The mean and variance of 10 observations were calculated as 15 and 15 respectively by a st…

Question

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is \_\_\_\_\_\_\_\_.

Answer: 2

Accepted Answer

$\sum x_i = 150$; $\sigma^2=15 \implies \sum x_i^2 = 10(15+225)=2400$

Replacing 25 by 15: $\sum x_i^{new} = 150-25+15=140$; correct mean $=14$

$\sum x_i^{2,new} = 2400-625+225=2000$

$$\sigma_{correct}^2 = \frac{2000}{10}-14^2 = 200-196=4 \implies \sigma_{correct}=2$$

Solutions · 1