Cov Txheej Txheem rau Kev Tsim Histograms ntawm Cov Ntaub Ntawv Sib Koom Ua Ke
Ib daim histogram yog ib qho cuab yeej nthuav qhia cov ntaub ntawv siv ntau zaus hauv kev suav lej, tshwj xeeb tshaj yog thaum cuam tshuam nrog cov ntaub ntawv sib sau ua pawg. Tsis zoo li daim ntawv qhia bar ib txwm muaj, uas qhia cov pawg sib cais, daim histogram qhia txog kev faib tawm zaus ntawm cov ntaub ntawv lej uas tau muab faib ua pawg sib txawv. Los ntawm daim histogram, peb tuaj yeem pom cov qauv faib tawm cov ntaub ntawv, cov qauv (piv txwv li, skewing mus rau sab xis lossis sab laug), thiab txawm tias qhov kwv yees ntawm cov duab faib tawm (ib txwm, skewed, bimodal, thiab lwm yam). Tsab xov xwm no tham txog cov txheej txheem rau kev tsim cov histograms rau cov ntaub ntawv sib sau ua pawg, los ntawm kev tsim lub rooj faib tawm zaus mus rau kev kos duab histogram kom raug.
1. Nkag Siab Txog Cov Ntaub Ntawv thiab Cov Histograms Uas Muab Sib Sau Ua Ib Pawg
Cov ntaub ntawv uas muab faib ua pawg yog cov ntaub ntawv lej uas tau muab sau ua ntau ntu ntawm chav kawm. Piv txwv li, cov qhab nia xeem ntawm cov tub ntxhais kawm tsis raug tso tawm ib leeg lawm tab sis raug muab faib ua pawg rau hauv ntau qhov ntau thiab tsawg 40–49, 50–59, 60–69, thiab lwm yam. Txhua ntu muaj zaus, uas yog tus lej ntawm cov ntsiab lus ntaub ntawv uas poob rau hauv ntu ntawd.
Ib daim histogram yog ib daim duab uas muaj cov kab sib nrug ze uas tsis muaj qhov sib txawv (lossis qhov sib txawv me me), vim nws sawv cev rau ntau yam nqi sib txuas. Qhov dav ntawm cov kab sawv cev rau qhov ntev ntawm lub sijhawm kawm, thaum qhov siab ntawm cov kab sawv cev rau qhov zaus lossis qhov ceev ntawm zaus (nyob ntawm seb qhov dav ntawm cov chav kawm puas zoo ib yam lossis txawv).
2. Sau ib daim ntawv qhia txog kev faib tawm zaus
Kauj ruam thawj zaug hauv kev tsim ib daim histogram yog los tsim ib daim ntawv faib zaus. Cov txheej txheem no feem ntau muaj xws li:
1. Txheeb xyuas qhov tsawg kawg nkaus thiab siab tshaj plaws ntawm cov ntaub ntawv.
2. Xam qhov ntau = qhov siab tshaj plaws − qhov tsawg kawg nkaus.
3. Txheeb xyuas tus naj npawb ntawm cov chav kawm (k).
4. Txheeb xyuas qhov ntev ntawm chav kawm (p) = ntau yam / k (puag ncig raws li qhov xav tau).
5. Npaj cov sijhawm kawm thiab xam qhov zaus ntawm txhua lub sijhawm kawm.
Muaj ntau txoj kev qhia txog kev txiav txim seb muaj pes tsawg chav kawm. Ib qho uas nrov yog tus qauv Sturges:
k = 1 + 3,3 log10(n)
qhov twg n yog tus naj npawb ntawm cov ntsiab lus ntaub ntawv. Qhov tshwm sim ntawm k yog puag ncig mus rau qhov ze tshaj plaws integer.
Piv txwv yooj yim: yog tias n = 40, ces k ≈ 1 + 3,3 log10(40) ≈ 1 + 3,3(1,602) ≈ 6,29 yog li 6 lossis 7 chav kawm tuaj yeem xaiv tau.
3. Kev Txheeb Xyuas Cov Ciam Teb ntawm Chav Kawm thiab Cov Ntug ntawm Chav Kawm
Ib qho yuam kev uas feem ntau tshwm sim thaum tsim cov histograms yog kev tsis meej pem cov ciam teb ntawm chav kawm nrog cov npoo ntawm chav kawm.
