Question

If $\overline{x}$ represents the mean of n observations $x_1,x_2,...,x_n$ then value of ${\sum }_{i=1}^n(x_i-\overline{x})$is :

• A. -1
• B. 0
• C. 1
• D. n-1

Answer 1

Answer: (B)

0

$\overline{x}$ is the average of all the observations. If we draw all the numbers and the mean on a number line, then half of the numbers will lie on the right side of the mean and other half on the left side. Hence, $(x_i-\overline{x})$ will give equal number of positive and negative terms whose sum will be $0$.