Calculate the mean deviation about the mean of the set of first natural numbers when is an even number.

Solution:

It is given that set of first natural numbers when is an even number.

We now need to find the mean deviation about the mean

It is known that the first natural numbers are . And given is even number.

Therefore the mean is,

Deviations of numbers from the mean are as shown below,

Or,

Above eq. can be written as

Or,

Therefore, the absolute values of deviation from the mean is

Sum of absolute values of deviations from the mean, is

It can be written as

It is known that the sum of first natural numbers

Hence, the mean deviation about the mean is

M.D

M.

M.

As a result, is the mean deviation about the mean of the set of first natural numbers when is an even number.