– Cov kev txwv ntawm chav kawm yog cov lej sau ua ntu zus, piv txwv li 50–59.
- Cov ciam teb ntawm chav kawm yog cov ciam teb uas sib cais cov chav kawm kom tsis muaj "qhov sib txawv" ntawm cov chav kawm.
Yog tias cov ntaub ntawv yog ib qho integer, ces qhov ntug ntawm chav kawm feem ntau yog txiav txim siab los ntawm kev ntxiv thiab rho tawm 0,5.
Piv txwv:
- Lub sijhawm sib txawv ntawm 50-59 muaj cov npoo ntawm 49,5-59,5
- Lub sijhawm sib txawv ntawm 60-69 muaj cov npoo ntawm 59,5-69,5
Yog li, cov npoo ntawm chav kawm sib ntsib ntawm 59,5 kom cov histogram zoo li sib koom ua ke thiab txuas ntxiv mus tas li.
Txawm li cas los xij, yog tias cov ntaub ntawv yog kev ntsuas tas mus li (piv txwv li, qhov siab hauv cm thiab tuaj yeem muaj cov lej lej), kev txiav txim siab txog cov ciam teb ntawm chav kawm nyob ntawm qhov tseeb ntawm kev ntsuas. Lub hauv paus ntsiab lus yog los tsim cov ciam teb ntawm chav kawm uas tsis sib tshooj thiab tsis muaj qhov sib txawv.
4. Txheeb xyuas qhov nplai ntawm X thiab Y Axis
Lub histogram muaj ob lub axis tseem ceeb:
- X axis (kab rov tav): qhia cov chav kawm sib nrug (feem ntau siv cov npoo chav kawm kom ntseeg tau tias muaj kev sib txuas).
- Y axis (ntsug): qhia zaus.
Yog tias txhua qhov sib nrug ntawm chav kawm muaj qhov dav sib npaug, ces qhov siab ntawm lub bar tsuas yog ntsuas siv zaus xwb. Txawm li cas los xij, yog tias qhov dav ntawm chav kawm sib nrug sib txawv, qhov siab ntawm lub bar yuav tsum ntsuas siv qhov ceev ntawm zaus:
Qhov ceev ntawm zaus = zaus / qhov dav ntawm chav kawm
Siv qhov ceev yog qhov tseem ceeb kom thaj chaw ntawm lub bar yog proportional rau qhov zaus tiag tiag. Txwv tsis pub, cov chav kawm dav dua yuav zoo li "loj dua" tsuas yog vim lawv qhov dav, tsis yog vim muaj ntau cov ntaub ntawv.
5. Kos duab Histogram Bars
Thaum txiav txim siab qhov nplai thiab qhov sib nrug, kauj ruam tom ntej yog kos lub bar.
Cov txheej txheem zoo rau kev kos duab histogram:
1. Kos cov npoo ntawm chav kawm ntawm X-axis ua ntu zus.
2. Ntawm txhua lub sijhawm, kos ib daim kab plaub fab uas nws qhov dav sib xws nrog lub sijhawm ntawd.
3. Qhov siab ntawm lub bar sib raug rau qhov zaus (lossis qhov ceev ntawm zaus yog tias qhov dav ntawm chav kawm tsis zoo ib yam).
4. Xyuas kom tseeb tias cov qia ze ua ke (tsis muaj qhov sib txawv).
5. Muab lub npe rau daim histogram, sau lub npe rau X thiab Y axes, thiab cov chav yog tias tsim nyog.
Piv txwv li, yog tias qhov sib nrug ntawm chav kawm yog 40–49, 50–59, 60–69, thiab lawv cov zaus yog 5, 12, 18, ces qhov bar rau chav kawm 60–69 yuav siab dua li lwm cov chav kawm vim nws qhov zaus yog qhov loj tshaj plaws.
6. Nyeem thiab txhais cov Histograms
Ib daim histogram tsis yog ib daim duab xwb, tab sis yog ib qho cuab yeej siv los tshuaj xyuas. Los ntawm daim histogram, peb tuaj yeem pom:
- Chav kawm hom: chav kawm nrog qhov bar siab tshaj plaws (zaus siab tshaj plaws).
