Cov Lus Nug Piv Txwv Sib Tham Txog Qib Nruab Nrab thiab Hom ntawm Cov Ntaub Ntawv Pawg
Hauv kev suav lej, qhov nruab nrab thiab hom yog ob qho kev ntsuas tseem ceeb heev ntawm qhov sib txawv ntawm qhov nruab nrab. Hauv tsab xov xwm no, peb yuav tham txog cov chav kawm nruab nrab thiab hom kom ntxaws hauv cov ntsiab lus ntawm cov ntaub ntawv sib sau ua ke, suav nrog ntau qhov teeb meem piv txwv los pab koj nkag siab.
Nkag Siab Txog Nruab Nrab thiab Hom
theem nrab
Tus nqi nruab nrab yog tus nqi nruab nrab ntawm cov ntaub ntawv thaum cov ntaub ntawv raug cais. Hauv cov ntaub ntawv uas tau muab faib ua pawg, tus nqi nruab nrab yog pawg uas faib cov ntaub ntawv ua ob feem sib npaug.
hom
Hom yog tus nqi lossis chav kawm uas tshwm sim ntau zaus hauv cov ntaub ntawv. Rau cov ntaub ntawv uas muab faib ua pawg, hom yog chav kawm uas muaj zaus ntau tshaj plaws.
Xam Qhov Nruab Nrab thiab Hom Chav Kawm ntawm Cov Ntaub Ntawv Muab Pawg
theem nrab
Yuav kom txiav txim siab qhov nruab nrab hauv cov ntaub ntawv sib sau ua ke, cov kauj ruam uas yuav tsum tau ua yog raws li nram no:
1. Xam qhov zaus sib sau ua ke (F).
2. Siv cov mis los txiav txim seb qhov chaw nruab nrab yog dab tsi:
\[
\text{Qhov Chaw Nruab Nrab} = \frac{n + 1}{2}
\]
Qhov twg n yog tus naj npawb ntawm cov ntaub ntawv.
3. Txheeb xyuas pawg nruab nrab, uas yog pawg uas qhov chaw nruab nrab nyob.
4. Siv cov mis nruab nrab rau cov ntaub ntawv sib sau ua pawg:
\[
\text{Median} = L + \left( \frac{\frac{n}{2} – F}{f} \right) \times c
\]
- L yog qhov txwv qis dua ntawm chav kawm nruab nrab.
- F yog qhov zaus sib sau ua ke ua ntej chav kawm nruab nrab.
- f yog qhov zaus ntawm chav kawm nruab nrab.
-c yog qhov ntev ntawm lub sijhawm kawm.
hom
Yuav kom txiav txim siab seb hom twg hauv cov ntaub ntawv uas tau muab faib ua pawg, cov kauj ruam uas yuav tsum tau ua yog:
1. Txheeb xyuas hom chav kawm, uas yog chav kawm uas muaj zaus siab tshaj plaws.
2. Siv cov qauv mis rau cov ntaub ntawv sib sau ua pawg:
\[
\text{Hom} = L + \left( \frac{d_1}{d_1 + d_2} \right) \times c
\]
- L yog qhov txwv qis dua ntawm chav kawm hom.
- \(d_1\) yog qhov sib txawv ntawm qhov zaus ntawm chav kawm hom thiab chav kawm dhau los.
- \(d_2\) yog qhov sib txawv ntawm zaus ntawm chav kawm hom thiab chav kawm tom ntej.
