Question

Find the median of the following data 53, 43, 34, 35, 60, 63, 57, 42, 55, 49. If 34 is replaced by 73 and 57 by 30 in the above data, find the new median?

Answer 1

Given numbers are 53, 43, 34, 35, 60, 63, 57, 42, 55, 49.

Arrange the numbers in ascending order. So, numbers are 34, 35, 42, 43, 49, 53, 55, 57, 60, 63.

Total number of observations is 10. Since, n is even,

Median = $\frac{1}{2}\left[\right(\frac{n}{2})th+(\frac{n}{2}+1\left)th\right]$observation.

Median = $\frac{1}{2}\left[\right(\frac{10}{2})th+(\frac{10}{2}+1\left)th\right]$ observation.

median = $\frac{1}{2}\times$(5th + 6th) observation

median = $\frac{1}{2}\times$(49 + 53)

median = 1022

median= 51

ATQ, 34 is replaced by 73 and 57 by 30. So, numbers are 30, 35, 42, 43, 49, 53, 55, 60, 63, 73. Total number of observations is 10. Since, n is even we have to use the formula to calculate the median of the given observations.

Median = $\frac{1}{2}\left[\right(\frac{n}{2})th+(\frac{n}{2}+1\left)th\right]$ observation.

Median = $\frac{1}{2}\left[\right(\frac{10}{2})th+(\frac{10}{2}+1\left)th\right]$ observation.

median = $\frac{1}{2}\times$(5th + 6th)observation

median = $\frac{1}{2}\times$(49 + 53)

median = $\frac{102}{2}$

median= 51

The new median of the given observations is 51.