- Cov duab faib tawm: symmetrical, skewed mus rau sab xis (positive skew), skewed mus rau sab laug (negative skew), lossis muaj ob lub ncov (bimodal).
- Kev faib cov ntaub ntawv: seb cov ntaub ntawv puas tau sib sau ua ke ntawm ib lub sijhawm lossis faib dav dav.
- Qhov qhia txog qhov tsis zoo: yog tias muaj ib chav kawm nyob rau thaum kawg uas muaj zaus me me thiab raug cais tawm ntawm pawg tseem ceeb.
Feem ntau kev txhais lus zoo yuav muaj kev xaus lus luv luv. Piv txwv li: "Feem ntau ntawm cov ntaub ntawv poob rau hauv qhov ntau ntawm 60–79, qhia tias cov qhab nia ntawm cov neeg koom nrog feem ntau nyob hauv pawg nruab nrab."
7. Tej Yam Yuam Kev Uas Feem Ntau Ua
Nov yog qee qhov yuam kev uas yuav tsum zam:
1. Muab qhov chaw nruab nrab ntawm cov kab kom nws zoo li daim duab qhia kab.
2. Siv cov ciam teb ntawm chav kawm, tsis yog cov ciam teb ntawm chav kawm, yog li ntawd muaj qhov sib txawv hauv cov ntaub ntawv.
3. Tsis kho qhov siab ntawm lub bar thaum qhov dav ntawm chav kawm txawv, yog li ntawd qhov kev sib piv zaus yuav tsis ncaj ncees.
4. Cov nplai ntawm lub axis tsis sib xws lossis tsis pib ntawm xoom ntawm lub zaus axis (tuaj yeem ua rau pom tsis meej).
5. Cov chav kawm sib nrug tsis sib law liag lossis sib tshooj, piv txwv li 50–60 thiab 60–70 yam tsis muaj kev piav qhia txog cov npoo ntawm chav kawm.
8. Cov Lus Qhia Siv Tau Zoo Rau Kev Ua Cov Histograms Muaj Cov Lus Qhia Ntau Ntxiv
Yuav kom ua rau cov histogram yooj yim to taub:
- Siv cov chav kawm kom tsim nyog (feem ntau yog 5-12 chav kawm, nyob ntawm seb muaj pes tsawg cov ntaub ntawv).
- Tsis txhob siv sijhawm nqaim dhau (ntau chav kawm dhau) vim tias cov histogram dhau los ua "suab nrov".
- Tsis txhob siv cov sijhawm sib txawv (xws li cov chav kawm tsawg dhau) vim tias cov qauv faib tawm yuav ploj mus.
- Muab cov ntaub ntawv los ntawm cov chaw muab cov ntaub ntawv, qhov loj ntawm cov qauv (n), thiab lwm yam ntaub ntawv yog tias tsim nyog rau hauv daim ntawv qhia.
Yog tias koj siv software xws li Excel, Google Sheets, lossis cov ntawv thov suav lej, ib txwm nkag siab lub tswv yim ntawm ntug chav kawm thiab qhov dav chav kawm kom cov txiaj ntsig histogram tsis yuam kev.
Kev kaw
Cov txheej txheem ntawm kev tsim cov histogram rau cov ntaub ntawv sib koom ua ke yuav tsum tau ua kom raug hauv kev tsim cov chav kawm sib nrug, txiav txim siab cov ciam teb chav kawm, thiab txiav txim siab qhov siab ntawm cov kab sib txawv. Yog tias cov chav kawm sib nrug sib npaug, tsuas yog siv zaus ua qhov siab ntawm cov kab sib txawv. Yog tias cov sib nrug tsis sib npaug, siv qhov ceev ntawm zaus kom tswj tau qhov pom tseeb thiab raug. Nrog rau cov histogram uas tau tsim kom zoo, peb tuaj yeem tau txais kev pom zoo sai sai ntawm cov qauv faib cov ntaub ntawv thiab ua cov kev txhais lus tseeb dua hauv kev tshuaj xyuas lej.
Yog tias koj xav tau, kuv tuaj yeem ntxiv cov ntaub ntawv piv txwv thiab ua tiav cov kauj ruam xam kom txog thaum cov histogram tiav (manually lossis nrog Excel/Sheets).
