The mean and standard deviation of 40 observations are 30 and 5 respectively.

Question

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If \sigma  is the standard deviation of the data after omitting the two wrong observations from the data, then $38\sigma^2$ is equal to \_\_\_\_\_\_\_\_\_.

Answer: 238

Accepted Answer

$\sum x_i = 40\times30=1200$; $\sigma^2=25 \implies \sum x_i^2 = 40(25+900)=37000$

After omitting 12 and 10: $\sum y_i = 1200-12-10=1178$; $\sum y_i^2 = 37000-144-100=36756$

$$\sigma^2 = \frac{36756}{38}-\left(\frac{1178}{38}\right)^2$$

$$38\sigma^2 = 36756-\frac{1178^2}{38} = 36756-36518=238$$

Solutions · 1