Question

The mean and variance of 15 observations is 20 and 64 respectively. If 55 is wrongly read as 40 as one of the observation, then the correct variance is:

• A. $\frac{247}{3}$
• B. $\frac{167}{2}$
• C. 118
• D. 96

Answer 1

Answer: (A)

$\frac{247}{3}$

Answer 2

Correct answer is (A) : $\frac{247}{3}$

$64=\frac{\sum x_i^2}{15}-(20)^2$

$\Rightarrow \sum x_i^2=6950$

$\sigma^2=\frac{6950-40^2+50^2}{15}-(21)^2$

$\frac{7850}{15}-441$

$=\frac{1235}{15}$

$=\frac{247}{3}$