ=~âíìÉääÉ=tÉêíÉ=ÄÉëëÉê=ÄÉêΩÅâëáÅÜíáÖÉåK== wìâìåÑíëéêçàÉâíáçåÉå=â∏ååÉå=åìê=ãáí=eáäÑÉ=ïÉáíÉêÉê=jÉíÜçÇÉå=EäáåÉ~êÉ=oÉÖêÉëëáçå=çÇÉê=ÉñJ éçåÉåíáÉääÉ=dä®ííìåÖF=ÉêêÉÅÜåÉí=ïÉêÇÉåK= jçå~íëíóéáëÅÜÉ=^ÄïÉáÅÜìåÖÉåW= ^ìÅÜ= ÇáÉ= p~áëçåÑáÖìê= ïáêÇ= åìê=~ìë=ÜáëíçêáëÅÜÉå=a~íÉå= ÉêJ êÉÅÜåÉíK= ^âíìÉääÉ= a~íÉå= ïÉêÇÉå= ÜáÉê= ÉÄÉåÑ~ääë= åìê= ìåòìêÉáÅÜÉåÇ= ÄÉêΩÅâëáÅÜíáÖí= ìåÇ= ãáí= ÜáëíçêáëÅÜÉå=a~íÉå=ÖäÉáÅÜÖÉïáÅÜíáÖ=îÉêêÉÅÜåÉíK== a~ë=jçÇÉää=áëí=ÇÉëíç=ÄÉëëÉêI=àÉ=âäÉáåÉê=ÇáÉ=áêêÉÖìä®êÉ=hçãéçåÉåíÉ=áëí=ìåÇ=àÉ=êÉÖÉäã®≈áÖÉê= ëáÅÜ=ÇáÉ=sÉê®åÇÉêìåÖÉå=ÇÉå=ä~åÖÑêáëíáÖÉåI=âçåàìåâíìêÉääÉå=ìåÇ=ãçå~íëíóéáëÅÜÉå=_ÉïÉJ ÖìåÖÉå=~åé~ëëÉåK= ^ÄëÅÜäáÉ≈ÉåÇ=ëáåÇ=åçÅÜ=òïÉá=ãÉíÜçÇáëÅÜÉ=^åãÉêâìåÖÉå=òì=ã~ÅÜÉåW= cΩê=âΩêòÉêÉ=p~áëçåÑáÖìêÉå=EòK_K=nì~êí~äëÇ~íÉåF=ãìëë=Ç~ë=fåíÉêî~ää=òìê=_ÉêÉÅÜåìåÖ=ÇÉê=ÖäÉáJ íÉåÇÉå=aìêÅÜëÅÜåáííÉ=ÉåíëéêÉÅÜÉåÇ=ÇÉê=îçêäáÉÖÉåÇÉå=p~áëçåÇ~ìÉê=~åÖÉé~ëëí=ïÉêÇÉåK=pç=áëí= ÄÉá=nì~êí~äëÇ~íÉå=ÇÉê=ÖäÉáíÉåÇÉ=aìêÅÜëÅÜåáíí=ÇÉê=lêÇåìåÖ=Q=òì=ï®ÜäÉåK=_Éá=p~áëçåÑáÖìêÉå= ãáí= ãÉÜê= fåíÉêî~ääÉå= EòK_K= ëíΩåÇäáÅÜÉê= píêçãîÉêÄê~ìÅÜ= éêç= q~ÖF= ï®Üäí= ã~å= ÉåíëéêÉÅÜÉåÇ= ÉáåÉå=ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáíí=Ü∏ÜÉêÉê=lêÇåìåÖ=EòK_K=lêÇåìåÖ=OQFK= a~ë= Ç~êÖÉëíÉääíÉ= jçÇÉää= òìê= p~áëçåÄÉêÉáåáÖìåÖ= Öáäí= åìê= ÑΩê= âçåëí~åíÉ=p~áëçåÑáÖìêÉåI= ÇK= ÜK= ÇáÉ=ë~áëçå~äÉå=pÅÜï~åâìåÖÉå=ëçääíÉå=áå=àÉÇÉê=p~áëçå=Éíï~=ÖäÉáÅÜ=Öêç≈=ëÉáåK=wÉáÖí=ëáÅÜI=Ç~ëë= ÇáÉ=^ìëëÅÜä®ÖÉ=E^ãéäáíìÇÉåF=ÇÉê=p~áëçåÑáÖìê=ãáí=ÇÉã=^åï~ÅÜëÉå=ÇÉê=Öä~ííÉå=hçãéçåÉåíÉ= ET= ìåÇ= wF= ÉÄÉåÑ~ääë= ~åï~ÅÜëÉåI= Ç~åå= ãìëë= Éáå= ^å~äóëÉãçÇÉää= ÑΩê= î~êá~ÄäÉ= p~áëçåÑáÖìêÉå= ÖÉï®Üäí=ïÉêÇÉå=EîÖäK=ÜáÉêòìW=xNzI=pK=TM=ÑÑKFK= c~òáíW= aáÉ= wÉáíêÉáÜÉå~å~äóëÉ= ãáííÉäë= ÖäÉáíÉåÇÉê= aìêÅÜëÅÜåáííÉ= ÉáÖåÉí= ëáÅÜ= áåëÄÉëçåÇÉêÉ= òìê=áåíÉåëáîÉå=^å~äóëÉ=ìåÇ=fåíÉêéêÉí~íáçå=ÜáëíçêáëÅÜÉê=båíïáÅâäìåÖÉåK=mêçÖåçëÉå=ÑΩê=ÇáÉ= wìâìåÑí=â∏ååÉå=åìê=ìåíÉê=wìÜáäÑÉå~ÜãÉ=~åÇÉêÉê=mêçÖåçëÉîÉêÑ~ÜêÉå=EäáåÉ~êÉ=oÉÖêÉëëáçåI= ÉñéçåÉåíáÉääÉ=dä®ííìåÖ=ìëïKF=ÖÉíêçÑÑÉå=ïÉêÇÉåK== =

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=

9

Import von Daten aus Datenbanken

9.1

Grundsätzliches

få= ÇáÉëÉã= h~éáíÉä= ëçää= Ç~ê~ìÑ= ÉáåÖÉÖ~åÖÉå= ïÉêÇÉåI= ïáÉ= a~íÉå= òìê= ëí~íáëíáëÅÜÉå= ^ìÑÄÉJ êÉáíìåÖ=~ìë=ÉáåÉê=îçêÜ~åÇÉåÉå=a~íÉåÄ~åâ=áå=ÉáåÉ=bñÅÉäJq~ÄÉääÉ=Éñíê~ÜáÉêí=ïÉêÇÉå=â∏åJ åÉåK== få= îáÉäÉå= c®ääÉå= îÉêÑΩÖÉå= råíÉêåÉÜãÉå= ÄÉêÉáíë= ΩÄÉê= Öêç≈É= a~íÉåÄ~åâÉå= ÑΩê= cáå~åòÄìÅÜJ Ü~äíìåÖI=`çåíêçääáåÖI=`ìëíçãÉê=oÉä~íáçåëÜáé=j~å~ÖÉãÉåí=E`ojF=ìåÇ=ëç=ïÉáíÉêK=aáÉëÉ=a~J íÉå=ëíÉÜÉå=áã=oÉÖÉäÑ~ääÉ=ÇÉå=jáí~êÄÉáíÉêå=ÑΩê=^ìëïÉêíìåÖÉå=éÉê=iÉëÉòìÖêáÑÑ=òìê=sÉêÑΩÖìåÖK= káÅÜí=ëÉäíÉå=ÉåíëíÉÜí=Ç~ÄÉá=ÇÉê=tìåëÅÜI=ëáÅÜ=ÉáåÉå=qÉáä=ÇÉê=a~íÉå=~ìë=ÇÉê=Öêç≈Éå=a~J íÉåÄ~åâ= áå= ÉáåÉ= éêáî~íÉ= bñÅÉäJq~ÄÉääÉ= ~ã= äçâ~äÉå= m`= òì= ÜçäÉåI= ìã= ëáÉ= Ç~åå= Ççêí= ãáí= ÇÉã=ÄÉäáÉÄíÉå=bñÅÉä=ÑΩê=áåÇáîáÇìÉääÉ=wïÉÅâÉ=~ìÑÄÉêÉáíÉåI=ëí~íáëíáëÅÜ=~ìëïÉêíÉåI=Öê~ÑáëÅÜ= Ç~êëíÉääÉå=òì=â∏ååÉåK==

