Piv txwv cov lus nug thiab kev sib tham txog Single Data Quartiles
Cov Quartiles hauv kev suav lej yog ib lub cuab yeej siv los faib cov ntaub ntawv ua plaub ntu, lossis quartiles, txhua tus muaj cov ntaub ntawv tib yam. Quartiles feem ntau siv los nkag siab txog kev faib cov ntaub ntawv thiab sib piv cov nqi hauv cov ntaub ntawv loj dua. Hauv tsab xov xwm no, peb yuav tham txog yuav ua li cas xam cov quartiles rau ib qho ntaub ntawv siv ntau qhov piv txwv. Peb yuav pom tias thawj quartile (Q1), thib ob quartile (Q2, tseem hu ua median), thiab thib peb quartile (Q3) raug suav thiab txhais li cas.
Kev txhais ntawm Quartile
Ua ntej yuav mus rau cov teeb meem piv txwv, nws yog ib qho tseem ceeb kom nkag siab txog cov lus txhais ntawm peb lub quartiles hauv cov ntaub ntawv teeb tsa:
1. Thawj Quartile (Q1): Cov ntaub ntawv hauv qab Q1 npog 25% ntawm cov ntaub ntawv los ntawm tag nrho cov ntaub ntawv teeb tsa.
2. Thib Ob Quartile (Q2 lossis Median): Cov chaw ntawm cov ntaub ntawv hauv qab Q2 npog 50% ntawm cov ntaub ntawv los ntawm tag nrho cov ntaub ntawv teeb tsa.
3. Peb Lub Quartile (Q3): Cov ntaub ntawv hauv qab Q3 npog 75% ntawm cov ntaub ntawv los ntawm tag nrho cov ntaub ntawv teeb tsa.
Cov Kauj Ruam Los Xam Cov Quartiles
Yuav kom xam tau cov quartiles, cov kauj ruam yuav tsum ua raws li muaj xws li:
1. Cais Cov Ntaub Ntawv: Xyuas kom tseeb tias cov ntaub ntawv raug cais los ntawm qhov me tshaj plaws mus rau qhov loj tshaj plaws.
2. Txheeb xyuas qhov chaw Quartile: Siv cov mis los txiav txim siab qhov chaw quartile.
– Q1 txoj hauj lwm = (N+1) / 4
– Q2 txoj hauj lwm = (N+1) / 2
– Q3 txoj hauj lwm = 3(N+1) / 4
Qhov twg N yog tag nrho cov ntaub ntawv.
3. Kev Siv Cov Nqi Quartile: Raws li cov chaw xam tau, siv lossis interpolate cov nqi quartile.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Piv txwv lus nug 1
Xav tias muaj cov ntaub ntawv hauv qab no: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29.
Kauj Ruam 1: Kev Cais Cov Ntaub Ntawv
Cov ntaub ntawv raug xaiv: 5, 7, 8, 12, 13, 14, 18, 21, 23, 29
Kauj Ruam 2: Txheeb xyuas qhov chaw ntawm cov quartiles
Tus naj npawb ntawm cov ntaub ntawv (N) yog 10.
– Txoj Haujlwm Q1 = (10+1) / 4 = 11 / 4 = 2.75
– Txoj Haujlwm Q2 = (10+1) / 2 = 11 / 2 = 5.5
– Txoj Haujlwm Q3 = 3(10+1) / 4 = 33 / 4 = 8.25
Kauj Ruam 3: Siv Cov Nqi Quartile
– Q1: Qhov chaw 2.75 qhia tias Q1 nyob nruab nrab ntawm cov ntaub ntawv thib 2 thiab thib 3 hauv kab zauv. Cov ntaub ntawv thib 2 yog 7 thiab cov ntaub ntawv thib 3 yog 8. Yog li ntawd, Q1 = 7 + 0.75(8-7) = 7.75.
– Q2 (Nruab Nrab): Txoj hauj lwm 5.5 qhia tias Q2 nyob nruab nrab ntawm cov ntaub ntawv thib 5 thiab thib 6. Cov ntaub ntawv thib 5 yog 13 thiab cov ntaub ntawv thib 6 yog 14. Yog li, Q2 = 13 + 0.5(14-13) = 13.5.
