Question

Show that the sum of deviations of the observation from their arithmetic mean is zero with the help of
suitable
example...
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Answer 1

Answer:

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 = (3+4+6+8+14) / 5

=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.

Answer 2

Answer:

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 = 3+4+6+8+14/5

=7

xi xi-1

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.