Question

find the median of the first five odd intigers. if the sixth odd intiger is also included, find the difference of medians in the two cases​

Answer 1

Answer:

If the sixth odd integer is also included, find the difference of medians in the two cases. 1, 3, 5, 7, 9. The number of variates = 5, which is odd. Therefore, median = 5+12th variate = 3th variate = 5.

Answer 2

Given :

First five odd integers.

Sixth integer is also included.

To Find :

(i) The median of the first five odd integers.

(ii)  The difference of medians when the sixth odd integer is also included

Solution :

(i) The first five odd integers are 1, 3, 5, 7, 9

The number of observation (n) is 5, which is odd.

We know, when n is odd, the( $\frac{n+1}{2}$)th observation is the median of the given data.

So, The median of first five odd integers =  ( $\frac{5 + 1}{2}$)th term

                                                                   =   3rd observation

                                                                   =   5

∴ The median of first five odd integers is 5

(ii) The first six odd integers are 1, 3, 5, 7, 9, 11

The number of observation (n) is 6, which is even.

As n is even, the mean of ($\frac{n}{2}$)th observation and [(

The median of the first six odd integers = $\frac{1}{2} [\frac{n}{2} th+ (\frac{n}{2} +1)th]$

                                                                  = $\frac{1}{2} [\frac{6}{2} th+ (\frac{6}{2} +1)th]$

                                                                  = $\frac{1}{2}$ [3rd term + 4th term]

                                                                  = $\frac{1}{2}$ × (5 + 7]

                                                                  = 6

∴ The median of first six odd integers is 6

∴ The difference of the median of first six odd integers and first five integers is (6 - 5) = 1