a) The mean of two samples of sizes 50 and 100 respectively are 54
1 and 50
3 and the S. D are 8 and 7. Obtain the mean and S.D of the sample of size 150 obtained by combining the two samples.
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Answer:
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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