Question

Find the median of the following observations : 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

Answer 1

Given numbers are
46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33
Arrange in increasing order
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
n =1(odd)

∴ Median = ${\displaystyle {\left(\frac{n+1}{2}\right)}^{th}value}$

              =  ${\displaystyle {\left(\frac{11+1}{2}\right)}^{th}value}$

               = ${\displaystyle 6^{th} value=58}$

               If 92 is replaced by 99 and 41 by 43
              Then, the new values are
              33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99
              ∴ n =11 (odd)

New median ${\displaystyle {\left(\frac{n+1}{2}\right)}^{th}}$value

                 =  ${\displaystyle {\left(\frac{11+1}{2}\right)}^{th}}$value

                 = ${\displaystyle 6^{th}value}$

                  = 58 .