The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is :

Question

The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is : (A) 4.01 (B) 3.99 (C) 3.98 (D) 4.02

Tardigrade Admin · Accepted Answer

(∑ xi/20) = 10 ⇒ ∑ xi = 200 ...(i) (∑ xi2/20) = 100 = 4 ⇒ ∑ xi 2= 2080 ...(ii) Actual mean = (200 - 9 + 11/20) = (202/20) Variance = (2080 - 81 + 121/20) - ((202/20))2 = 3.99

Q. The mean and variance of $20$ observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was $11$ . Then the correct variance is :

$4.01$

$3.99$

$3.98$

$4.02$

$\frac{\sum x _{i}}{20} = 10 \Rightarrow \sum x_{i} = 200 ... (i)$
$\frac{\sum x _{i}^{2}}{20} = 100 = 4 \Rightarrow \sum x_{i}^{2} = 2080 ... (ii)$
Actual mean $= \frac{200 - 9 + 11}{20} = \frac{202}{20}$
Variance $= \frac{2080 - 81 + 121}{20} - (\frac{202}{20})^{2} = 3.99$

Q. The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is :

4.01

3.99

3.98

4.02