9.2

Import aus MS-Access

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== _áäÇ=VKNW=q~ÄÉääÉ=Personal=ÉáåÉê=^ÅÅÉëëJa~íÉåÄ~åâ== ^ìÑ= ÉáåÉ= ëçäÅÜÉ= a~íÉåÄÉëí~åÇëJq~ÄÉääÉ= ãáí= ÇÉå=îçääëí®åÇáÖÉå=^åÖ~ÄÉå= òì= ~ääÉå=mÉêëçåÉå= ïáêÇ= ïçÜä=åáÉã~äë=Éáå=jáí~êÄÉáíÉê= ÇáêÉâí= òìÖêÉáÑÉå= ÇΩêÑÉå=Ó= Ç~ë= áëí= Éáå=dêìåÇéêáåòáé=ÇÉê= a~íÉåÄ~åâ~êÄÉáíI= ÄÉá= ÇÉê= ÇáÉ= páÅÜÉêÜÉáí=ÇÉê=a~íÉåI= îçê= ~ääÉã= ~ìÅÜ= ÖÉÖÉå= ìåÄÉÑìÖíÉ= báåJ ëáÅÜíå~ÜãÉI=~äë=Éáå=ÄÉÇÉìíÉåÇÉë=hêáíÉêáìã=~åÖÉëÉÜÉå=ïáêÇK== sáÉäãÉÜê=ïáêÇ=ÇìêÅÜ=ÇÉå=^ÅÅÉëëJa~íÉåÄ~åâ~Çãáåáëíê~íçê=ÑΩê=àÉÇÉå=^êÄÉáíëéä~íòI=îçå=ÇÉã= ~ìë= ~ìÑ= ÇáÉ= a~íÉåÄ~åâ= òìÖÉÖêáÑÑÉå= ïÉêÇÉå= Ç~êÑI= äÉÇáÖäáÅÜ= ÉáåÉ= é~ëëÉåÇÉI= ÉáåëÅÜê®åâÉåÇÉ= ^ÄÑê~ÖÉ=îçêÄÉêÉáíÉíK== báåÉ=^ÄÑê~ÖÉ=áëí=Éáå=mêçÖê~ããI=Ç~ë=ëíÉíë=åìê=ÉáåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉëI=áå=ÇÉê=oÉÖÉä= ïáÉÇÉê=áå=q~ÄÉääÉåÑçêãI=äáÉÑÉêíK=== pí~êíÉí=Éáå=jáí~êÄÉáíÉê=ÇáÉ=ÑΩê=áÜå=ìåÇ=ëÉáåÉå=^êÄÉáíëéä~íò=îçêÄÉêÉáíÉíÉ=^ÄÑê~ÖÉI=Ç~åå=ÉêÜ®äí= Éê=ÇÉåàÉåáÖÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉëI=ÇÉå=Éê=ÉáåëÉÜÉå=ìåÇ=~ìëïÉêíÉå=Ç~êÑK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=

V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=

NSM

få=_áäÇ=VKO=áëí=òì=ëÉÜÉåI=Ç~ëë=ÇáÉ=^ÄÑê~ÖÉ= Fuer_MusterfrauI=ÇáÉ=ÇÉê=a~íÉåÄ~åâ~Çãáåáëíê~íçê= ÑΩê= ÇáÉëÉ= jáí~êÄÉáíÉêáå= îçêÄÉêÉáíÉí= Ü~íI= çÑÑÉåëáÅÜíäáÅÜ= åìê= ÉáåáÖÉ=^åÖ~ÄÉå= ~ìë= ÇÉã= mÉêëçJ å~äÇ~íÉåÄÉëí~åÇ= éêÉáëÖáÄí= Ó= ìåÇ= Ç~êΩÄÉê= Üáå~ìë= åìê= ÇáÉàÉåáÖÉå= mÉêëçåÉå= ~ìëäáëíÉíI= ÇáÉ= áå= lêíÉå=ãáí=ÇÉã=^åÑ~åÖëÄìÅÜëí~ÄÉå=B=ïçÜåÉåK==

== _áäÇ=VKOW=aáÉ=^ÄÑê~ÖÉ=Fuer_Musterfrau=äáÉÑÉêí=ÉáåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉë== aáÉëÉåI=ÑΩê=ëáÉ=~äëç=ÑêÉáÖÉÖÉÄÉåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉë=Ç~êÑ=ÇáÉ=_É~êÄÉáíÉêáå=åìå=åìíJ òÉåI=~ìëïÉêíÉåI=~å~äóëáÉêÉåK== páÉ= ã∏ÅÜíÉ= Ç~ÑΩê= áÜê= îÉêíê~ìíÉë= bñÅÉä= îÉêïÉåÇÉåK= ^äëç= ï®Üäí= ëáÉ= áå= ^ÅÅÉëë= òìÉêëí= a^J qbfbumloqfbobk=E_áäÇ=VKPFK==

= _áäÇ=VKPW=bñéçêí=îÉê~åä~ëëÉå=

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VKP==báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë= =

NSN

^åëÅÜäáÉ≈ÉåÇ=Ó=ìåÇ=Ç~ë=áëí=ïáÅÜíáÖ=Ó=ãìëë=ëáÉ=áã=cÉåëíÉê= Dateityp=ÇáÉ=bñÅÉäJsÉêëáçå=ÉáåJ ëíÉääÉåI=ãáí=ÇÉê=ëáÉ=~êÄÉáíÉí=E_áäÇ=VKQFK=tÉåå=ëáÉ=âÉáåÉå=ÉáÖÉåÉå=a~íÉáå~ãÉå=Éáåíê®ÖíI=îÉêJ ïÉåÇÉí=^ÅÅÉëë=ÑΩê=ÇáÉ=òì=ÉêòÉìÖÉåÇÉ=bñÅÉäJa~íÉá=ÇÉå=k~ãÉå=ÇÉê=^ÄÑê~ÖÉK====