-c yog qhov ntev ntawm lub sijhawm kawm.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Piv txwv lus nug 1: Nruab nrab
Cov hauv qab no yog qhov faib zaus ntawm cov txiaj ntsig xeem lej rau 40 tus tub ntxhais kawm:
| Tus nqi | Zaus (f) |
|————-|———————|
| 50 – 59 | 5 |
| 60 – 69 | 10 |
| 70 – 79 | 15 |
| 80 – 89 | 7 |
| 90 – 99 | 3 |
Yuav xam tus nqi nruab nrab, peb xub suav tus naj npawb ntawm cov ntaub ntawv (n):
\[
n = 5 + 10 + 15 + 7 + 3 = 40
\]
Txoj hauj lwm nruab nrab:
\[
\text{Qhov Chaw Nruab Nrab} = \frac{40 + 1}{2} = 20.5
\]
Tom ntej no, peb xam cov zaus sib sau ua ke:
| Tus nqi | Zaus (f) | Zaus sib sau ua ke (F) |
|————-|———————|————————-|
| 50 – 59 | 5 | 5 |
| 60 – 69 | 10 | 15 |
| 70 – 79 | 15 | 30 |
| 80 – 89 | 7 | 37 |
| 90 – 99 | 3 | 40 |
Qhov chaw nruab nrab (20.5) yog nyob rau hauv chav kawm 70 - 79.
Peb siv cov qauv nruab nrab:
– L = 70 (qhov txwv qis dua ntawm chav kawm nruab nrab)
– F = 15 (zaus sib sau ua ntej chav kawm nruab nrab)
– f = 15 (zaus nruab nrab ntawm chav kawm)
– c = 10 (lub sijhawm kawm)
\[
\text{Median} = 70 + \sab laug (\frac{\frac{40}{2} – 15}{15} \right) \times 10 = 70 + \sab laug (\frac{20 – 15}{15} \right) \times 10 = 70 + \sab laug (\frac{5}{15} \right) \times 10 = 70 + 3.33 = 73.33
\]
Yog li, qhov nruab nrab ntawm cov ntaub ntawv yog 73.33.
Piv txwv lus nug 2: Hom
Cov ntaub ntawv ntawm cov khoom muag tau los ntawm ib lub khw muag khoom rau ib lub lim tiam yog cov hauv qab no:
| Tus naj npawb ntawm cov khoom muag | Zaus (f) |
|——————–|———————|
| 10 – 19 | 3 |
| 20 – 29 | 7 |
| 30 – 39 | 12 |
| 40 – 49 | 5 |
| 50 – 59 | 3 |
Yuav nrhiav tau hom:
– Chav kawm hom yog 30 – 39 (zaus siab tshaj = 12).
- L = 30 (qhov txwv qis dua ntawm chav kawm hom).
– \(d_1 = 12 – 7 = 5\) (zaus ntawm chav kawm hom – zaus ntawm chav kawm dhau los).
– \(d_2 = 12 – 5 = 7\) (zaus ntawm chav kawm hom – zaus ntawm chav kawm tom ntej).
– c = 10 (lub sijhawm kawm).
Peb siv cov qauv ntawm hom:
\[
\text{Hom} = 30 + \left( \frac{5}{5 + 7} \right) \times 10 = 30 + \left( \frac{5}{12} \right) \times 10 = 30 + 4.17 = 34.17
\]
Yog li, hom ntawm cov ntaub ntawv yog 34.17.
Xaus
Kev nkag siab txog yuav ua li cas xam qhov nruab nrab thiab hom hauv cov ntaub ntawv pawg yog ib qho kev txawj tseem ceeb hauv kev suav lej. Qhov nruab nrab muab rau peb tus nqi nruab nrab ntawm cov ntaub ntawv, thaum qhov hom muab rau peb tus nqi lossis chav kawm uas tshwm sim ntau tshaj plaws. Los ntawm kev ua raws li cov kauj ruam thiab siv cov qauv uas tau teev tseg saum toj no, koj tuaj yeem txiav txim siab tau yooj yim ob qho kev ntsuas ntawm qhov sib txawv nruab nrab los ntawm cov ntaub ntawv pawg.
Los ntawm cov piv txwv teeb meem uas tau tham txog, cov nyeem ntawv yuav tsum nkag siab zoo dua txog lub tswv yim thiab kev siv ntawm nruab nrab thiab hom hauv cov ntaub ntawv pawg. Rau cov ntaub ntawv nyuaj dua lossis kev faib tawm zaus ntev dua, cov ntsiab cai tib yam tuaj yeem siv tau meej. Xyaum ntau cov teeb meem kom txhawb koj txoj kev nkag siab thiab kev txawj ntse hauv kev suav lej.
