A sample of 35 observations has the mean 80 and S.D as 4. A second sample of 65 observations from the same population has mean 70 and S.D. 3. The s.d. of the combined sample is
A
5.85
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B
5.58
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C
3.42
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D
none of these
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Solution
The correct option is A 5.85 Heren1=35,¯x1=80,σ1=4,n2=65,¯x2=70,σ2=3∴¯x2=35×80+65×7035+60=73.5σ12=√[35(16+42×25)+65(9+12×25)100]=√34.21=5.85