== _áäÇ=VKQW=qóé=ÇÉê=wáÉäÇ~íÉá=ÉáåëíÉääÉåI=k~ãÉ=îÉêÖÉÄÉå=== a~ë=áëí=ëÅÜçå=~ääÉëK=kìå=ëáåÇ=ÇáÉ=a~íÉå=~ìë=ÇÉê=^ÄÑê~ÖÉ=~ìÑ=ÇÉã=m`=îçå=cê~ì=jìëíÉêÑê~ì=áå= ÉáåÉê=bñÅÉäJq~ÄÉääÉ=îÉêÑΩÖÄ~êI=ìåÇ=ëáÉ=â~åå=å~ÅÜ=eÉêòÉåëäìëí=Ç~ãáí=~êÄÉáíÉåK== ^ääÉêÇáåÖëW= pçääíÉ= ëáÅÜ= å~ÅÜ= ÉáåáÖÉê= wÉáí= áã= òÉåíê~ä=îÉêï~äíÉíÉå=a~íÉåÄÉëí~åÇ= ÉáåÉ= ûåÇÉJ êìåÖ=ÉêÖÉÄÉåI=ÇáÉ=~ìÅÜ=ÇáÉ=häáÉåíÉä=îçå=cê~ì=jìëíÉêã~åå=ÄÉíêáÑÑí=Ó=Éë=ÖáÄí=å~íΩêäáÅÜ=Ç~åå= âÉáåÉ=~ìíçã~íáëÅÜÉ=^âíì~äáëáÉêìåÖ=áÜêÉê=bñÅÉäJq~ÄÉääÉI=ïáÉ=ëçääíÉ=Éë=~ìÅÜ\== aáÉ=jáí~êÄÉáíÉêáå=ãΩëëíÉ=ëáÅÜ=ÉêåÉìí=ÄÉá=^ÅÅÉëë=~åãÉäÇÉåI=áÜêÉ=^ÄÑê~ÖÉ=ïáÉÇÉê=ëí~êíÉåI=ÇáÉ= a~íÉå=ÉêåÉìí=ÉñéçêíáÉêÉå=ìåÇ=ëç=ïÉáíÉêK== tΩåëÅÜÉåëïÉêí=ï®êÉ=~äëç=ÜáÉê=ÉáåÉ=^ìÑêÉÅÜíÉêÜ~äíìåÖ=ÇÉê=sÉêÄáåÇìåÖ=òìê=a~íÉåÄ~åâI=ëç= Ç~ëë=ÖÉïáëëÉêã~≈Éå=~ìÑ=håçéÑÇêìÅâ=îçå=bñÅÉä=~ìë=EìåÇ=çÜåÉ=ÇáÉ=^ÅÅÉëëJ^ÄÑê~ÖÉ=ÉêåÉìí= ëí~êíÉå=òì=ãΩëëÉåF=ÇáÉ=a~íÉå=áå=ÇÉê=àÉïÉáäë=~âíìÉääÉå=cçêã=~åÖÉÑçêÇÉêí=ïÉêÇÉå=â∏ååÉåK== a~ãáí= ïΩêÇÉå= ~ìÅÜ= áå= bñÅÉä= ëíÉíë=~âíìÉääÉ=a~íÉå=îÉê~êÄÉáíÉíK= fã=^ÄëÅÜåáíí=VKRKO= ~ìÑ= pÉáíÉ= NSU=ïáêÇI=ÄÉáëéáÉäÜ~Ñí=ÄÉòçÖÉå=~ìÑ=ÉáåÉ=lê~ÅäÉJa~íÉåÄ~åâI=ÇÉê=jÉÅÜ~åáëãìë=ÄÉëÅÜêáÉÄÉåI= ãáí=ÇÉã=ÇáÉëÉê=tìåëÅÜ=ÉêÑΩääí=ïÉêÇÉå=â~ååK=

9.3

Einrichtung eines ODBC-Treibers

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V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=

NSO

^ìÑ=ÇÉã=m`=ÇÉë=^åïÉåÇÉêë=ãìëë=Éáå=ÉåíëéêÉÅÜÉåÇÉê=la_`JqêÉáÄÉê=EléÉå=a~í~Ä~ëÉ= `çååÉÅíáîáíóF= áåëí~ääáÉêí= ëÉáåK= báåáÖÉ= ÇáÉëÉê= qêÉáÄÉê= ëáåÇ= áã= fåëí~ää~íáçåëìãÑ~åÖ= îçå= táåÇçïë=um=ÉåíÜ~äíÉåK= fååÉêÜ~äÄ=ÇÉë=jp=lÑÑáÅÉ=m~âÉíÉë=ãìëë=Ç~ë=qççä=MS Query=áåëí~ääáÉêí=ëÉáåK= få= ÇáÉëÉã= ^ÄëÅÜåáíí= ïáêÇ= òìÉêëí= pÅÜêáíí= ÑΩê= pÅÜêáíí= ÇáÉ= báåêáÅÜíìåÖ=ÇÉë=la_`JqêÉáÄÉêë= ÄÉJ ëÅÜêáÉÄÉåK=fã=ÑçäÖÉåÇÉå=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NSP=ïáêÇ=Ç~åå=ÇáÉ=sçêÖÉÜÉåëïÉáëÉ=òìê=bñíê~âJ íáçå=ÇÉê=a~íÉå=ÄÉëÅÜêáÉÄÉåK== aáÉ= báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë= ïáêÇ= ~åÜ~åÇ= ÇÉë= _ÉíêáÉÄëëóëíÉãë= jp= táåÇçïë= um= mêçÑÉëëáçå~ä= îÉê~åëÅÜ~ìäáÅÜíK= aÉê= ëé®íÉê= ÄÉå∏íáÖíÉ= la_`JqêÉáÄÉê= ÑΩê= lê~ÅäÉ= ÖÉÜ∏êí= ÜáÉê= òìã=iáÉÑÉêìãÑ~åÖ=ÇÉë=_ÉíêáÉÄëëóëíÉãëK= aáÉ= ^Çãáåáëíê~íáçå= ÇáÉëÉê= qêÉáÄÉê= ÑáåÇÉí= ã~å= ΩÄÉê= pq^oqbfkpqbiirkdbkpvpqbjpqbrbJ orkdsbot^iqrkd=E_áäÇ=VKRFW=

= _áäÇ=VKRW=råíÉêÖêìééÉ=VERWALTUNG=áå=ÇÉê=póëíÉãëíÉìÉêìåÖ=îçå=táåÇçïë=um==

== _áäÇ=VKSW=pí~åÇ~êÇã®≈áÖ=îçêÜ~åÇÉåÉ=a~íÉåèìÉääÉå=

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=

VKQ==wìÖêáÑÑ=~ìÑ=âçåâêÉíÉ=a~íÉåÄ~åâÉå=

NSP

aÉê= ^ìÑêìÑ= ÇÉë= póãÄçäë= Datenquellen (ODBC)= ∏ÑÑåÉí= Ç~ë= cÉåëíÉê= ÇÉë= la_`Ja~íÉåèìÉääÉåJ ^Çãáåáëíê~íçêëI=áå=ÇÉëëÉå=cÉåëíÉê= Benutzerdatenquellen ëáÅÜ=ÄÉêÉáíë=ÉáåáÖÉ=ÇÉê=ëí~åÇ~êÇã®J ≈áÖ=îçêÜ~åÇÉåÉå=a~íÉåèìÉääÉå=ÄÉÑáåÇÉå=E_áäÇ=VKSFK=

= _áäÇ=VKTW=sÉêÑΩÖÄ~êÉ=la_`JqêÉáÄÉê=ìåíÉê=jp=táåÇçïë=um=mêçÑÉëëáçå~ä= aáÉ=_ÉåìíòÉêJapk=ëáåÇ=ÇáÉ=ÉáåÖÉêáÅÜíÉíÉå=a~íÉåèìÉääÉåI=ÇáÉ=åìê=ÇÉã=~âíìÉää=~ã=m`=~åÖÉJ ãÉäÇÉíÉå=_ÉåìíòÉê=òìê=sÉêÑΩÖìåÖ=ëíÉÜÉåK== pçää=ÉáåÉ=ïÉáíÉêÉ=a~íÉåèìÉääÉ=ÜáåòìÖÉÑΩÖí=ïÉêÇÉåI=Ç~åå=áëí=ãáííÉäë= Hinzufügen =Ç~ë=cÉåëJ íÉê=Neue Datenquelle erstellen=E_áäÇ=VKTF=òì=∏ÑÑåÉåX=Ççêí=â~åå=Ç~åå=~ìëÖÉï®Üäí=ïÉêÇÉåK==

