Question

The algebraic sum of the deviations from arithmetic mean is always:

• A. zero
• B. one
• C. equal
• D. unequal

Answer 1

The correct option is A zero

The algebraic sum of the deviations from the arithmetic mean is always zero.

For example: $2,5,8,11,14$ be the observations.

The arithmetic mean is $\overline{x}=\frac{2+5+8+11+14}{5}=\frac{40}{5}=8$

The algebraic sum of the deviations from the arithmetic mean is $\sum (x_i-\overline{x})$

$⟹\sum (x_i-8)=(2-8)+(5-8)+(8-8)+(11-8)+(14-8)$

$=-6-3+0+3+6=0$

Therefore, the algebraic sum of the deviations from the arithmetic mean is always zero.