Standard Deviation vs Mean
Hauv kev piav qhia thiab kev txheeb xyuas tsis txaus ntseeg, ntau qhov ntsuas tau siv los piav qhia cov ntaub ntawv teeb tsa sib raug rau nws qhov nruab nrab nyiam, tawg thiab skewness. Hauv kev txheeb cais, cov no feem ntau hu ua tus kwv yees txij li lawv kwv yees tus naj npawb ntawm cov pejxeem.
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. Dispersion yog tus nqi ntawm kev sib kis ntawm cov ntaub ntawv los ntawm qhov chaw ntawm kev faib khoom. Qhov sib txawv thiab tus qauv sib txawv yog cov kev ntsuas feem ntau siv ntawm dispersion. Pearson's skewness coefficients yog siv los piav txog qhov skewness ntawm kev faib cov ntaub ntawv. Ntawm no, skewness yog hais txog seb cov ntaub ntawv teev yog sib npaug ntawm qhov chaw los yog tsis thiab yog tias tsis yog nws skewed li cas.
txhais li cas?
Mean yog qhov feem ntau siv qhov ntsuas ntawm lub hauv paus nyiam. Muab cov ntaub ntawv teev cov ntsiab lus 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. Luas=70 + 62 + 65 + 72 + 80 + 70 + 63 + 72 + 77 + 79=710. Mean=(sum) / (number of data)=710 / 10=71 (in kilograms).
Raws li hauv qhov piv txwv no, tus nqi nruab nrab ntawm cov ntaub ntawv teeb tsa yuav tsis yog cov ntaub ntawv ntawm cov teeb tab sis yuav yog qhov tshwj xeeb rau cov ntaub ntawv muab. Txhais tau tias yuav muaj tib chav nyob raws li cov ntaub ntawv qub. Yog li ntawd, nws tuaj yeem raug cim rau ntawm tib axis raws li cov ntaub ntawv thiab tuaj yeem siv rau hauv kev sib piv. Tsis tas li ntawd, tsis muaj kev txwv kos npe rau lub ntsiab lus ntawm cov ntaub ntawv teev. Nws yuav yog qhov tsis zoo, xoom lossis qhov zoo, vim tias cov lej ntawm cov ntaub ntawv teeb tsa tuaj yeem yog qhov tsis zoo, xoom lossis zoo.
Dab tsi yog tus qauv sib txawv?
qauv sib txawv yog qhov feem ntau siv qhov ntsuas ntawm kev tawg. Txhawm rau 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. Tus lej ntawm qhov sib txawv ntawm qhov sib txawv yog (-1)2+ (-9)2+ (-6)2+ 1 2+92+ (-1)2+ (-8)2 + 12+ 62 + 82=366. Tus qauv sib txawv yog √(366/10)=6.05 (kg). Los ntawm qhov no, nws tuaj yeem xaus lus tias feem ntau ntawm cov ntaub ntawv yog nyob rau lub sijhawm 71 ± 6.05, muab cov ntaub ntawv teev tsis zoo heev skewed, thiab nws yog tiag tiag li nyob rau hauv no xyov piv txwv.
Vim qhov kev sib txawv ntawm tus qauv muaj tib yam li cov ntaub ntawv qub, nws muab peb qhov ntsuas ntawm qhov sib txawv ntawm cov ntaub ntawv los ntawm qhov chaw; ntau dua tus qauv sib txawv ntau dua qhov dispersion. Tsis tas li ntawd, tus qauv sib txawv yuav yog qhov tsis muaj txiaj ntsig txawm hais tias qhov xwm txheej ntawm cov ntaub ntawv hauv cov ntaub ntawv teev.
Qhov sib txawv ntawm tus qauv sib txawv thiab txhais li cas?
• Standard deviation yog ib qho kev ntsuas ntawm dispersion ntawm qhov chaw, whereas txhais tau tias ntsuas qhov chaw ntawm qhov chaw ntawm cov ntaub ntawv teev.
• Standard deviation yog ib txwm ib tug nonnegative tus nqi, tab sis txhais tau tias yuav coj tus nqi tiag tiag.
