Central Tendency vs Dispersion
Hauv kev piav qhia thiab kev txheeb xyuas tsis txaus ntseeg, ntau qhov ntsuas tau siv los piav qhia cov ntaub ntawv sib txuas nrog nws lub hauv paus nyiam, dispersion, thiab skewness: peb qhov tseem ceeb tshaj plaws uas txiav txim siab tus txheeb ze ntawm cov ntaub ntawv faib tawm.
Dab tsi yog qhov kev xav hauv nruab nrab?
Central tendency hais txog thiab nrhiav qhov chaw nruab nrab ntawm kev faib cov txiaj ntsig. Lub ntsiab lus, hom, thiab nruab nrab yog cov feem ntau siv indices los piav txog lub hauv paus nyiam ntawm cov ntaub ntawv teev. Yog hais tias cov ntaub ntawv teev yog symmetric, ces ob qho tib si nruab nrab thiab qhov nruab nrab ntawm cov ntaub ntawv teev coincide nrog ib leeg.
Muab cov ntaub ntawv teev tseg, qhov nruab nrab yog xam los ntawm kev noj cov lej ntawm tag nrho cov ntaub ntawv muaj nuj nqis thiab muab faib los ntawm tus lej ntawm cov ntaub ntawv. Piv txwv li, qhov hnyav ntawm 10 tus neeg (hauv kilograms) ntsuas yog 70, 62, 65, 72, 80, 70, 63, 72, 77 thiab 79. Ces qhov hnyav nruab nrab ntawm kaum tus neeg (hauv kilograms) tuaj yeem ua tau. xam raws li nram no. Qhov sib npaug ntawm qhov hnyav yog 70 + 62 + 65 + 72 + 80 + 70 + 63 + 72 + 77 + 79=710. Mean=(sum) / (ntau cov ntaub ntawv)=710 / 10=71 (hauv kilograms). Nws yog to taub hais tias outliers (cov ntaub ntawv cov ntsiab lus uas deviate los ntawm ib txwm zoo) yuav muaj feem xyuam rau qhov txhais tau tias. Yog li, nyob rau hauv lub xub ntiag ntawm outliers txhais tau tias ib leeg yuav tsis muab ib daim duab tseeb txog qhov chaw ntawm cov ntaub ntawv teev.
Qhov nruab nrab yog cov ntaub ntawv taw qhia pom ntawm qhov nruab nrab ntawm cov ntaub ntawv teev tseg. Ib txoj hauv kev los suav qhov nruab nrab yog xaj cov ntaub ntawv cov ntsiab lus hauv kev nce qib, thiab tom qab ntawd nrhiav cov ntaub ntawv taw qhia hauv nruab nrab. Piv txwv li, yog tias ib zaug xaj cov ntaub ntawv dhau los zoo li, 62, 63, 65, 70, 70, 72, 72, 77, 79, 80. Yog li ntawd, (70 + 72) / 2=71 yog nyob nruab nrab. Los ntawm qhov no, nws pom tau tias qhov nruab nrab yuav tsum tsis txhob muaj nyob rau hauv cov ntaub ntawv teev. Qhov nruab nrab tsis cuam tshuam los ntawm qhov pom ntawm cov outliers. Yog li ntawd, qhov nruab nrab yuav ua tau zoo dua qhov kev ntsuas ntawm lub hauv paus nyiam nyob rau hauv lub xub ntiag ntawm outliers.
hom yog tus nqi tshwm sim ntau tshaj plaws hauv cov ntaub ntawv. Hauv qhov piv txwv dhau los, tus nqi 70 thiab 72 ob qho tib si tshwm sim ob zaug thiab yog li, ob qho tib si yog hom. Qhov no qhia tau hais tias, hauv qee qhov kev faib khoom, muaj ntau tshaj li ib qho qauv nqi. Yog tias tsuas muaj ib hom, cov ntaub ntawv teev tau hais tias yog unimodal, qhov no, cov ntaub ntawv teev yog bimodal.
Dab tsi yog kev tawg?
Dispersion yog tus nqi sib kis ntawm cov ntaub ntawv hais txog qhov chaw ntawm kev faib tawm. Kev sib txawv thiab tus qauv sib txawv yog qhov kev ntsuas feem ntau siv ntawm kev tawg.
Qhov ntau tsuas yog tus nqi siab tshaj tawm tus nqi qis tshaj. Hauv qhov piv txwv yav dhau los, tus nqi siab tshaj plaws yog 80 thiab tus nqi qis tshaj yog 62, yog li qhov ntau yog 80-62=18. Tab sis ntau yam tsis muab ib daim duab txaus txog qhov dispersion.
Yuav xam tus qauv sib txawv, thawj qhov sib txawv ntawm cov ntaub ntawv muaj nuj nqis los ntawm qhov nruab nrab yog xam. Lub hauv paus square txhais tau tias ntawm deviations yog hu ua tus qauv sib txawv. Hauv qhov piv txwv dhau los, qhov sib txawv ntawm qhov nruab nrab yog (70 - 71)=-1, (62 - 71)=-9, (65 - 71)=-6, (72 - 71)=1, (80 - 71)=9, (70–71)=-1, (63–71)=-8, (72–71)=1, (77–71)=6 thiab (79–71)=8. squares of deviation is (-1)2 + (-9)2 + (-6)2 +12 + 92 + (-1)2 + (-8) 2 + 12 + 62 + 82=366 Tus qauv sib txawv yog √(366/10)=6.05 (hauv kilograms). Tshwj tsis yog tias cov ntaub ntawv teeb tsa tau zoo heev, los ntawm qhov no nws tuaj yeem txiav txim siab tias feem ntau ntawm cov ntaub ntawv yog nyob rau lub sijhawm 71 ± 6.05, thiab nws yog qhov tseeb hauv qhov piv txwv no.
Dab tsi yog qhov txawv ntawm qhov nruab nrab nyiam thiab tawg?
• Central nyiam yog hais txog thiab nrhiav qhov chaw nruab nrab ntawm kev faib cov txiaj ntsig
• Dispersion yog qhov sib kis ntawm cov ntaub ntawv hais txog qhov nruab nrab ntawm cov ntaub ntawv teev.
