Yuav Ua Li Cas Muab Cov Ntaub Ntawv Ua Pawg Rau Hauv Chav Kawm
Kev muab cov ntaub ntawv ua pawg ua ntu zus yog ib kauj ruam tseem ceeb hauv kev piav qhia txog cov ntaub ntawv. Lub hom phiaj yog ua kom yooj yim rau cov ntaub ntawv raw kom yooj yim nyeem, txheeb xyuas, thiab nthuav tawm hauv cov lus faib zaus lossis cov histograms. Thaum cov ntaub ntawv muaj ntau yam thiab tawg ua ntau dhau, nws feem ntau nyuaj rau pom cov qauv. Cov ntu zus npaj cov ntaub ntawv rau hauv cov pab pawg tshwj xeeb, uas ua rau peb nkag siab meej dua txog kev faib cov ntaub ntawv, cov nqi uas tshwm sim ntau zaus, thiab txawm tias qhov kev hloov pauv tseem ceeb.
Tsab xov xwm no tham txog lub ntsiab lus ntawm cov chav kawm sib nrug, thaum twg xav tau, nrog rau cov kauj ruam ua tau rau kev muab cov ntaub ntawv sib sau ua ke rau hauv cov chav kawm sib nrug ua ke nrog cov piv txwv siv.
1. Nkag Siab Txog Lub Sijhawm Kawm
Ib lub sijhawm kawm yog ib qho ntawm cov nqi siv los pab pawg cov ntaub ntawv hauv kev faib zaus. Txhua lub sijhawm feem ntau muaj qhov txwv qis dua thiab siab dua. Piv txwv li, lub sijhawm 10–19 qhia tias txhua cov ntaub ntawv nrog cov nqi ntawm 10 thiab 19 poob rau hauv chav kawm ntawd.
Hauv daim ntawv faib zaus, cov chav kawm sib nrug ua haujlwm ua "cov thawv" rau cov nqi zoo sib xws. Qhov no ua rau cov ntaub ntawv luv dua li teev tag nrho cov nqi ib tus zuj zus. Cov chav kawm sib nrug kuj tsim lub hauv paus rau kev tsim cov duab xws li histograms thiab cov polygons zaus.
2. Thaum twg cov ntaub ntawv yuav tsum tau muab faib ua pawg?
Tsis yog txhua cov ntaub ntawv yuav tsum tau muab faib ua pawg sib txawv. Feem ntau, kev sib sau ua pawg yog qhov tsim nyog thaum:
1. Cov ntaub ntawv ntau heev, piv txwv li ntau dua 30 lossis 50 qhov kev soj ntsuam.
2. Cov ntaub ntawv ntau yam, yog li cov nqi tau nthuav dav thiab nyuaj nyeem.
3. Peb xav pom tus qauv faib tawm, piv txwv li kom paub seb cov ntaub ntawv puas zoo li qub, tsis sib xws, lossis muaj ob lub ncov.
4. Cov ntaub ntawv yuav raug nthuav tawm hauv daim histogram, vim tias daim histogram xav tau cov chav kawm sib nrug.
Yog tias cov ntaub ntawv me me (piv txwv li 10 tus nqi), feem ntau ib lub rooj zaus xwb txaus lawm yam tsis muaj qhov sib nrug.
3. Cov Kauj Ruam Rau Kev Muab Cov Ntaub Ntawv Ua Pawg Ua Ib Pawg
Nram no yog cov kauj ruam uas siv ntau tshaj plaws los tsim cov sijhawm sib nrug ntawm chav kawm.
Kauj Ruam 1: Txheeb Xyuas Cov Ntaub Ntawv Yam Tsawg Kawg Nkaus thiab Qhov Siab Tshaj Plaws
Ua ntej, txheeb xyuas qhov tsawg tshaj plaws (yam tsawg kawg nkaus) thiab qhov loj tshaj plaws (yam siab tshaj plaws) ntawm cov ntaub ntawv.
- Tus nqi tsawg kawg nkaus = \( x_{\min} \)
- Tus nqi siab tshaj plaws = \( x_{\max} \)
Tus nqi no yuav raug siv los xam qhov ntau ntawm cov ntaub ntawv.
Kauj Ruam 2: Xam Qhov Ntau Yam
Qhov ntau thiab tsawg yog qhov sib txawv ntawm qhov siab tshaj plaws thiab qhov tsawg kawg nkaus:
\[
R = x_{\max} – x_{\min}
\]
Ntau yam muab ib lub tswv yim ntawm qhov dav ntawm cov ntaub ntawv faib tawm.
