what is the population variance of the data 16,14,15,12,24,13
Answers
Answer:
=
10
6+8+10+12+14+16+18+20+22+24
=
10
150
=15
Variance=
10
∑(x−
x
)
2
=
10
(6−15)
2
+(8−15)
2
+(10−15)
2
+(12−15)
2
+(14−15)
2
+(16−15)
2
+(18−15)
2
+(20−15)
2
+(22−15)
2
+(24−15)
2
=
10
(−9)
2
+(−7)
2
+(−5)
2
+(−3)
2
+(−1)
2
+(1)
2
+(3)
2
+(5)
2
+(7)
2
+(9)
2
=
10
81+49+25+9+1+1+9+25+49+81
=
10
330
=33
∴ Variance =33
Given : observation: 16,14,15,12,14,13
To Find : population variance of the data
Solution:
= (16 + 14 + 15 + 12 + 14 + 13) /6
= ( 84)/6
= 14
x (x- ) (x- ) ²
16 2 4
14 0 0
15 1 1
12 -2 4
14 0 0
13 -1 1
10
Population Variance = (1/n)∑ (x- )²
= (1/6)10
= 10/6
= 5/3
= 1.667
Additional Info:
Sample Variance = (1/(n-1))∑ (x-)²
= (1/5) 10
= 2
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