I can`t understand example 2 plz. explain it i have my maths exam on Friday.

In the said example, we have to find that value of a natural number n for which the values corresponding to 25 times the mean deviation about the median of the first (2n − 1) even natural numbers and 24 times the mean deviation about the mean of the first 2n odd natural numbers are equal.

**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.

**Try to go through it 2-3 times and study carefully. It just involves simple calculations based on the formula for mean deviation about median and mean. **

**
**