The mean of two samples of the sizes 250 and 320 were found to be 20,12 respectively. Their standard deviations were 2 & 5, respectively. Find the variance of combined sample of size 650.
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Answer:
The mean of two samples of sizes 200 and 300 were found to be 25 and 10 respectively. Their standard deviations were 3 and 4 respectively. The varience of combined sample size of 500 is67.2
Step-by-step explanation:
Given : First sample size(n
1
)=200, Second sample size(n
2
)=300
First mean (
x
ˉ
1
)=25, Second mean (
x
ˉ
2
)=10
S.D.(σ
1
)=3 and S.D.(σ
2
)=4
Combined mean,
x
ˉ
=
500
200×25+300×10
=
5
80
=16
Let d
1
=
x
1
ˉ
−
x
ˉ
=25−16=9
and d
2
=
x
2
ˉ
−
x
ˉ
=10−16=−6
∴σ
2
=
n
1
+n
2
n
1
(σ
1
2
+d
1
2
)+n
2
(σ
2
2
+d
2
2
)
=
500
200(9+81)+300(16+36)
=67.2
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