9.4

Zugriff auf konkrete Datenbanken

9.4.1

Microsoft SQL-Server

aÉê=pniJpÉêîÉêI=Éáå=jáÅêçëçÑíJmêçÇìâíI=áëí=Éáå=äÉáëíìåÖëÑ®ÜáÖÉë=a~íÉåÄ~åâJpóëíÉãI=Ç~ë=áå= îáÉäÉå=_ÉêÉáÅÜÉå=^åïÉåÇìåÖ=ÑáåÇÉíK== ^ìÅÜ= Ççêí= ïáêÇ= ãáí= eáäÑÉ= îçå= ^ÄÑê~ÖÉå= ÑΩê= àÉÇÉå= ^êÄÉáíëéä~íò= åìê= ÉáåÉ= ëçäÅÜÉ= qÉáäãÉåÖÉ= ÇÉë=a~íÉåÄÉëí~åÇÉë=ÄÉêÉáíÖÉëíÉääíI=ÇáÉ=ÇÉê=hçãéÉíÉåò=ìåÇ=ÇÉã=fåÑçêã~íáçåëÄÉÇΩêÑåáë=ÇÉë= àÉïÉáäáÖÉå=_É~êÄÉáíÉêë=ÉåíëéêáÅÜíK== aáÉ= sÉêëáçå= bñÅÉä= OMMP= ÄáÉíÉí= ÉáåÉ= iÉáëíìåÖ= Add-In für SQL Server Analysis Services= ~åI= ÇáÉ=áå== http://go.microsoft.com/?linkid= 1140024

ïáÉ=ÑçäÖí=ÄÉëÅÜêáÉÄÉå=áëíW== dêÉáÑÉå=páÉ=ëÅÜåÉää=ìåÇ=éêçÄäÉãäçë=~ìÑ=ãìäíáÇáãÉåëáçå~äÉ=a~íÉå=òìI=ÑΩÜêÉå=páÉ=ÇÉí~áääáÉêíÉ= a~íÉå~å~äóëÉå=ÇìêÅÜ=ìåÇ=ÉêëíÉääÉå=páÉ=ÑäÉñáÄäÉI=áåíÉê~âíáîÉ=_ÉêáÅÜíÉ=áå=jáÅêçëçÑí=bñÅÉäK==

9.4.2

Oracle

cΩê=ÇáÉ=hçåÑáÖìêáÉêìåÖ=ÇÉë=la_`JqêÉáÄÉêë=ÑΩê=lê~ÅäÉ=ãìëë=ÇÉê=sÉêÄáåÇìåÖëÄÉòÉáÅÜåÉê= ETNS-AliasF=ÑΩê=ÇáÉ=a~íÉåÄ~åâ=ÄÉâ~ååí=ëÉáåI=ÜáÉê=ëçääíÉ=ã~å=ëáÅÜ=~å=ÇÉå=^Çãáåáëíê~íçê= ïÉåÇÉåK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=

NSQ

V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=

tÉáíÉêÜáå=ãìëë=ÇáÉ=lê~ÅäÉ=`äáÉåí=pçÑíï~êÉ=ÄÉêÉáíë=áåëí~ääáÉêí=ëÉáåK=aáÉë=áëí=áããÉê=Ç~åå=ÇÉê= c~ääI= ïÉåå= ÇÉê= _ÉåìíòÉê= ÄÉêÉáíë= ãáí= `äáÉåíJpÉêîÉêJ^åïÉåÇìåÖÉå= ~êÄÉáíÉíI= ÇáÉ= ~ìÑ= lê~ÅäÉJ a~íÉåÄ~åâÉå=Ä~ëáÉêÉåK= få= ÇÉå= ãÉáëíÉå= lê~ÅäÉJa~íÉåÄ~åâÉå= áëí= Éáå= pí~åÇ~êÇÄÉåìíòÉê= å~ãÉåë= scott= Em~ëëïçêí= tigerF=òì=pÅÜìäìåÖëòïÉÅâÉå=ãáí=ÉáåÖÉêáÅÜíÉíK== bë=ÖáÄí=~ÄÉê=àÉíòí=ãáí=ÉáåÉê=åÉì=îÉêÑΩÖÄ~êÉå=sÉêëáçå=lê~ÅäÉ=a~í~Ä~ëÉ=bñéêÉëë=bÇáíáçå=EOracle Database XEF=ÉáåÉ=òìê=Öêç≈Éå=a~íÉåÄ~åâ=âçãé~íáÄäÉ=sÉêëáçå=îçå=lê~ÅäÉ=NMÖK=páÉ=áëí=äÉJ ÇáÖäáÅÜ=äáãáíáÉêíI=Ç~ëë=ã~ñáã~ä=Éáå=mêçòÉëëçêI=N=d_=e~ìéíëéÉáÅÜÉê=ìåÇ=ã~ñáã~ä=Q=d_=a~J íÉå=îÉêïÉåÇÉí=ïÉêÇÉå=â∏ååÉåK=j~å=â~åå=ëáÉ=âçëíÉåäçë=ÜÉêìåíÉê=ä~ÇÉå=ìåÇ=ÄÉåìíòÉåI=~ìÅÜ= ÑΩê=âçããÉêòáÉääÉ=wïÉÅâÉK== få= ÇÉê= a~íÉåÄ~åâ= Oracle Database XE= E~ìÑ= ÇáÉ= áå= ÇáÉëÉã= ^ÄëÅÜåáíí= _ÉòìÖ= ÖÉåçããÉå= ïáêÇF=ãÉäÇÉí=ã~å=ëáÅÜ=~äë=_ÉåìíòÉê=hr=ãáí=ÇÉã=ÖäÉáÅÜä~ìíÉåÇÉå=m~ëëïçêí=hr ~åK====== aÉê= _ÉåìíòÉê= hr= áëí= ~ÄÉê= ~ìÅÜ= áå= àÉÇÉê= Öêç≈Éå= lê~ÅäÉ=NMÖJa~íÉåÄ~åâ= îçêÜ~åÇÉåI= ëçÑÉêå= ÄÉá=ÇÉê=fåëí~ää~íáçå=ÇáÉ=_ÉáëéáÉäJpÅÜÉã~ë=ãáí=áåëí~ääáÉêí=ïìêÇÉåK= lÄïçÜä=áå=ÇáÉëÉã=_ÉáëéáÉä=~ìÑ=ÉáåÉ=lê~ÅäÉJa~íÉåÄ~åâ=òìÖÉÖêáÑÑÉå=ïáêÇI=áëí=ÇáÉ=sçêÖÉJ ÜÉåëïÉáëÉ=ÑΩê=~åÇÉêÉ=a~íÉåÄ~åâÉåI=òK_K=jp=pni=pÉêîÉêI=f_j=a_LO=ìëïK=~å~äçÖK= k~ÅÜ=_Éí®íáÖÉå=ÇÉë=_ìííçåë= Hinzufügen =E_áäÇ=VKS=~ìÑ=pÉáíÉ=NSOF=ï®Üäí=ã~å=~äëç=~ìë=ÇÉê= iáëíÉ=ÇÉê=îÉêÑΩÖÄ~êÉå=qêÉáÄÉê=ÇÉå=lê~ÅäÉJqêÉáÄÉê=E_áäÇ=VKT=~ìÑ=pÉáíÉ=NSPF=~ìëK== pçääíÉ=ÇáÉ=lê~ÅäÉ=`äáÉåíJpçÑíï~êÉ=åáÅÜí=áåëí~ääáÉêí=ëÉáåI=ÉêÜ®äí=ã~å=ÉáåÉ=cÉÜäÉêãÉäÇìåÖ=E_áäÇ= VKUFK= få= ÇáÉëÉã= c~ää= ãìëë= ÇáÉ= fåëí~ää~íáçå= ÇÉê= lê~ÅäÉJhçãéçåÉåíÉå= ESQL*Net ClientF= Éêëí= å~ÅÜÖÉÜçäí=ïÉêÇÉåK==

