Mehlala ea Lipotso tse Buisanang ka Phapang le Phapang e Tloaelehileng ea Lintlha tsa Sehlopha
Pendahuluan
Lipalopalong, phapang le ho kheloha ho tloaelehileng ke litekanyo tse peli tsa lipalo-palo tse bohlokoa bakeng sa ho utloisisa ho hasana, kapa ho ata ha data ho tloha ho karolelano. Phapang e lekanya hore na data e hasana hakae ho tloha ho karolelano, ha phapang e tloaelehileng e le motso o sekoere oa phapang, e fanang ka tekanyo e ka har'a li-unit tse tšoanang le data ea pele.
Tlhaloso
– Phapang (σ² kapa S²): Ke karolelano ea lisekoere tsa liphapang lipakeng tsa boleng bo bong le bo bong ba data le karolelano ea data.
– Phapang e Tloaelehileng (σ kapa S): Ke motso o sekoere wa phapang.
Foromo ea Phapang le Phapang e Tloaelehileng ea Lintlha tsa Sehlopha
Bakeng sa data ea sehlopha, re sebelisa makhetlo a data sehlopheng ka seng. Foromo ke ena:
Fetoha
\[ S^2 = \frac{ \sum f_i \left( x_i – \bar{x} \right)^2 }{ N-1 } \]
Ho kheloha ho tloaelehileng
\[ S = \sqrt{S^2} \]
Moo:
– \( f_i \) = makhetlo a sehlopha ka seng.
– \( x_i \) = ntlha e bohareng ba sehlopha ka seng.
– \( \bar{x} \) = karolelano ea data ea sehlopha.
– \( N \) = palo yohle ya data.
Lipotso tsa Mehlala le Puisano
A re re re na le data ea boima ba sehlopha sa batho ba arotsoeng ka lihlopha.
| Nako ea Boima (kg) | Maqhubu (f) |
|————————|————–|
| 50 – 54 | 2 |
| 55 – 59 | 5 |
| 60 – 64 | 8 |
| 65 – 69 | 7 |
| 70 – 74 | 3 |
Mohato oa pele ke ho fumana ntlha e bohareng ea sehlopha ka seng ( \( x_i \) ) ebe o bala karolelano (\( \bar{x} \)).
1. Ho bala Bohareng ba Ntlha ( \( x_i \) )
\[ \text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \]
| Nako ea Boima (kg) | Maqhubu (f) | Bohareng (\( x_i \) ) |
|——————|————–|———————|
| 50 – 54 | 2 | 52 |
| 55 – 59 | 5 | 57 |
| 60 – 64 | 8 | 62 |
| 65 – 69 | 7 | 67 |
| 70 – 74 | 3 | 72 |
2. Ho Bala Karolelano ( \( \bar{x} \) )
\[ \bar{x} = \frac{ \sum f_i x_i }{ N } \]
Palo yohle ya data \( N \):
\[ N = 2 + 5 + 8 + 7 + 3 = 25 \]
\[ \ kakaretso f_i x_i = (2 \ makhetlo a 52) + (5 \ makhetlo a 57) + (8 \ makhetlo a 62) + (7 \ makhetlo a 67) + (3 \ makhetlo a 72) \]
\[ = 104 + 285 + 496 + 469 + 216 = 1570 \]
Kahoo, karolelano (\( \bar{x} \)):
\[ \bar{x} = \frac{ 1570 }{ 25 } = 62.8 \]
3. Ho Bala Phapang ( \( S^2 \) )
Re hloka ho bala \( \sum f_i ( x_i – \bar{x} )^2 \):
\[
\begin{align}
(x_i – \bar{x})^2: & (52 – 62.8)^2 = 118.84 \\
& (57 – 62.8)^2 = 33.64 \\
& (62 – 62.8)^2 = 0.64 \\
& (67 – 62.8)^2 = 17.64 \\
& (72 – 62.8)^2 = 84.64
\end{align}
\]
Ho atisa ka makhetlo:
\[
\begin{align}
f_i (x_i – \bar{x})^2: & 2 \makgetlo a 118.84 = 237.68 \\
& 5 \makhetlo a 33.64 = 168.2 \\
& 8 \makhetlo a 0.64 = 5.12 \\
& 7 \makgetlo a 17.64 = 123.48 \\
& 3 \makhetlo a 84.64 = 253.92
\end{align}
\]
\[
\kakaretso f_i (x_i – \bar{x})^2 = 237.68 + 168.2 + 5.12 + 123.48 + 253.92 = 788.4
\]
Jwale re ka bala phapang (\( S^2 \)):
\[ S^2 = \frac{ 788.4 }{ 25 – 1 } = \frac{ 788.4 }{ 24 } \hoo e ka bang 32.85 \]
4. Ho Bala Phapang e Tloaelehileng ( \( S \) )
Phapang e tloaelehileng ( \( S \)):
\[ S = \sqrt{ S^2 } \]
\[ S = \sqrt{ 32.85 } \hoo e ka bang 5.73 \]
Qetello
Ho latela mehlala ea lintlha tse kaholimo, re na le:
– Ho bala boima ba 'mele bo tloaelehileng: 62.8 kg
– Ho bala phapang: 32.85 kg²
– Ho bala kheloho e tloaelehileng: 5.73 kg
Tlhaloso ea ho kheloha ho tloaelehileng ke hore ho kheloha ho tloaelehileng ha data ea boima ho tloha ho karolelano ke hoo e ka bang 5.73 kg. Sena se bontša ho ata ha data mabapi le karolelano, e leng se ka thusang ho fumana hore na data ea rona e fetoha hakae.
Kutloisiso e batsi ea phapang le ho kheloha ho tloaelehileng ke ea bohlokoa, haholo-holo bakeng sa ba sebetsang lipalo-palo, lipatlisiso le liteko, ha ba ntse ba leka ho utloisisa lintlha ka mokhoa oa lihlopha kapa kabo. Ho tseba ho bala le ho hlalosa litekanyo tsena tse peli ho ka thusa ho etsa liqeto tse betere ho latela lintlha tse teng.
