Feem pua ntawm Cov Ntaub Ntawv Pab Pawg: Kev Nkag Siab thiab Kev Siv
Kev ua cov ntaub ntawv suav lej yog ib qho tseem ceeb ntawm kev tshuaj xyuas cov ntaub ntawv, siv dav hauv ntau qhov chaw xws li kev lag luam, kev nyiaj txiag, kev noj qab haus huv, thiab kev sib raug zoo hauv zej zog. Ib lub tswv yim feem ntau siv hauv kev tshuaj xyuas cov ntaub ntawv yog feem pua. Feem pua yog tus nqi uas faib cov ntaub ntawv ua ib puas feem sib npaug. Hauv cov ntsiab lus ntawm cov ntaub ntawv sib sau ua pawg, kev nkag siab thiab kev xam cov feem pua yuav nyuaj dua li cov ntaub ntawv ib leeg lossis tsis muaj pawg. Tsab xov xwm no lub hom phiaj yog los tshawb nrhiav lub tswv yim ntawm feem pua hauv cov ntaub ntawv sib sau ua pawg, yuav ua li cas xam lawv, thiab lawv daim ntawv thov hauv kev tshuaj xyuas cov ntaub ntawv.
Nkag Siab Txog Feem Pua
Hais yooj yim xwb, feem pua yog ib txoj kev ntsuas siv hauv kev suav lej los txiav txim qhov chaw sib piv ntawm tus nqi hauv cov ntaub ntawv teeb tsa. Piv txwv li, 25th feem pua (P25) yog tus nqi hauv qab uas 25% ntawm cov ntaub ntawv poob. Hauv lwm lo lus, 75% ntawm cov ntaub ntawv yuav poob siab dua tus nqi no. Ib yam li ntawd, 50th feem pua (median) thiab 75th feem pua yog siv.
Cov feem pua txawv ntawm quartiles thiab deciles tsuas yog nyob rau hauv tus naj npawb ntawm cov khoom uas lawv tsim tawm: quartiles faib cov ntaub ntawv ua plaub feem, deciles ua kaum feem, thiab percentiles ua ib puas feem.
Cov Ntaub Ntawv Pab Pawg
Cov ntaub ntawv ua pawg, lossis cov ntaub ntawv sib sau ua pawg, yog cov ntaub ntawv uas tau muab faib ua pawg lossis pawg. Hauv cov ntaub ntawv sib sau ua pawg, cov nqi ntawm cov ntaub ntawv tsis raug saib ib tus zuj zus lawm, tab sis ua pawg. Qhov no feem ntau ua nrog cov ntaub ntawv lej nrog ntau tus neeg soj ntsuam los pab txhawb kev txhais lus thiab kev tshuaj xyuas. Piv txwv ntawm cov ntaub ntawv sib sau ua pawg suav nrog cov hnub nyoog, cov nyiaj tau los, lossis cov qhab nia xeem sib sau ua pawg.
Xam Cov Feem Pua Hauv Cov Ntaub Ntawv Uas Muab Ua Pawg
Kev suav cov feem pua ntawm cov ntaub ntawv uas tau muab faib ua pawg yuav tsum muaj cov qauv sib txawv dua li cov ntaub ntawv uas tsis tau muab faib ua pawg vim tias cov ntaub ntawv tau teeb tsa hauv kev faib zaus. Cov kauj ruam hauv qab no piav qhia txog cov txheej txheem suav:
1. Kev Txheeb Xyuas Cov Kev Txwv ntawm Chav Kawm thiab Qhov Zaus Sib Sau Ua Ke
Kauj ruam thawj zaug yog txiav txim siab txog cov ciam teb ntawm chav kawm thiab cov zaus sib sau ua ke. Cov ciam teb ntawm chav kawm yog cov lej uas txhais txhua lub sijhawm (chav kawm) hauv kev faib cov ntaub ntawv. Cov zaus sib sau ua ke yog qhov sib sau ua ke ntawm cov zaus ntawm txhua chav kawm, txij li chav kawm thawj zaug mus rau ib chav kawm tshwj xeeb.
2. Txheeb Xyuas Qhov Feem Pua
Yuav kom nrhiav tau qhov chaw ntawm qhov feem pua ntawm \( P_k \), peb yuav tsum xub txiav txim siab qhov chaw ntawm chav kawm feem pua ntawd. Qhov kth feem pua hais txog tus nqi hauv qab uas \( k% \) ntawm cov ntaub ntawv nyob.
Qhov chaw kth feem pua yog: \( \frac{k}{100} \times N \)
qhov twg \( N \) yog tag nrho cov kev soj ntsuam.
3. Txheeb xyuas cov chav kawm feem pua
Siv cov feem pua uas tau xam los, peb tuaj yeem txheeb xyuas qhov nruab nrab lossis chav kawm uas muaj lawv. Qhov no ua tiav los ntawm kev maj mam saib cov zaus sib sau ua ke ntawm cov chav kawm kom txog thaum peb pom chav kawm uas qhov feem pua nyob.
