Piv txwv ntawm cov lus nug sib tham txog qhov loj ntawm qhov chaw tso kawm
Kev ntsuas qhov chaw yog ib qho tseem ceeb hauv ntau yam kev kawm, tshwj xeeb tshaj yog kev suav lej, kev lag luam, thiab kev tswj hwm. Kev ntsuas qhov chaw suav nrog ntau yam kev ntsuas siv los ntsuas qhov chaw sib piv ntawm cov ntaub ntawv hauv ib qho kev faib tawm, xws li quartiles, deciles, percentiles, thiab lwm yam. Kev nkag siab txog yuav ua li cas ntsuas thiab tshuaj xyuas kev ntsuas qhov chaw yog qhov tseem ceeb rau ntau yam kev tshuaj xyuas cov ntaub ntawv, kev txiav txim siab, thiab kev tshawb fawb.
Hauv tsab xov xwm no, peb yuav tham txog ntau yam teeb meem piv txwv ntsig txog kev ntsuas qhov chaw thiab yuav daws li cas. Cov teeb meem no lub hom phiaj yog kom piav qhia txog lub tswv yim thiab kev siv ntawm kev ntsuas qhov chaw hauv ntau yam xwm txheej.
Piv txwv lus nug 1: Xam cov Quartiles
Lo lus nug:
Muab cov ntaub ntawv hauv qab no: 5, 7, 8, 12, 13, 14, 18, 21, 23, 30. Xam Q1 (thawj quartile), Q2 (median/second quartile), thiab Q3 (third quartile).
Kev daws teeb meem:
Kauj ruam thawj zaug hauv kev xam cov quartiles yog kev txiav txim cov ntaub ntawv los ntawm qhov me tshaj plaws mus rau qhov loj tshaj plaws. Hauv qhov teeb meem no, cov ntaub ntawv twb tau raug xaiv lawm.
-n (tus naj npawb ntawm cov ntaub ntawv) = 10
Xam Q1:
Q1 yog tus nqi uas nyob hauv txoj haujlwm \(\frac{n + 1}{4}\).
\[
Q1 = \frac{10 + 1}{4} = \frac{11}{4} = 2.75
\]
Vim tias cov txiaj ntsig tsis puag ncig, peb siv kev sib txuas ntawm cov ntaub ntawv thib 2 thiab thib 3.
Cov ntaub ntawv thib 2 = 7
Cov ntaub ntawv thib 3 = 8
\[
Q1 = 7 + 0.75 \times (8 – 7) = 7 + 0.75 = 7.75
\]
Xam Q2 (Nruab Nrab):
Q2 yog tus nqi uas nyob hauv nruab nrab. Vim tias n yog tus lej sib npaug, Q2 yog tus nqi nruab nrab ntawm cov nqi hauv qhov chaw thib 5 thiab thib 6.
\[
Q2 = \frac{13 + 14}{2} = \frac{27}{2} = 13.5
\]
Xam Q3:
Q3 yog tus nqi uas nyob hauv txoj haujlwm \(\frac{3(n + 1)}{4}\).
\[
Q3 = \frac{3 \times (10 + 1)}{4} = \frac{33}{4} = 8.25
\]
Peb siv kev sib txuas ntawm cov ntaub ntawv thib 8 thiab thib 9.
Cov ntaub ntawv thib 8 = 21
Cov ntaub ntawv thib 9 = 23
\[
Q3 = 21 + 0.25 \times (23 – 21) = 21 + 0.5 = 21.5
\]
Yog li ntawd, Q1 = 7.75, Q2 = 13.5, thiab Q3 = 21.5.
Piv txwv lus nug 2: Siv cov feem pua
Lo lus nug:
Muab cov ntaub ntawv hauv qab no: 15, 18, 20, 24, 30, 32, 35, 40, 42, 45. Txheeb xyuas tus nqi 70th percentile.
Kev daws teeb meem:
Kauj ruam thawj zaug yog xyuas kom tseeb tias cov ntaub ntawv tau raug xaiv los ntawm qhov me tshaj plaws mus rau qhov loj tshaj plaws, thiab cov ntaub ntawv saum toj no tau raug xaiv.
Tus naj npawb ntawm cov ntaub ntawv, n = 10
Tus lej feem pua 70 txhais tau tias peb tab tom nrhiav tus nqi uas nyob hauv 70% ntawm tag nrho cov ntaub ntawv.
\[
P_{70} = \frac{70}{100} \times (n + 1) = 0.70 \times 11 = 7.7
\]
Vim tias qhov tshwm sim yog tus lej tsis yog integer, peb siv interpolation ntawm cov ntaub ntawv thib 7 thiab thib 8.
