Question

The mean of two samples of size 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. Obtain the mean and standard deviation of the sample of size 150 obtained by combining the two samples.

Answer 1

Answer:

Mean 51.6 (approx)

Std dev 7.3 (approx)

Step-by-step explanation:

The mean will just be the weighted average of the given means:

$\text{mean} = \frac{50\times 54.1 + 100\times 50.3}{50+100} = \frac{7735}{150} \approx 51.6$

For the standard deviation, this will depend upon whether you are using the so-called "sample standard deviation" here or the "population standard deviation".  You're probably using the sample standard deviation, so I'll do that one first.

We're kinda doing weighted averages again, but we need to be careful of the fact that divisions (and so multiplications that "undo" previous divisions) are "degrees of freedom", not "number of values".  So...

$\sigma_{\text{sample}} = \sqrt{\frac{8^2\times(50-1) + 7^2\times(100-1)}{50+100-1}}= \sqrt{\frac{7987}{149}} \approx 7.32$

Otherwise, in case you need it,

$\sigma_{\text{population}} = \sqrt{\frac{8^2\times50 + 7^2\times100}{50+100}}= \sqrt{\frac{8100}{150}} = \sqrt{54} \approx 7.35$

Answer 2

Answer:

Step-by-step explanation

it will. help you