4. Xam Cov Nqi Feem Pua
Thaum pom cov chav kawm feem pua, peb tuaj yeem siv cov qauv hauv qab no los xam tus nqi feem pua:
\[ P_k = L + \left( \frac{\frac{k}{100} \times N – F}{f} \right) \times i \]
Qhov twg:
– \( P_k \) = kth feem pua uas nrhiav
– \( L \) = qhov txwv qis dua ntawm chav kawm feem pua
– \( F \) = zaus sib sau ua ke ua ntej chav kawm feem pua
– \( f \) = feem pua ntawm chav kawm zaus
– \( i \) = lub sijhawm kawm
Piv txwv ntawm kev suav feem pua
Cia peb saib ib qho piv txwv kom yooj yim to taub:
Xav tias peb muaj cov ntaub ntawv qhab nia xeem rau 100 tus tub ntxhais kawm uas tau muab faib ua pawg raws li nram no:
| Lub Sijhawm Qhab Nia | Zaus |
|——————|———–|
| 0 – 10 | 5 |
| 10 – 20 | 10 |
| 20 – 30 | 20 |
| 30 – 40 | 25 |
| 40 – 50 | 20 |
| 50 – 60 | 10 |
| 60 – 70 | 5 |
Kauj ruam thawj zaug yog xam qhov zaus sib sau ua ke:
| Lub Sijhawm Qhab Nia | Zaus | Zaus Sib Sau Ua Ke |
|——————|————–|—————————|
| 0 – 10 | 5 | 5 |
| 10 – 20 | 10 | 15 |
| 20 – 30 | 20 | 35 |
| 30 – 40 | 25 | 60 |
| 40 – 50 | 20 | 80 |
| 50 – 60 | 10 | 90 |
| 60 – 70 | 5 | 95 |
Xav tias peb xav nrhiav qhov feem pua ntawm 75th (P75):
1. Txheeb xyuas qhov chaw P75:
\[ \text{Txoj Haujlwm P75} = \frac{75}{100} \times 100 = 75 \]
2. Txheeb xyuas pawg uas muaj qhov chaw 75. Los ntawm cov lus qhia txog zaus sib sau ua ke, peb pom tias qhov chaw 75 nyob rau hauv qhov qhab nia nruab nrab 40-50.
3. Xam tus nqi P75 siv cov mis uas tau muab:
\[
P_{75} = 40 + \sab laug ( \frac{75 – 60}{20} \sab xis) \times 10
\]
\[
P_{75} = 40 + \sab laug (\frac{15}{20} \sab xis) \times 10
\]
\[
P_{75} = 40 + 7.5 = 47.5
\]
Yog li, qhov qhab nia uas ciam teb qis tshaj 75% hauv kev faib cov ntaub ntawv no yog 47,5.
Kev Siv Cov Feem Pua Hauv Cov Ntaub Ntawv Pab Pawg
Kev siv cov feem pua hauv cov ntaub ntawv pab pawg neeg muaj txiaj ntsig zoo rau ntau yam xwm txheej ntawm kev tshuaj xyuas cov ntaub ntawv, suav nrog:
1. Kev Ntsuam Xyuas Kev Ua Tau Zoo ntawm Cov Tub Ntxhais Kawm: Hauv kev kawm ntawv, feem pua yog siv los ntsuam xyuas seb tus tub ntxhais kawm ua tau zoo li cas piv rau lwm tus tub ntxhais kawm. Los ntawm kev paub tias tus tub ntxhais kawm qhov qhab nia poob rau hauv feem pua twg, peb tuaj yeem nkag siab lawv txoj haujlwm hauv pawg.
2. Kev Noj Qab Haus Huv: Hauv kev kho mob, feem ntau siv cov feem pua los ntsuas kev loj hlob ntawm cov menyuam yaus. Piv txwv li, tus kws kho mob tuaj yeem txiav txim siab seb qhov siab lossis qhov hnyav ntawm tus menyuam puas nyob hauv 70th feem pua piv rau cov pej xeem ib txwm muaj ntawm cov menyuam yaus uas muaj hnub nyoog zoo ib yam.
3. Kev Lag Luam thiab Cov Nyiaj Tau Los: Cov feem pua yog siv los nkag siab txog kev faib tawm ntawm cov nyiaj tau los thiab kev nplua nuj hauv ib pawg neeg. Qhov no pab hauv kev tshuaj xyuas kev tsis sib luag thiab kev txom nyem, nrog rau kev npaj txoj cai kev lag luam.
4. Kev Xav thiab Kev Sib Raug Zoo: Cov feem pua pab faib cov qhab nia xeem kev xav, yog li ua rau cov kws kho mob puas siab puas ntsws txiav txim siab seb cov neeg teb puas nyob hauv qeb nruab nrab, qis dua qhov nruab nrab, lossis siab dua qhov nruab nrab hauv ib qho peev xwm tshwj xeeb.
5. Kev Lag Luam thiab Kev Lag Luam: Hauv kev tshuaj xyuas kev ua lag luam, cov feem pua yog siv los faib cov neeg siv khoom raws li cov nyiaj tau los, kev siv nyiaj, lossis lwm yam kev coj cwj pwm ntawm cov neeg siv khoom los coj kev lag luam thiab kev tshaj tawm zoo dua.
Xaus
Cov feem pua yog ib qho cuab yeej muaj txiaj ntsig zoo hauv kev suav lej rau kev nkag siab txog qhov chaw sib piv ntawm cov nqi hauv kev faib cov ntaub ntawv. Txawm hais tias kev suav lawv hauv cov ntsiab lus ntawm cov ntaub ntawv pawg yog qhov nyuaj dua li rau cov ntaub ntawv ib leeg, nws tseem tuaj yeem ua tiav nrog txoj hauv kev tsim kho. Lub peev xwm los txhais thiab suav cov feem pua hauv cov ntaub ntawv pawg qhib ntau lub sijhawm rau kev tshuaj xyuas cov ntaub ntawv tob dua thiab muaj txiaj ntsig zoo hauv ntau qhov chaw ua haujlwm.
Yog tias nkag siab zoo, feem pua tuaj yeem yog ib qho cuab yeej muaj zog heev rau kev ua kom yooj yim qhov nyuaj ntawm cov ntaub ntawv, tso cai rau cov kws tshuaj ntsuam xyuas thiab cov kws tshawb fawb txiav txim siab zoo dua raws li cov ntaub ntawv uas lawv tau txais.
