Mean vs Median vs Hom
Mean, qhov nruab nrab, thiab hom yog qhov kev ntsuas tseem ceeb ntawm lub hauv paus nyiam siv hauv kev piav qhia txheeb cais. Lawv sib txawv kiag li thiab cov xwm txheej uas lawv siv los sau cov ntaub ntawv kuj txawv.
Mean
Tus lej lej yog cov lej ntawm cov ntaub ntawv muaj txiaj ntsig muab faib los ntawm tus lej ntawm cov ntaub ntawv muaj nuj nqis, piv txwv li
[latex]\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{x_{1}+x_{2} +x_{3}+…+x_{n}}{n}[/latex]
Yog tias cov ntaub ntawv yog los ntawm qhov chaw piv txwv nws hu ua tus qauv txhais tau tias ([latex]\bar{x} [/latex]), uas yog ib qho kev piav qhia ntawm cov qauv. Txawm hais tias nws yog qhov kev piav qhia feem ntau siv rau cov qauv, nws tsis yog ib qho kev txheeb xyuas zoo. Nws yog rhiab heev rau cov outliers thiab oscillations.
Piv txwv li, xav txog cov nyiaj tau los nruab nrab ntawm cov pej xeem ntawm ib lub nroog. Txij li thaum tag nrho cov ntaub ntawv muaj nuj nqis yog summed thiab muab faib, cov nyiaj khwv tau los ntawm ib tug neeg nplua nuj heev cuam tshuam rau lub ntsiab lus tseem ceeb. Yog li ntawd, tus nqi nruab nrab tsis yog tus sawv cev zoo ntawm cov ntaub ntawv ib txwm.
Tsis tas li, nyob rau hauv rooj plaub ntawm kev hloov pauv, qhov tam sim no dhau los ntawm lub caij nyoog hloov pauv ntawm qhov kev taw qhia zoo mus rau qhov tsis zoo thiab rov ua dua. Yog tias peb coj qhov nruab nrab tam sim no dhau los ntawm lub caij hauv ib lub sijhawm, nws yuav muab 0, txhais tau tias tsis muaj tam sim no dhau los ntawm lub caij, uas pom tseeb tsis muaj tseeb. Yog li ntawd, nyob rau hauv cov ntaub ntawv no ib yam nkaus thiab, tus lej lej tsis yog ib qho kev ntsuas zoo.
Tus lej lej yog qhov qhia tau zoo thaum cov ntaub ntawv raug faib sib npaug. Rau ib txwm faib, qhov nruab nrab yog sib npaug rau hom thiab nruab nrab. Nws kuj muaj qhov seem qis tshaj plaws thaum xav txog lub hauv paus txhais tau tias qhov yuam kev squared; yog li ntawd, qhov kev piav qhia zoo tshaj plaws thaum nws yuav tsum tau sawv cev rau cov ntaub ntawv los ntawm ib tus lej.
Median
Qhov tseem ceeb ntawm qhov nruab nrab cov ntaub ntawv taw qhia tom qab npaj tag nrho cov ntaub ntawv tseem ceeb hauv kev txiav txim siab nce mus yog txhais tau tias yog qhov nruab nrab ntawm cov ntaub ntawv. Qhov nruab nrab yog 2nd quartile, 5th decile thiab 50 feem pua.
• Yog tias tus naj npawb ntawm kev soj ntsuam (cov ntsiab lus cov ntsiab lus) yog khib, ces qhov nruab nrab yog qhov kev soj ntsuam raws nraim hauv nruab nrab ntawm daim ntawv xaj.
• Yog tias tus naj npawb ntawm kev soj ntsuam (cov ntaub ntawv cov ntsiab lus) yog, ces qhov nruab nrab yog qhov nruab nrab ntawm ob qhov kev soj ntsuam nruab nrab hauv daim ntawv xaj.
