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 1

$\frac {∑x_i^2}{15} - 8^2 = 9$
$⇒ ∑x_i^2 = 15 × 73=1095$
Let $\bar x_c$ be corrected mean $\bar x_c=9$
$∑x_c^2= 1095 - 25 + 400 = 1470$
Correct variance,
$= \frac {1470}{15} - (9)^2$
$= 98 - 81$
$= 17$

So, the correct variance is $17$.