= _áäÇ=VKUW=cÉÜäÉêãÉäÇìåÖ=ÄÉá=åáÅÜí=îçêÜ~åÇÉåÉê=lê~ÅäÉJ`äáÉåíJpçÑíï~êÉ= fã= c~ääÉI= Ç~ëë= ÇáÉ= lê~ÅäÉ= `äáÉåíJpçÑíï~êÉ= ÄÉêÉáíë= îçêÜ~åÇÉå= áëíI= ÉêëÅÜÉáåí= ÇÉê= aá~äçÖ= ~ìë= _áäÇ=VKVX=áã=_áäÇ=ëáåÇ=ÇêÉá=báåÖ~ÄÉå=ÄÉêÉáíë=ÇìêÅÜÖÉÑΩÜêí=ïçêÇÉåK==

= _áäÇ=VKVW=kçíïÉåÇáÖÉ=báåÖ~ÄÉå=ÑΩê=ÇÉå=lê~ÅäÉJla_`JqêÉáÄÉê= aÉê=a~íÉåèìÉääÉåå~ãÉ=áëí=Ç~ÄÉá=ÉáåÉ=ÑêÉá=ï®ÜäÄ~êÉ=_ÉòÉáÅÜåìåÖI=ìåíÉê=ïÉäÅÜÉê=ÇÉê=_ÉåìíJ òÉê=ëé®íÉê=áã= MS Query=ÇáÉ=a~íÉåÄ~åâ=~åÖáÄíI=~ìë=ÇÉê=ÇáÉ=a~íÉå=ëí~ããÉå=ëçääÉåK=aáÉ=_ÉJ ëÅÜêÉáÄìåÖ=áëí=çéíáçå~äI=â~åå=~äëç=ÑêÉá=ÖÉä~ëëÉå=ïÉêÇÉåK=aÉê=_ÉåìíòÉêå~ãÉ=áëí=ÇÉê=hçåíçJ å~ãÉ=áå=ÇÉê=a~íÉåÄ~åâI=áå=_áäÇ=VKV=ïìêÇÉ=Ç~ÑΩê=ÇÉê=lê~ÅäÉJubJrëÉê=hr=ÉáåÖÉíê~ÖÉåK=

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=

VKR==bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ= =

NSR

eáåíÉê= ÇÉê= _ÉòÉáÅÜåìåÖ= pÉêîÉê= Eáå= _áäÇ= VKV= ÄÉäÉÖí= ãáí= xeF= îÉêÄáêÖí= ëáÅÜ= Éáå= ëç= ÖÉå~ååíÉê= TNS-AliasI= Ç~ë= áëí= Éáå= hΩêòÉä= ÑΩê= ÉáåÉ= lê~ÅäÉJa~íÉåÄ~åâJsÉêÄáåÇìåÖI= ÇáÉ= áå= ÇÉê= lê~ÅäÉJ `äáÉåíJpçÑíï~êÉ=ÄÉâ~ååí=ëÉáå=ãìëëK=a~ÑΩê=ãìëë=ã~å=ëáÅÜ=ÖÉÖÉÄÉåÉåÑ~ääë=~å=ëÉáåÉå=a~íÉåJ Ä~åâ~Çãáåáëíê~íçê=ïÉåÇÉåK== EpçÑÉêå=ÇáÉëÉ=^äá~ëJk~ãÉå=åáÅÜí=ìåíÉêåÉÜãÉåëïÉáí=òÉåíê~ä=îÉêï~äíÉí=ïÉêÇÉåI=ÜáäÑí=~ìÅÜ=Éáå= _äáÅâ=áå=ÇáÉ=a~íÉá=%ORACLE_HOME%\network\admin\tnsnames.oraI=ÇáÉë=~ÄÉê=åìê=ÑΩê=fåëáÇÉêFK= iÉáÇÉê= áëí= Éë= ~å= ÇáÉëÉê= píÉääÉ= ìåÇ= òì= ÇáÉëÉã= wÉáíéìåâí= åçÅÜ= åáÅÜí= ã∏ÖäáÅÜI= ÇáÉ= âçêêÉâíÉ= sÉêÄáåÇìåÖ=òìê=a~íÉåÄ~åâ=ÖäÉáÅÜ=òì=íÉëíÉåI=ÇáÉë=â~åå=Éêëí=ëé®íÉê=áã=^ÄÑê~ÖÉïÉêâòÉìÖ= MS Query=îÉêáÑáòáÉêí=ïÉêÇÉåK= aáÉ=hçåÑáÖìê~íáçå=ÇÉë=la_`JqêÉáÄÉêë=áëí=~ÄÉê=Ç~ãáí=~ÄÖÉëÅÜäçëëÉåK=

9.5

Excel-Zugriff auf Oracle

9.5.1

Daten importieren

k~ÅÜ= ÇÉã= pí~êíÉå= îçå= bñÅÉä= ï®Üäí= ã~å= a^qbkbuqbokb= a^qbk= fjmloqfbobkkbrb= ^_J co^db=bopqbiibk=~ìëK== pçääíÉ=Ç~ë=lÑÑáÅÉJtÉêâòÉìÖ=MS Query=åáÅÜí=áåëí~ääáÉêí=ëÉáåI=ïΩêÇÉ=åìå=ÉáåÉ=ÉåíëéêÉÅÜÉåÇÉ= cÉÜäÉêãÉäÇìåÖ=ÉêëÅÜÉáåÉå=ìåÇ=ÇáÉëÉ=fåëí~ää~íáçå=ãΩëëíÉ=Éêëí=ãáí=eáäÑÉ=ÇÉê=jp=lÑÑáÅÉJ`a= å~ÅÜÖÉÜçäí=ïÉêÇÉåK= ^åëçåëíÉå=ÉêëÅÜÉáåí=ÇÉê=aá~äçÖI=ÇÉê=ÇáÉ=îçêÜ~åÇÉåÉå=DSN=EÇ~í~=ëçìêÅÉ=å~ãÉF=~ìÑäáëíÉíK=eáÉê= ëçääíÉ=ÇáÉ=îçêÜáå=âçåÑáÖìêáÉêíÉ=a~íÉåÄ~åâîÉêÄáåÇìåÖ=îçêÖÉÑìåÇÉå=ïÉêÇÉå=E_áäÇ=VKNMFK=

== _áäÇ=VKNMW=iáëíÉ=ÇÉê=áã=póëíÉã=ÄÉâ~ååíÉå=a~íÉåèìÉääÉå=EDSNF= k~ÅÜ=ÇÉê=^ìëï~Üä=ÇÉê=é~ëëÉåÇÉå=a~íÉåèìÉääÉ=ÉêëÅÜÉáåí=ÇáÉ=m~ëëïçêíJ^ÄÑê~ÖÉ=E_áäÇ=VKNNFK==

