EXPLAIN IT STEP WISE 

Dear student,
 

Solution:

In order to solve it, firstly we find the mean deviation about the median of the first (2n − 1) even natural numbers and then the mean deviation about the mean of the first 2n odd natural numbers and finally equate them as per the given condition.

Mean deviation about the median of the first (2n − 1) even natural numbers:

We know that the first (2n − 1) even natural numbers are:

2, 4, 6, 8 …… 2(2n − 1)

Since n is a natural number, therefore for any value of n, (2n − 1) must be an odd number.

The median (M) of the data 2, 4, 6, 8 …… 2(2n − 1) is given by

 [using the formula for last term of AP series]

Hence, the mean deviation about the median of the first (2n − 1) even natural numbers is given by

Mean deviation about the mean of the first 2n odd natural numbers:

Again, we know that the first 2n odd natural numbers are:

1, 3, 5 ….. 4n − 1

The mean () of these numbers is given by

Hence, the mean deviation about the mean of the first 2n odd natural numbers is given by

 [using, the formula for sum of n terms of an ap]

= n

Now, according to the given condition,

24 × M.D. () = 25 × M.D (M) 

Since n is a natural number, n = 13.

Regards