Cov ntaub ntawv thib 7 = 35
Cov ntaub ntawv thib 8 = 40
\[
P_{70} = 35 + 0.7 \times (40 – 35) = 35 + 3.5 = 38.5
\]
Yog li, tus nqi 70th feem pua ntawm cov ntaub ntawv yog 38.5.
Piv txwv lus nug 3: Xam Deciles
Lo lus nug:
Muab cov ntaub ntawv tshwm sim ntawm kev xeem hauv qab no: 55, 63, 67, 72, 75, 78, 80, 82, 86, 90. Xam qhov decile thib 4 (D4).
Kev daws teeb meem:
Kauj ruam thawj zaug yog xyuas kom meej tias cov ntaub ntawv tau raug xaiv los ntawm qhov me tshaj plaws mus rau qhov loj tshaj plaws. Cov ntaub ntawv saum toj no twb tau raug xaiv lawm.
Tus naj npawb ntawm cov ntaub ntawv, n = 10
Tus lej plaub txhais tau tias peb tab tom nrhiav tus nqi uas nyob hauv 40% ntawm tag nrho cov ntaub ntawv.
\[
D_4 = \frac{4 \times (n + 1)}{10} = \frac{4 \times 11}{10} = 4.4
\]
Vim tias qhov tshwm sim yog tus lej tsis yog integer, peb siv interpolation ntawm cov ntaub ntawv thib 4 thiab thib 5.
Cov ntaub ntawv thib 4 = 72
Cov ntaub ntawv thib 5 = 75
\[
D_4 = 72 + 0.4 \times (75 – 72) = 72 + 1.2 = 73.2
\]
Yog li, qhov thib 4 decile ntawm cov ntaub ntawv yog 73.2.
Piv txwv lus nug 4: Daim ntawv thov hauv kev faib nyiaj tau los
Lo lus nug:
Ib txoj kev tshawb fawb txog kev lag luam tau sau cov ntaub ntawv txog cov nyiaj tau los txhua hli rau ntau tus neeg raws li nram no: 2000, 2200, 2400, 2500, 2700, 3000, 3200, 3500, 3700, 4000, 4200, 4500, 4700, 5000, 5500. Txheeb xyuas qhov nruab nrab thiab quartiles ntawm cov ntaub ntawv.
Kev daws teeb meem:
Ua ntej, peb xyuas kom meej tias cov ntaub ntawv raug xaiv los ntawm qhov me tshaj plaws mus rau qhov loj tshaj plaws, thiab cov ntaub ntawv saum toj no raug xaiv.
Tus naj npawb ntawm cov ntaub ntawv, n = 15
Xam Tus Nruab Nrab (Q2):
Tus median yog cov ntaub ntawv uas nyob hauv nruab nrab.
\[
\text{Qhov chaw nruab nrab} = \frac{n + 1}{2} = \frac{15 + 1}{2} = 8
\]
Cov ntaub ntawv thib 8 = 3500
Yog li, qhov nruab nrab (Q2) yog 3500.
Xam Q1:
Q1 yog tus nqi uas nyob hauv txoj haujlwm \(\frac{n + 1}{4}\).
\[
Q1 = \frac{15 + 1}{4} = \frac{16}{4} = 4
\]
Cov ntaub ntawv thib 4 = 2500
Yog li, Q1 yog 2500.
Xam Q3:
Q3 yog tus nqi uas nyob hauv txoj haujlwm \(\frac{3(n + 1)}{4}\).
\[
Q3 = \frac{3 \times (15 + 1)}{4} = \frac{3 \times 16}{4} = 12
\]
Cov ntaub ntawv thib 12 = 4500
Yog li, Q3 yog 4500.
Yog li, qhov nruab nrab (Q2) yog 3500, Q1 yog 2500, thiab Q3 yog 4500.
Xaus
Kev ntsuas kev faib tawm yog cov cuab yeej muaj txiaj ntsig zoo heev hauv kev tshuaj xyuas cov ntaub ntawv, pab peb nkag siab thiab txhais cov ntaub ntawv faib tawm. Los ntawm kev siv cov kev ntsuas xws li quartiles, deciles, thiab percentiles, peb tuaj yeem tau txais daim duab meej dua ntawm kev faib tawm thiab cov qauv ntawm cov ntaub ntawv raug tshuaj xyuas. Tsab xov xwm no muab ntau qhov piv txwv teeb meem thiab kev daws teeb meem, vam tias yuav pab cov nyeem ntawv nkag siab yuav ua li cas xam thiab siv cov kev ntsuas kev faib tawm hauv ntau qhov xwm txheej.