= _áäÇ=VKNNW=m~ëëïçêíJ^ÄÑê~ÖÉ=

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=

V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=

NSS

aÉê=_ÉåìíòÉêå~ãÉ=ìåÇ=ÇáÉ=a~íÉåÄ~åâ=ëáåÇ=Ççêí=òï~ê=ÄÉêÉáíë=ÉáåÖÉíê~ÖÉåI=â∏ååíÉå=ÜáÉê=~ÄÉê= åçÅÜ=~ÄÖÉ®åÇÉêí=ïÉêÇÉå=EaáÉ=ÉáÖÉåíäáÅÜÉ=la_`JhçåÑáÖìê~íáçå=®åÇÉêí=ëáÅÜ=Ç~ÇìêÅÜ=åáÅÜíFK== táÉ= ëÅÜçå= Éêï®ÜåíI= ïáêÇ= ÜáÉê= Ç~ë= îçå= lê~ÅäÉ= ãáí= ÇÉê= sÉêëáçå= ub= ÑΩê= iÉêåÉåÇÉ= ÄÉêÉáíÖÉJ ëíÉääíÉ=m~~ê=hrLhr=ÑΩê=_ÉåìíòÉêå~ãÉ=ìåÇ=hÉååïçêí=îÉêïÉåÇÉíK== pçÑÉêå=ÇáÉ=báåêáÅÜíìåÖ=ÇÉë=la_`JqêÉáÄÉêë=âçêêÉâí=ï~êI=ëí~êíÉí=àÉíòí=áã=eáåíÉêÖêìåÇ=Ç~ë= mêçÖê~ãã=MS QueryK== få= ÉáåÉã= aá~äçÖÑÉåëíÉê= ÉêëÅÜÉáåÉå= åìå= ~ääÉ= lÄàÉâíÉ= ÇÉê= lê~ÅäÉJa~íÉåÄ~åâ= Eq~ÄÉääÉåI= sáÉïëL^åëáÅÜíÉåI=póåçåóãÉFI=~ìÑ=ÇáÉ=ÇÉê=~åÖÉãÉäÇÉíÉ=_ÉåìíòÉê=EÜáÉêW=hrF=wìÖêáÑÑ=ÄÉëáíòíK= fã=_áäÇ=VK= NO=ïìêÇÉ=ÄÉêÉáíë=Äáë=òìê=q~ÄÉääÉ= EMPLOYEES=E^åÖÉëíÉääíÉåJq~ÄÉääÉF=ÖÉëÅêçääí=ìåÇ= ÇÉê=^åÑ~åÖ=ÇÉê=q~ÄÉääÉåëíêìâíìê=~åÖÉòÉáÖíK=

== _áäÇ=VKNOW=iáëíÉ=ÇÉê=lÄàÉâíÉ=ÇÉë=a~íÉåÄ~åâÄÉåìíòÉêë= eáÉê=â∏ååÉå=åìå=ÉåíïÉÇÉê=ÇáÉ=ÖÉë~ãíÉ=q~ÄÉääÉ=çÇÉê=ÉáåòÉäåÉ=pé~äíÉå=áå=ÇáÉ=^ÄÑê~ÖÉ=ΩÄÉêJ åçããÉå=ïÉêÇÉåK== fã=_ÉáëéáÉä=E_áäÇ=VKNPF=ïáêÇ=ÇáÉ=ÖÉë~ãíÉ=q~ÄÉääÉåëíêìâíìê=éÉê=häáÅâ=~ìÑ= > =ΩÄÉêåçããÉåK==

== _áäÇ=VKNPW=§ÄÉêåçããÉåÉ=pé~äíÉå= k~ÅÜ= Weiter > = ÉêëÅÜÉáåí= Éáå= aá~äçÖI= ãáí= ïÉäÅÜÉã= ÇáÉ= òì= ëÉäÉâíáÉêÉåÇÉå= a~íÉå= ÉáåÖÉJ ëÅÜê®åâí=ïÉêÇÉå=â∏ååÉåK==

cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=

VKR==bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ= =

NST

fã=_ÉáëéáÉä=E_áäÇ=VKNQF=ïÉêÇÉå=åìê=~ääÉ=ÇáÉàÉåáÖÉå=^åÖÉëíÉääíÉå=~ìëÖÉï®ÜäíI=ÇáÉ=áå=aÉé~êJ íÉãÉåíë=ãáí=ÉáåÉê=aÉé~êíãÉåíJkìããÉê=ìåíÉêÜ~äÄ=îçå=RM=~êÄÉáíÉå=Eáå=pni=ï®êÉ=ÇáÉë=ÉáåÉ= WHEREJ_ÉÇáåÖìåÖFK=a~=ÇÉê=^ëëáëíÉåí=ÇáÉ=^êÄÉáí=ã~ñáã~ä=ÉêäÉáÅÜíÉêå=ïáääI=ÖêÉáÑí=Éê=ÄÉêÉáíë=~ìÑ= ÇáÉ=a~íÉåÄ~åâ=òì=ìåÇ=ÉêãáííÉäí=~ääÉ=ã∏ÖäáÅÜÉå=tÉêíÉ=ÑΩê=ÇáÉ=êÉÅÜíÉ=tÉêíÉäáëíÉK== aáÉë=â~åå=ÄÉá=ëÉÜê=Öêç≈Éå=a~íÉåãÉåÖÉå=òì=t~êíÉòÉáíÉå=ÑΩÜêÉåK= =

= _áäÇ=VKNQW=báåëÅÜê®åâìåÖ=ÇÉê=a~íÉåãÉåÖÉ=

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NSU

aÉê= å®ÅÜëíÉ= aá~äçÖ= E_áäÇ= VKNRF= äÉÖí= ã∏ÖäáÅÜÉ= pçêíáÉêâêáíÉêáÉå= ÇÉê= a~íÉå= ÑÉëí= Eáå= pni= ÄÉJ â~ååí=~äë=ORDER BYFW= kìå= ÉêëÅÜÉáåí= ÇÉê= äÉíòíÉ= aá~äçÖ= ÇÉë= ^ëëáëíÉåíÉå= E_áäÇ= VKNSF= ìåÇ= ÖáÄí= ÇáÉ= j∏ÖäáÅÜâÉáíI= ÇáÉ= a~íÉå=ÉåíïÉÇÉê=ÖäÉáÅÜ=~å=bñÅÉä=òì=äáÉÑÉêå=çÇÉê=ÇáÉ=^ÄÑê~ÖÉ=áå=MS Query=Éêëí=åçÅÜ=ïÉáíÉê=òì= ÄÉ~êÄÉáíÉåK=_áäÇ=VKNS=òÉáÖíI=Ç~ëë=ÜáÉê=ÄÉáëéáÉäÜ~Ñí=ÇáÉ=äÉíòíÉêÉ=s~êá~åíÉ=ÖÉï®Üäí=ïìêÇÉK== = =

= _áäÇ=VKNTW=MS Query=ãáí=~ìëÖÉÑΩÜêíÉê=^ÄÑê~ÖÉ= cçäÖäáÅÜ=ÉêëÅÜÉáåí=MS Query=E_áäÇ=VKNTF=ìåÇ=òÉáÖí=ÇáÉ=~ìëÖÉï®ÜäíÉå=a~íÉå=~åK= pçÑÉêå=ã~å=ÇáÉ=^ÄÑê~ÖÉëéê~ÅÜÉ=pni=ÄÉÜÉêêëÅÜíI=â~åå=ÜáÉê=ÇáÉ=^ÄÑê~ÖÉ=ÇìêÅÜ=häáÅâ=~ìÑ=ÇÉå= _ìííçå= SQL =åçÅÜ=Éáåã~ä=å~ÅÜîçääòçÖÉå=ïÉêÇÉåK== få=ÇáÉëÉã=c~ää=ïáêÇ=ÑçäÖÉåÇÉë=~åÖÉòÉáÖíW= SELECT

