Question

A scientist conducted a research and got the observations: $20,30,50,20,40$ and $80$. Find the sum of the deviations of the observations from their mean.

• A. $10$
• B. $20$
• C. $30$
• D. $0$

Answer 1

Answer: (D)

$0$

Let the mean be $\overline{x}$.
Now deviation about mean will be $\overline{x}-x_i$.
Hence
$(\overline{x}-20)+(\overline{x}-30)+(\overline{x}-50)+(\overline{x}-20)+...$
$=N\left(\overline{x}\right)-(20+30+50+...)$
$=N\left(\overline{x}\right)-\sum x_i$
$=N\left(\overline{x}\right)-N\left(\overline{x}\right)$
$=0$