– Q3: Txoj hauj lwm 8.25 qhia tias Q3 nyob nruab nrab ntawm cov ntaub ntawv thib 8 thiab thib 9. Cov ntaub ntawv thib 8 yog 21 thiab cov ntaub ntawv thib 9 yog 23. Yog li, Q3 = 21 + 0.25(23-21) = 21.5.
Piv txwv lus nug 2
Cov ntaub ntawv hauv qab no tau muab: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
Kauj Ruam 1: Kev Cais Cov Ntaub Ntawv
Cov ntaub ntawv raug xaiv: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
Kauj Ruam 2: Txheeb xyuas qhov chaw ntawm cov quartiles
Tus naj npawb ntawm cov ntaub ntawv (N) yog 11.
– Txoj Haujlwm Q1 = (11+1) / 4 = 12 / 4 = 3
– Txoj Haujlwm Q2 = (11+1) / 2 = 12 / 2 = 6
– Txoj Haujlwm Q3 = 3(11+1) / 4 = 36 / 4 = 9
Kauj Ruam 3: Siv Cov Nqi Quartile
– Q1: Txoj hauj lwm 3 txhais tau tias Q1 yog cov ntaub ntawv thib 3. Yog li Q1 = 6.
– Q2 (Median): Txoj hauj lwm 6 txhais tau tias Q2 yog cov ntaub ntawv thib 6. Yog li Q2 = 12.
– Q3: Txoj hauj lwm 9 txhais tau tias Q3 yog cov ntaub ntawv thib 9. Yog li Q3 = 18.
Txhais Quartiles
Thaum tau txais cov nqi ntawm Q1, Q2, thiab Q3, peb tuaj yeem siv lawv los tshuaj xyuas cov ntaub ntawv. Piv txwv li:
1. Interquartile Range (IQR): Yog qhov sib txawv ntawm Q3 thiab Q1. IQR = Q3 – Q1. IQR yog siv los txheeb xyuas cov ntaub ntawv faib tawm thiab nrhiav cov outliers.
2. Cov yam tsis zoo: Cov ntaub ntawv uas nyob deb ntawm lwm cov ntaub ntawv tuaj yeem txheeb xyuas tau los ntawm kev siv cov kev txwv qis dua thiab siab dua.
– Qhov txwv qis dua = Q1 – 1.5 IQR
– Qhov txwv siab tshaj = Q3 + 1.5 IQR
Cov ntaub ntawv uas poob sab nraum cov ciam teb no suav tias yog cov ntaub ntawv outlier.
Kev siv IQR hauv Piv txwv lus nug 1
– IQR = Q3 – Q1 = 21.5 – 7.75 = 13.75
– Qhov txwv qis dua = 7.75 – 1.5(13.75) = 7.75 – 20.625 = -12.875
– Qhov txwv siab tshaj = 21.5 + 1.5(13.75) = 21.5 + 20.625 = 42.125
Cov ntaub ntawv -12.875 txog 42.125 yog kev faib tawm ib txwm tsis muaj outliers hauv piv txwv lo lus nug 1.
Kev siv IQR hauv Piv txwv lus nug 2
– IQR = Q3 – Q1 = 18 – 6 = 12
– Qhov txwv qis dua = 6 – 1.5(12) = 6 – 18 = -12
– Qhov txwv siab tshaj = 18 + 1.5(12) = 18 + 18 = 36
Cov ntaub ntawv -12 txog 36 yog kev faib tawm ib txwm tsis muaj outliers hauv piv txwv lo lus nug 2.
Xaus
Kev nkag siab thiab xam cov quartiles pab txheeb xyuas cov ntaub ntawv faib tawm thiab tshuaj xyuas ntau yam ntawm kev faib tawm cov ntaub ntawv. Hauv tsab xov xwm no, peb yuav tshawb nrhiav cov kauj ruam koom nrog hauv kev xam cov quartiles rau ib qho ntaub ntawv teeb tsa los ntawm ntau qhov teeb meem piv txwv thiab lawv cov kev sib tham. Cov kauj ruam no suav nrog kev txheeb xyuas cov ntaub ntawv, txiav txim siab qhov chaw ntawm cov quartiles, thiab xam cov nqi quartile tsim nyog. Thaum siv kom raug, quartiles dhau los ua ib qho cuab yeej tseem ceeb hauv kev txheeb cais rau kev nkag siab tob dua ntawm cov ntaub ntawv teeb tsa.