EMPLOYEES.EMPLOYEE_ID, EMPLOYEES.FIRST_NAME, EMPLOYEES.LAST_NAME, EMPLOYEES.EMAIL, EMPLOYEES.PHONE_NUMBER, EMPLOYEES.HIRE_DATE, EMPLOYEES.JOB_ID, EMPLOYEES.SALARY, EMPLOYEES.COMMISSION_PCT, EMPLOYEES.MANAGER_ID, EMPLOYEES.DEPARTMENT_ID FROM HR.EMPLOYEES EMPLOYEES WHERE (EMPLOYEES.DEPARTMENT_ID<50) ORDER BY EMPLOYEES.SALARY DESC

aÉê=^ìÑêìÑ=îçå=MS Query=áëí=~ÄÉê=~ìë=ÉáåÉã=~åÇÉêÉå=dêìåÇ=ëáååîçääW== aáÉ=ÉêëíÉääíÉ=^ÄÑê~ÖÉ=â~åå=ÖÉëéÉáÅÜÉêí=ïÉêÇÉå=Eãáí=a^qbfpmbf`ebok=rkqboFK=pçäÅÜÉ=^ÄJ Ñê~ÖÉå=ÉêÜ~äíÉå=ÇáÉ=a~íÉáÉåÇìåÖ= DQY=ìåÇ=â∏ååÉå=~ìë=bñÅÉä=ÄÉäáÉÄáÖ=çÑí=ïáÉÇÉê=~ìÑÖÉêìJ ÑÉå=ïÉêÇÉåK= ^äë= äÉíòíÉ= ^âíáçå= ï®Üäí= ã~å= åìå= a^qbfa^qbk= ^k= jf`olplcq= bu`bi= wro§`hdb_bkX= Ç~åå= ïáêÇ=ÖÉÑê~ÖíI=áå=ïÉäÅÜÉå=_ÉêÉáÅÜ=ÇÉë=bñÅÉäJq~ÄÉääÉåÄä~ííÉë=ÇáÉ=a~íÉå=Éáåòìíê~ÖÉå=ëáåÇK== _áäÇ=VKNU=òÉáÖí=ëÅÜäáÉ≈äáÅÜI=ïáÉ=áå=ÇÉê=bñÅÉäJq~ÄÉääÉ=ÇáÉ=~ÄÖÉÑê~ÖíÉå=a~íÉå=òì=ëÉÜÉå=ëáåÇK== aáÉ= ÖÉëéÉáÅÜÉêíÉ= ^ÄÑê~ÖÉ= â~åå= ΩÄÉê= a^qbkbuqbokb= a^qbkdbpmbf`eboqb= ^_co^db= ^rpJ c§eobk=ÄÉäáÉÄáÖ=çÑí=ïáÉÇÉêÜçäí=ïÉêÇÉåK=

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9.5.2

NSV

Daten visualisieren und aktuell halten

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= _áäÇ=VKNUW=a~íÉå=~ìë=MS Query=áã=bñÅÉä=

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cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=

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NTM

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Anhang 1: Vom Problem zur Excel-Lösung bë=áëí=ÉáåÉ=fääìëáçå=îçå=Eå~áîÉåF=^ì≈ÉåëíÉÜÉåÇÉåI=Ç~ëë=ÇáÉ=i∏ëìåÖ=ÉáåÉë=mêçÄäÉãë=Ç~ãáí= ÄÉÖáååÉI= Ç~ëë= ã~å= ëáÅÜ= ÉáåÑ~ÅÜ= ~å= ÇÉå= m`= ëÉíòíI= bñÅÉä= ëí~êíÉíI= tÉêíÉ= ìåÇ= cçêãÉäå= ãáí= çÇÉê=çÜåÉ=cìåâíáçåÉå=Éáåíê®ÖíI=cçêãÉäå=ÖÉÉáÖåÉí=âçéáÉêí=ìåÇ=~åëÅÜäáÉ≈ÉåÇ=Ç~ë=bêÖÉÄåáë= ÑêÉìÇáÖ=òìê=hÉååíåáë=åáããíK== aáÉëÉë= sçêÖÉÜÉå= ÑìåâíáçåáÉêí= åìê= ÄÉá= ëÉÜêI= ëÉÜê= ÉáåÑ~ÅÜÉå= mêçÄäÉãëíÉääìåÖÉå= ìåÇ= áëí= áãJ ãÉê=ãáí=ÇÉã=oáëáâç=ÄÉÜ~ÑíÉíI=Ç~ëë=ÖêìåÇäÉÖÉåÇÉ=aÉåâÑÉÜäÉê=EäçÖáëÅÜÉ=cÉÜäÉêF=~ìÑíêÉíÉåI=ÇáÉ= ëáÅÜ=Ç~åå=ãáí=_ÉÇáÉåìåÖëÑÉÜäÉêå=îçå=bñÅÉä=EòK=_K=îÉêÖÉëëÉåÉã=çÇÉê=Ñ~äëÅÜ=ÖÉëÉíòíÉã=açäJ ä~êòÉáÅÜÉåF= ΩÄÉêä~ÖÉêå= ìåÇ= òì= EpÅÜÉáåJF= bêÖÉÄåáëëÉå= ÑΩÜêÉåI= ÇÉåÉå= ã~å= ã∏ÖäáÅÜÉêïÉáëÉ= ~ìÑ=^åÜáÉÄ=åáÅÜí=Éáåã~ä=~åëáÉÜíI=Ç~ëë=ëáÉ=Ñ~äëÅÜ=ëáåÇK== pÅÜä~ÖÉå=ïáê=Ç~òì=ÇÉå=_çÖÉå=òìê=báåäÉáíìåÖ=ÇáÉëÉë=_ìÅÜÉë=ìåÇ=ÇÉã=Ççêí=~ìÑ=pÉáíÉ=NQ=îçêJ ÖÉÑΩÜêíÉå=_ÉáëéáÉä=òìê=_ÉêÉÅÜåìåÖ=ÇÉê=pìããÉå=ÇÉê=mêÉáëÉ=ÇÉê=TBJ=ÄòïK=ÇÉê=NVBJ^êíáâÉäK= _Éåìíòí=ã~å=Ç~ë=açää~êòÉáÅÜÉå=åáÅÜíI=Ç~åå=áëí=ÉáåÉ=e®äÑíÉ=ÇÉê=oÉÅÜåìåÖ=êáÅÜíáÖI=ÇáÉ=~åÇÉêÉ= Ç~ÖÉÖÉå=Ñ~äëÅÜK== tÉê=ïáää=Ç~ë=ÇÉå=w~ÜäÉåïÉêíÉå=~åëÉÜÉå\== bë=ÉãéÑáÉÜäí=ëáÅÜ=~äëç=ÇêáåÖÉåÇI=ÇÉå=mêçÄäÉãä∏ëìåÖëéêçòÉëë=áå=pÅÜêáííÉ=òì=òÉêäÉÖÉåI=àÉÇÉå= pÅÜêáíí=áå=ëÉáåÉå=^ìÑÖ~ÄÉå=ìåÇ=bêÖÉÄåáëëÉå=ëçïáÉ=ëÉáåÉå=péÉòáÑáâ~=ÖÉå~ì=òì=ÇÉÑáåáÉêÉåK===== _Éï®Üêí=Ü~í=ëáÅÜ=Ç~ë=ëíìÑÉåïÉáëÉ=eÉê~åÖÉÜÉå=áå=ëÉÅÜë=pÅÜêáííÉåW== =

Beispiel bzw. Problem

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Theorie

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=K1 = K1 (1 + p )

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NTP

råÇ=ëç=ïÉáíÉêI=ÇK=ÜK=~ääÖÉãÉáå=Öáäí== E^KMPF=

=K t = K t −1 (1 + p )

f ür

t = 1, ..., T

wìã=oÉÅÜÉåëÅÜÉã~W=aáÉ=q~ÄÉääÉåÑçêã=ÄáÉíÉí=ëáÅÜ=~åI=ìã=òìÉêëí=ÇáÉ=ÖÉÖÉÄÉåÉå=a~íÉå=ãáí= k~ãÉ=ìåÇ=tÉêí=òìë~ããÉåòìëíÉääÉåK== „Name“

„Wert“

„Kapital“

K0

„Zinssatz“

p

„Jahre“

T

q~ÄK=^NW=dÉÖÉÄÉåÉ=a~íÉå= aáÉ=q~ÄÉääÉåÑçêã=ÄáÉíÉí=ëáÅÜ=~ÄÉê=~ìÅÜ=~åI=ìã=ãáí=ÉáåÉê=âä~êÉå=póãÄçäáâI=ÇáÉ=ïÉáíÉê=ìåíÉå= ~ääÖÉãÉáå=Ç~êÖÉëíÉääí=ïáêÇI=ÇáÉ=~ìëòìÑΩÜêÉåÇÉå=oÉÅÜÉåëÅÜêáííÉ=ΩÄÉêëáÅÜíäáÅÜ=Ç~êòìëíÉääÉåW== „Jahr“

„Kapital“

t0 ← 0

K0 ← K0

t1 ← t0 +1 .. .

