The mean and standard deviation of 15 observations are found to be 8 and 3 respectively.

Question

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to \_\_\_\_

Answer: 17

Accepted Answer

$\sum x_i^2/15-64=9 \implies \sum x_i^2 = 15\times73=1095$

Corrected mean $= 9$ (using the standard companion correction, sum becomes $120-5+20=135 \Rightarrow 135/15=9$).

Corrected sum of squares $= 1095-25+400=1470$

$$\text{Correct variance} = \frac{1470}{15}-9^2 = 98-81=17$$

Solutions · 1