Cov Ntaub Ntawv Ib Leeg Quartile: Kev Nkag Siab tob txog Kev Faib Cov Ntaub Ntawv hauv Kev Txheeb Xyuas
Ib qho ntawm cov tswv yim tseem ceeb hauv kev suav lej yog kev faib cov ntaub ntawv ua quartiles. Quartiles yog siv los nkag siab txog kev faib cov ntaub ntawv kom ntxaws dua li tsuas yog saib ntawm qhov nruab nrab lossis qhov nruab nrab. Hauv tsab xov xwm no, peb yuav tham txog quartiles ntawm ib pawg ntaub ntawv, yuav ua li cas xam lawv, thiab lawv cov ntawv thov hauv ntau yam kev tshuaj xyuas cov ntaub ntawv.
Quartile yog dab tsi?
Cov Quartiles yog cov nqi tshwj xeeb uas faib cov ntaub ntawv txheeb cais ua plaub ntu sib npaug. Hais yooj yim, cov quartiles yog cov pawg ntawm cov ntaub ntawv txheeb cais, nrog txhua lub quartile npog kwv yees li 25% ntawm cov ntaub ntawv.
Cov Quartiles muaj peb lub cim tseem ceeb:
1. Thawj quartile (Q1): faib 25% qis tshaj plaws ntawm cov ntaub ntawv los ntawm lwm qhov.
2. Tus lej thib ob (Q2) lossis Median: faib cov ntaub ntawv ua ob feem sib npaug, 50% ntawm cov ntaub ntawv nyob hauv qab tus nqi no thiab 50% nyob saum tus nqi no.
3. Lub quartile thib peb (Q3): faib 25% ntawm cov ntaub ntawv siab tshaj plaws los ntawm lwm qhov.
Txhua lub quartile ua haujlwm ua tus sawv cev ntawm ib feem ntawm cov ntaub ntawv thiab muaj ntau yam kev siv, los ntawm kev piav qhia cov ntaub ntawv mus rau kev tshuaj xyuas outlier.
Yuav Ua Li Cas Xam Quartiles
Yuav xam cov quartiles, thawj kauj ruam yog txheeb cov ntaub ntawv raws li qhov kev txiav txim siab. Cia peb saib cov kauj ruam ntxaws ntxaws rau kev xam cov quartiles ntawm ib qho dataset:
Kev Cais Cov Ntaub Ntawv
Xav tias peb muaj cov ntaub ntawv hauv qab no:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Kauj ruam thawj zaug yog xyuas kom tseeb tias cov ntaub ntawv raug xaiv:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Kev Txheeb Xyuas Qhov Chaw Quartile
Tom ntej no, peb txiav txim siab qhov chaw quartile. Rau cov ntaub ntawv ntawm qhov loj me \( N \):
– Txoj hauj lwm Q1 = \( \frac{(N+1)}{4} \)
– Txoj hauj lwm Q2 = \( \frac{(N+1)}{2} \)
– Txoj hauj lwm Q3 = \( \frac{3(N+1)}{4} \)
Rau peb cov ntaub ntawv (N = 10):
– Txoj hauj lwm Q1 = \( \frac{(10+1)}{4} = 2.75 \)
– Txoj hauj lwm Q2 = \( \frac{(10+1)}{2} = 5.5 \)
– Txoj hauj lwm Q3 = \( \frac{3(10+1)}{4} = 8.25 \)
Kev Sib Txuas Quartiles
Yog tias qhov chaw quartile yog tus lej decimal, ces peb interpolate ntawm ob tus nqi ntaub ntawv sib ze.
– Q1 (Txoj Haujlwm 2.75):
Muab cov nqi ntawm cov ntaub ntawv tso rau hauv qhov chaw thib 2 `15` thiab qhov chaw thib 3 `36` ua ke.
Q1 = 15 + 0.75 (36 – 15) = 15 + 0.75 21 = 15 + 15.75 = 30.75
– Q2 (Nruab nrab ntawm txoj hauj lwm 5.5):
Muab cov nqi ntawm cov ntaub ntawv tso rau hauv qhov chaw thib 5 `40` thiab qhov chaw thib 6 `41` ua ke.
Q2 = 40 + 0.5 (41 - 40) = 40 + 0.5 1 = 40.5
– Q3 (Txoj Haujlwm 8.25):
Muab cov nqi ntawm cov ntaub ntawv tso rau hauv qhov chaw thib 8 `43` thiab qhov chaw thib 9 `47` ua ke.
Q3 = 43 + 0.25 (47 – 43) = 43 + 0.25 4 = 43 + 1 = 44
Yog li, cov quartiles ntawm peb cov ntaub ntawv yog:
– Q1 = 30.75
– Q2 = 40.5
– Q3 = 44
Daim Ntawv Thov Plaub Ntug
Kev Piav Qhia Txog Kev Txheeb Xyuas
Cov quartiles yog siv ua ib feem ntawm cov lus piav qhia txog kev suav lej los muab kev pom dav dav ntawm kev faib cov ntaub ntawv. Kev paub txog cov quartiles ua rau peb nkag siab zoo dua txog kev sib xws, kev sib npaug, thiab kev kis ntawm cov ntaub ntawv.
