Question

The algebraic sum of deviations of 8,3,7from the arithmetic mean 6 is

Answer 1

Answer:

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 xˉ=52+5+8+11+14=540=8

The algebraic sum of the deviations from the arithmetic mean is ∑(xi−xˉ)

⟹∑(xi−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.