Kauj Ruam 3: Txheeb Xyuas Tus Naj Npawb ntawm Cov Chav Kawm (k)
Tus naj npawb ntawm cov chav kawm tuaj yeem txiav txim siab tau ntau txoj hauv kev. Txoj kev nrov tshaj plaws yog siv Txoj Cai Sturges:
\[
k = 1 + 3 {,}3 \log_{10}(n)
\]
qhov twg \( n \) yog qhov ntau ntawm cov ntaub ntawv.
Cov txiaj ntsig ntawm kev xam feem ntau raug muab puag ncig mus rau tus lej tag nrho ze tshaj plaws (lossis siab dua) kom tus lej ntawm cov chav kawm tsis tsawg dhau.
Ntxiv rau Sturges, muaj ib qho kev coj ua uas ib txwm muaj: xaiv qhov loj ntawm chav kawm ntawm 5 thiab 12, nyob ntawm seb koj xav tau dab tsi thiab qhov loj ntawm cov qauv piv txwv. Txawm li cas los xij, Sturges zoo heev rau cov ntaub ntawv me me.
Kauj Ruam 4: Xam Qhov Dav ntawm Chav Kawm (i)
Qhov dav ntawm chav kawm yog qhov ntev ntawm txhua chav kawm. Tus qauv yog:
\[
i = \frac{R}{k}
\]
Vim tias qhov dav ntawm chav kawm yuav tsum yooj yim siv, feem ntau lawv raug puag ncig mus rau tus lej "zoo nkauj" (piv txwv li, 5, 10, 2, lossis 0,5, nyob ntawm cov ntsiab lus ntawm cov ntaub ntawv). Qhov kev puag ncig no yog qhov tseem ceeb kom ntseeg tau tias qhov sib nrug yooj yim nyeem thiab zam kev tsis meej pem.
Yog tias cov txiaj ntsig ntawm kev sib npaug tiv thaiv tag nrho cov ntaub ntawv kom tsis txhob muaj, qhov dav ntawm chav kawm tuaj yeem nce me ntsis.
Kauj Ruam 5: Txheeb Xyuas Cov Kev Txwv ntawm Chav Kawm
Pib nrog tus nqi tsawg kawg nkaus ua qhov txwv qis tshaj plaws ntawm thawj chav kawm. Tom qab ntawd tsim cov sijhawm sib law liag kom txog thaum lawv suav nrog tus nqi siab tshaj plaws.
Piv txwv li, yog tias tus nqi tsawg kawg yog 32 thiab qhov dav ntawm chav kawm yog 5, ces chav kawm tuaj yeem tsim tau:
– 32–36
– 37–41
– 42–46
- thiab lwm yam.
Tseem Ceeb: Xyuas kom tseeb tias tsis muaj qhov sib txawv lossis sib tshooj ntawm cov chav kawm. Txhua tus nqi ntawm cov ntaub ntawv yuav tsum poob rau hauv ib chav kawm.
Kauj Ruam 6: (Xaiv Tau) Tsim Cov Ciam Teb Hauv Chav Kawm
Yog tias cov ntaub ntawv yog cov lej (piv txwv li, cov qhab nia xeem), feem ntau cov ciam teb ntawm chav kawm raug tsim los ua kom chav kawm txuas ntxiv mus. Qhov no ua tiav los ntawm kev ntxiv 0,5 rau ciam teb sab saud thiab rho tawm 0,5 ntawm ciam teb sab qis.
Piv txwv li, chav kawm 32–36, qhov ntug chav kawm dhau los ua:
– 31,5–36,5
Qhov no muaj txiaj ntsig zoo rau cov histograms kom cov kab sib txuas tsis muaj qhov sib txawv.
Kauj Ruam 7: Xam Qhov Zaus ntawm Txhua Chav Kawm
Thaum txiav txim siab qhov sib nrug ntawm cov chav kawm lawm, suav seb muaj pes tsawg lub ntsiab lus poob rau hauv txhua qhov sib nrug. Cov txiaj ntsig tau sau rau hauv kab zaus (f).
Rau cov ntaub ntawv loj, siv txoj kev suav lej kom sai dua thiab txo qhov yuam kev.