Kev Tshawb Fawb Txog Qhov Tsis Zoo
Cov Quartiles kuj tseem muaj txiaj ntsig zoo rau kev txheeb xyuas cov outliers. Outliers yog cov nqi ntawm cov ntaub ntawv uas nyob deb ntawm feem ntau ntawm cov ntaub ntawv teeb tsa. Txhawm rau nrhiav cov outliers, txoj kev "Interquartile Range (IQR)" feem ntau yog siv.
IQR yog xam raws li qhov sib txawv ntawm Q3 thiab Q1:
\[ \text{IQR} = Q3 – Q1 \]
Cov nqi ntawm cov ntaub ntawv raug suav hais tias yog outliers yog tias lawv nyob hauv qab \(Q1-1.5 \times \text{IQR} \) lossis siab dua \(Q3+1.5 \times \text{IQR} \).
Hauv cov ntaub ntawv teev saum toj no:
– IQR = 44 – 30.75 = 13.25
– Qhov txwv qis dua rau cov outliers = Q1 – 1.5 IQR = 30.75 – 1.5 13.25 = 30.75 – 19.875 = 10.875
– Qhov txwv siab tshaj plaws rau cov outliers = Q3 + 1.5 IQR = 44 + 1.5 13.25 = 44 + 19.875 = 63.875
Yog li, cov nqi ntaub ntawv hauv qab 10.875 lossis siab dua 63.875 raug suav hais tias yog outliers. Txij li thaum peb cov ntaub ntawv teeb tsa poob rau hauv qhov ntau ntawd, tsis muaj outliers.
Kev Tswj Xyuas Cov Ntaub Ntawv Nyuaj
Ntxiv rau kev siv rau hauv cov ntaub ntawv yooj yim, cov quartiles kuj tseem siv tau rau cov ntaub ntawv nyuaj dua. Hauv kev tshuaj xyuas nyiaj txiag, piv txwv li, quartiles tuaj yeem pab txheeb xyuas qhov kev ua tau zoo ntawm ib qho khoom lag luam tshwj xeeb hauv kev ua lag luam. Hauv kev kawm, quartiles tuaj yeem siv los txheeb xyuas cov tub ntxhais kawm qhov kev kawm hauv ib qho kev xeem tshwj xeeb.
Lub thawv ntawv
Ib qho cuab yeej siv los ua kom pom kev uas siv cov quartiles yog Box Plot lossis Tukey Box Plot. Ib qho Box Plot muab cov duab kos ntawm tsib qhov tseem ceeb hauv cov ntaub ntawv: tus nqi tsawg kawg nkaus, thawj quartile (Q1), nruab nrab (Q2), thib peb quartile (Q3), thiab tus nqi siab tshaj plaws. Ib txoj hauv kev yooj yim los nrhiav cov outliers yog siv Box Plot, qhov twg cov outliers feem ntau pom tias yog cov ntsiab lus sab nraum "whiskers" (cov kab ntxoov ntxoo ntawm qhov tsawg kawg nkaus, Q1, Q3, thiab siab tshaj plaws).
Xaus
Kev suav thiab nkag siab txog cov quartiles hauv ib qho dataset muab kev nkag siab tob dua txog cov qauv ntaub ntawv, nws qhov kev faib tawm, thiab qhov muaj lossis tsis muaj cov outliers. Thoob plaws ntau yam kev siv, los ntawm cov lus piav qhia yooj yim mus rau kev tshuaj xyuas nyuaj dua xws li kev tshawb pom outlier thiab kev siv cov phiaj xwm thawv, quartiles ua lub luag haujlwm tseem ceeb hauv kev tshuaj xyuas cov ntaub ntawv thiab kev txhais lus. Nrog rau cov cuab yeej no, kev tshuaj xyuas cov ntaub ntawv dhau los ua qhov system thiab muaj txiaj ntsig ntau dua, paving txoj hauv kev rau kev nkag siab tob dua thiab kev tshawb pom muaj txiaj ntsig ntau dua hauv ntau qhov kev kawm. Quartiles tsis yog tsuas yog pab txhawb cov lus piav qhia txog kev suav lej xwb tab sis kuj muab cov kev nkag siab tseem ceeb rau kev txiav txim siab los ntawm cov ntaub ntawv.
Kev nkag siab zoo txog cov quartiles thiab lawv siv li cas hauv kev tshuaj xyuas cov ntaub ntawv yog ib qho kev txawj ntse uas tuaj yeem siv tau rau ntau yam kev coj ua, los ntawm kev tshawb fawb mus rau kev lag luam, ua rau peb ntse dua ntawm kev tshuaj xyuas thiab txhais cov ntaub ntawv.
