Question

The variance of data $1001,1003,1006,1007,1009,1010$ is

• A. $10$
• B. $15$
• C. $20$
• D. $50$

Answer 1

The correct option is A $10$

Variance remains unchanged on subtraction
i.e., variance of $1001,1003,1006,1007,1009,1010$ will be same as that of $1,3,6,7,9,10$
$\text{Variance}=\frac{\sum x_i^2}{n}-(\overline{x}{)}^2$
$\therefore \text{Variance}=\frac{1^2+3^2+6^2+7^2+9^2+{10}^2}{6}-{\left(\frac{1+3+6+7+9+10}{6}\right)}^2$
$=\frac{276}{6}-{\left(\frac{36}{6}\right)}^2$
$=46-36=10$