Kauj Ruam 8: Tsim Ib Daim Ntawv Qhia Txog Kev Faib Tawm Zaus
Daim ntawv faib tawm zaus tsawg kawg nkaus muaj:
- Lub sijhawm kawm
– Zaus (f)
Koj tuaj yeem ntxiv lwm cov kab xws li:
– Nruab nrab ntawm chav kawm (xi)
- Zaus sib sau ua ke
- Qhov zaus sib piv (feem pua)
4. Piv txwv ntawm kev faib cov ntaub ntawv ua pawg
Piv txwv li, muaj cov ntaub ntawv qhab nia xeem los ntawm 40 tus tub ntxhais kawm nrog qhov qhab nia tsawg kawg yog 42 thiab siab tshaj plaws yog 94.
1. Yam tsawg kawg nkaus = 42, Qhov siab tshaj = 94
2. Ntau:
\[
R = 94 – 42 = 52
\]
3. Tus naj npawb ntawm cov chav kawm (Sturges):
\[
k = 1 + 3 {,} 3 \log(40)
\kwv yees li 1 + 3{,}3(1{,}602)
\kwv yees li 6{,}29
\]
Muab puag ncig mus txog 6 lossis 7 chav kawm. Peb xaiv 7 chav kawm kom paub meej ntxiv.
4. Qhov dav ntawm chav kawm:
\[
kuv = \frac{52}{7} \approx 7{,}43
\]
Puag ncig mus rau 8.
5. Cov qauv sib nrug pib ntawm 42 nrog qhov dav ntawm 8:
– 42–49
– 50–57
– 58–65
– 66–73
– 74–81
– 82–89
– 90–97
Lub sijhawm kawg tau txog 97, yog li tus nqi siab tshaj plaws ntawm 94 tseem tau txais kev pab.
6. Tom ntej no, xam qhov zaus ntawm txhua lub sijhawm raws li cov ntaub ntawv (piv txwv li, siv ib kab). Lub rooj kawg yuav qhia tias muaj pes tsawg tus tub ntxhais kawm poob rau hauv qee qhov qhab nia, uas cia peb ntsuas kev ua tau zoo sai sai.
5. Cov Lus Qhia rau Kev Ua Kom Lub Sijhawm Kawm Zoo Dua
1. Siv cov chav kawm dav sib xws kom cov rooj sib piv tau yooj yim.
2. Tsis txhob muaj ntau chav kawm, vim tias lub rooj yuav ntev thiab nyuaj nyeem.
3. Tsis txhob muaj chav kawm tsawg dhau, vim tias cov ntaub ntawv tseem ceeb yuav "ploj mus" thiab kev faib tawm yuav zoo li tsis zoo.
4. Kho qhov kev sib hloov ntawm qhov dav ntawm chav kawm kom haum rau cov ntsiab lus ntawm cov ntaub ntawv. Rau qhov kub thiab txias, 1 lossis 0,5 tej zaum yuav tsim nyog; rau cov qhab nia xeem, 5 lossis 10 feem ntau yog tsim nyog.
5. Xyuas ob zaug seb cov ciam teb ntawm chav kawm puas muaj tseeb tiag kom paub tseeb tias cov ntaub ntawv raug sau tsis muaj cov nqi ploj lawm.
Xaus
Kev muab cov ntaub ntawv ua pawg ua ntu zus yog ib txoj kev tseem ceeb rau kev ua kom cov ntaub ntawv yooj yim thiab qhia meej txog kev faib tawm. Cov kauj ruam suav nrog kev txiav txim siab qhov tsawg kawg nkaus thiab qhov siab tshaj plaws, xam qhov ntau thiab tsawg, txiav txim siab tus naj npawb ntawm cov chav kawm (feem ntau siv Sturges' Rule), xam qhov dav ntawm chav kawm, tsim cov ntu zus, thiab tom qab ntawd xam qhov zaus ntawm txhua chav kawm. Nrog rau cov ntu zus zoo, cov ntaub ntawv nyoos nyuaj tuaj yeem hloov pauv mus ua cov ntaub ntawv yooj yim nkag siab, txawm tias nyob hauv cov lus lossis cov duab.
Yog tias koj xav tau, kuv kuj tuaj yeem tsim ib qho piv txwv tiav nrog cov ntaub ntawv raw (daim ntawv teev cov nqi) thiab tom qab ntawd sau ua ke lub rooj faib zaus nrog histogram.