K1 ← K0 (1+p) .. .

tT ← tT-1 +1

KT ← KT-1 (1+p)

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„Kapital“

t0 ← 0

K0 ← K0

ti ← ti-1 +1

Ki ← Ki-1 (1+p)

i=1, … ,T

q~ÄW=^OÄW=sÉêâΩêòíÉë=oÉÅÜÉåëÅÜÉã~=ÑΩê=ÇáÉ=h~éáí~äÉåíïáÅâäìåÖ= wìê=fãéäÉãÉåíáÉêìåÖW=kìå=ëáåÇ=ÇáÉ=sçêÄÉêÉáíìåÖÉå=~ÄÖÉëÅÜäçëëÉåI=ÇáÉ=q~ÄÉääÉå=ÇÉê=a~íÉå= ìåÇ=ÇÉê=îÉêâΩêòíÉå=oÉÅÜÉåëÅÜÉã~í~=â∏ååÉå=áå=bñÅÉäJq~ÄÉääÉEåF=ÉáåÖÉíê~ÖÉå=ïÉêÇÉåK== aáÉëÉê=sçêÖ~åÖ=ïáêÇ=~äë=fãéäÉãÉåíáÉêìåÖ=ÄÉòÉáÅÜåÉíK= aÉê=ÉêëíÉ=pÅÜêáíí=ÇÉê=fãéäÉãÉåíáÉêìåÖ=ëçääíÉ=ïÉáíÉêÜáå=åçÅÜ=~ì≈ÉêÜ~äÄ=îçå=bñÅÉä=ìåÇ=âçåJ òÉåíêáÉêí=ÖÉÇ~åâäáÅÜ=ÉêÑçäÖÉåW==

============================================================ ^åÜ~åÖ=NW=sçã=mêçÄäÉã=òìê=bñÅÉäJi∏ëìåÖ= NTQ aáÉ=q~ÄÉääÉå=^N=ìåÇ=^O~=ÑΩê=ÇáÉ=tÉêíÉ=ìåÇ=ÇáÉ=h~éáí~äÉåíïáÅâäìåÖ=ïÉêÇÉå=ÉêÖ®åòí=ÇìêÅÜ= ÇáÉ= ^ÇêÉëëÉå= ÇÉê= wÉääÉåI= áå= ÇÉåÉå= ÇáÉ= ^ìëÖ~åÖëïÉêíÉ= ÉáåÖÉíê~ÖÉå= ìåÇ= ÇáÉ= oÉÅÜÉåÉêÖÉÄJ åáëëÉ=ÉåíëíÉÜÉå=ëçääÉåW==== A1: „Name“

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B4: T

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E1: „Kapital“

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E3: K1 ← K0 (1+p) .. .

D(T+2): tT ← tT-1 +1

E(T+2): KT ← KT-1 (1+p)

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Wert/Formel/Aktion

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Jahr

E1

Kapital

D2

0

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D4:E17

Paste D3

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2000 5%

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Wert/Formel/Aktion

D3:E17

DeleteUp

PK=c~ääW=aáÉ=a~ìÉê=ÇÉê=^åä~ÖÉ=ÉêÜ∏Üí=ëáÅÜ=~ìÑ=OM=g~ÜêÉK== Bereich

Wert/Formel/Aktion

D18:E22

Paste D17:E17

aáÉ=aáëâìëëáçå=ÉêÑçäÖí=áå=q~ÄÉääÉåÑçêãI=ïçÄÉá=ÇìêÅÜ~ìë=EëáÉÜÉ=ÇÉå=ÇêáííÉå=c~ääF=ÉáåáÖÉ=^âJ íáçåÉå=òìë®íòäáÅÜ=ÜáåòìâçããÉå=â∏ååÉåK== tÉåÇÉå=ïáê=ìåë=åìå=ÖäÉáÅÜ=ÇÉê=cçêã~äáëáÉêìåÖ=òì=Ó=ïÉäÅÜÉ=_ÉÇÉìíìåÖ=Epóåí~ñF=Ü~ÄÉå= ÇáÉ=^âíáçåëîçâ~ÄÉäå=Paste, Delete ìëïK=\== páÉ=ëáåÇ=áå=ÇÉê=ÑçäÖÉåÇÉå=§ÄÉêëáÅÜí=Éêâä®êíW== Aktion

Kommentar

Paste

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Delete [Richtung]

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Move

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Insert [Richtung]

få=ÇÉå=wáÉäÄÉêÉáÅÜ=ïÉêÇÉå=wÉääÉå=ÉáåÖÉÑΩÖíK=fëí=ÇÉê=wáÉäJ ÄÉêÉáÅÜ=åáÅÜí=ÉáåÉ=jÉåÖÉ=îçå=pé~äíÉå=çÇÉê=wÉáäÉåI=ëç=áëí= ÇáÉ=^åÖ~ÄÉ=ÇÉê=oáÅÜíìåÖ=åçíïÉåÇáÖK= Down=ÄÉÇÉìíÉíI=Ç~ëë= ÇáÉ= wÉääÉå= å~ÅÜ= ìåíÉå= îÉêëÅÜçÄÉå= ïÉêÇÉåK= ToRight= ÄÉJ ÇÉìíÉíI=Ç~ëë=ÇáÉ=wÉääÉå=å~ÅÜ=êÉÅÜíë=îÉêëÅÜçÄÉå=ïÉêÇÉåK=

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NTT

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Beispiel

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Zu 4.5: Grafische Darstellung von Pivot-Tabellen (ab Seite 84)

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Zu 5.3: Kumulierte relative Häufigkeiten (ab Seite 98) wì= ÇáÉëÉã= ^ÄëÅÜåáíí= ëáåÇ= âÉáåÉ= ïÉáíÉêÉå= eáåïÉáëÉ= å∏íáÖI= ÇáÉ= ~åÇÉêë~êíáÖÉë= sçêÖÉÜÉå= ÄÉá= bñÅÉä=OMMT=ÄÉëÅÜêÉáÄÉå=ãΩëëíÉåK== táÉ=ëÅÜçå=~ìÑ=pÉáíÉ=NUQ=ãáíÖÉíÉáäíI=ÑáåÇÉå=ëáÅÜ=ÇáÉ=ÄÉáÇÉå=pÅÜ~äíÑä®ÅÜÉå=òìê=pçêíáÉêìåÖ=áã= jÉåΩ= Start=ÇÉê=jìäíáÑìåâíáçåëäÉáëíÉ=áå=ÇÉê=iÉáëíìåÖëÖêìééÉ= Bearbeiten=ìåíÉê= Sortieren und FilternK==

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Zu 9.1: Grundsätzliches (ab Seite 159), zu 9.2: Import aus MS-Access (ab Seite 159), zu 9.3: Einrichtung eines ODBC-Treibers (ab Seite 161), zu 9.4: Zugriff auf konkrete Datenbanken (ab Seite 163) a~=ÇáÉëÉ=îáÉê=^ÄëÅÜåáííÉ=ëáÅÜ=ãáí=ÄÉÖêáÑÑäáÅÜÉå=dêìåÇä~ÖÉå=ìåÇ=cê~ÖÉå=ÇÉë=_ÉíêáÉÄëëóëíÉãë= ÄÉëÅÜ®ÑíáÖÉåI=ëéáÉäí=ÜáÉê=ÇáÉ=cê~ÖÉI=ïÉäÅÜÉ=bñÅÉäJsÉêëáçå=îÉêïÉåÇÉí=ïáêÇI=âÉáåÉ=oçääÉK==

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