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Standard XII

Mathematics

Standard Deviation

A sample of 3...

Question

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

5.85

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5.58

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3.42

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none of these

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Solution

The correct option is A 5.85
$H e r e n_{1} = 35,_{1} = 80, σ_{1} = 4, n_{2} = 65,_{2} = 70, σ_{2} = 3 ∴_{2} = \frac{35 \times 80 + 65 \times 70}{35 + 60} = 73.5 σ_{12} = \sqrt{[\frac{35 (16 + 42 \times 25) + 65 (9 + 12 \times 25)}{100}]} = \sqrt{34.21} = 5.85$

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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

The correct option is A 5.85Here n1=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

The correct option is A 5.85
$H e r e n_{1} = 35,_{1} = 80, σ_{1} = 4, n_{2} = 65,_{2} = 70, σ_{2} = 3 ∴_{2} = \frac{35 \times 80 + 65 \times 70}{35 + 60} = 73.5 σ_{12} = \sqrt{[\frac{35 (16 + 42 \times 25) + 65 (9 + 12 \times 25)}{100}]} = \sqrt{34.21} = 5.85$