Question

A sample of 35 observations has the mean 80 and standard deviation as 4. A second sample of 65 observations from the same population has mean 60 and standard deviation 3. Then the standard deviation of the combined sample is

• A. 5.85
• B. 5.58
• C. 10.12
• D. 9.12

Answer 1

The correct option is C

10.12

$n_1=35,{\overline{x}}_1=80,{\sigma }_1=4n_2=65,{\overline{x}}_2=60,{\sigma }_2=3{\sigma }^2=\frac{n_1({\sigma }_1^2+d_1^2)+n_2({\sigma }_2^2+d_2^2)}{n_1+n_2}$
Continued mean =$\frac{35\times 80+65\times 60}{100}=67d_1=80-67=13,d_2=60-67=-7{\sigma }^2=102.45\sigma =10.12$