Median faib qhov kev soj ntsuam ua ob pawg; i.e. ib pab pawg (50%) ntawm qhov muaj nuj nqis siab dua thiab ib pab pawg (50%) ntawm cov nqi qis dua qhov nruab nrab. Cov neeg nruab nrab yog siv tshwj xeeb hauv kev faib tawm skewed thiab sawv cev rau cov ntaub ntawv zoo dua li tus lej lej.
Mode
Mode yog tus lej tshwm sim ntau tshaj plaws hauv cov kev soj ntsuam. Hom ntawm Cov Ntaub Ntawv Teeb yog xam los ntawm kev nrhiav qhov zaus ntawm txhua lub hauv paus hauv qhov teeb tsa.
• Yog tias tsis muaj nqi tshwm sim ntau dua ib zaug, ces cov ntaub ntawv teev tsis muaj hom.
• Txwv tsis pub, txhua tus nqi uas tshwm sim nrog ntau zaus yog hom ntawm cov ntaub ntawv teev.
Ntau tshaj 1 hom tuaj yeem muaj nyob hauv ib txheej; yog li ntawd, hom tsis yog ib qho kev txheeb cais tshwj xeeb ntawm cov ntaub ntawv. Nyob rau hauv ib qho kev faib tawm, muaj ib hom. Hom ntawm qhov kev faib tawm qhov tshwm sim tsis sib xws yog qhov chaw uas qhov tshwm sim loj ua haujlwm mus txog nws qhov siab tshaj plaws. Raws li kev txhais lus saum toj no, peb tuaj yeem hais tias lub ntiaj teb maxima yog hom.
Xav txog daim ntawv thov ntawm peb qhov kev ntsuas rau cov ntaub ntawv hauv qab no.
DATA: {1, 1, 2, 3, 5, 5, 5, 5, 6, 6, 8, 8, 9, 9, 9, 9, 10, 10, 10, 14, 14, 15, 15, 15}
Mean=(1+ 1+ 2+ 3+ 5+ 5+ 5+ 5+ 5+ 6+ 6+ 8+ 8+ 9+ 9+ 9+ 9+ 10+ 10+ 10+ 14+ 14+ 15+ 15+ 15) / 25=8.12
Median=9 (13th element)
Mode=9 (frequency of 9=5)
Qhov txawv ntawm Mean, Median thiab Hom yog dab tsi?
• Arithmetic mean yog tus lej ntawm qhov tseem ceeb (kev soj ntsuam) muab faib los ntawm tus lej ntawm kev soj ntsuam. Nws tsis yog ib qho kev txheeb xyuas ruaj khov, thiab hnyav heev nyob ntawm qhov kev faib tawm ib txwm nyob hauv qhov kev faib tawm. Ib qho outlier tuaj yeem ua rau muaj kev hloov pauv tseem ceeb hauv qhov txhais tau tias muab cov txiaj ntsig tsis tseeb. Lub tswv yim tuaj yeem txuas ntxiv mus rau qhov ntsuas geometric, lub ntsiab lus sib haum xeeb, qhov ntsuas qhov hnyav thiab lwm yam.
• Median yog qhov tseem ceeb nruab nrab ntawm cov txheej txheem kev soj ntsuam, thiab nws tsis tshua muaj kev cuam tshuam los ntawm cov outliers. Nws tuaj yeem muab qhov kev kwv yees zoo raws li cov ntaub ntawv sau tseg hauv cov xwm txheej tsis txaus ntseeg.
• hom yog qhov kev soj ntsuam ntau tshaj plaws hauv cov ntaub ntawv. Yog tias qhov kev faib tawm yog qhov zoo skewed, hom yog sab laug mus rau qhov nruab nrab thiab, yog tias tsis zoo skewed, hom lies rau qhov nruab nrab.
• Yog hais tias zoo skewed, txhais tau tias yog txoj cai rau nruab nrab; yog hais tias tsis zoo skewed txhais tau tias yog rau sab laug ntawm qhov nruab nrab.
• Nyob rau hauv ib txwm faib, tag nrho peb, txhais tau tias, hom thiab nruab nrab yog sib npaug.
