Question

How prove this statement that (the sum of the deviation of observation from their arithmetic mean is equal to zero.) by using group data.Can you Explain the statement by giving an example?

Answer 1

Explanation:

The sum of the deviations of a given set of observations from their arithmetic mean is always zero. It is due to the property that the arithmetic mean is characterised as the centre of gravity. i.e. sum of positive deviation from the mean is equal to the sum of negative deviations.

For example:

3,4,6,8,14

x=53+4+6+8+14=7

xi       xi−x

3          −4

4          −3

6          −1

8             1

14           7

 

∑(xi−x)=−8+8=0

Hence, the sum of the deviations about mean is 0.