Question

Find the value of median if mode of following data is 20:15,20,25,18,13,15,25,15,18,17,20,25,20,18

Answer 1

The value of median is 18.

Step-by-step explanation:

We are the following data below;

15, 20, 25, 18, 13, 15, 25, 15, 18, 17, 20, 25, 20, 18

Now, arranging the above data in ascending order we get;

13, 15, 15, 15, 17, 18, 18, 18, 20, 20, 20, 25, 25, 25

For calculating median we have to first observe that the number of observations (n) in the data is even or odd;

• If n is odd, then the formula for calculating median is;

                        Median  =  $(\frac{n+1}{2} )^{th}$ observation

• If n is even, then the formula for calculating median is;

                        Median  =  $\frac{(\frac{n}{2})^{th} obs. +(\frac{n}{2}+1)^{th}obs. }{2}$

Now, in our data the number of observations is even, i.e. n = 14.

So,   Median  =  $\frac{(\frac{n}{2})^{th} obs. +(\frac{n}{2}+1)^{th}obs. }{2}$

                      =  $\frac{(\frac{14}{2})^{th} obs. +(\frac{14}{2}+1)^{th}obs. }{2}$

                      =  $\frac{(7)^{th} obs. +(8)^{th}obs. }{2}$

                      =  $\frac{18 +18 }{2}$

                      =  $\frac{36}{2}$ = 18

Hence, the median of the given data is 18.