Question:
Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57. If 58 is replaced by 85, what will be the new median?
Solution:
Given the numbers are 41, 43, 127, 99, 61, 92, 71, 58, 57
Arranging the numbers in ascending order
41, 43, 57, 58, 61, 71, 92, 99, 127
n = 9 (odd)
$\therefore$ New Median $=\left(\frac{\mathrm{n}+1}{2}\right)^{\text {th }}$ value
$=\left(\frac{9+1}{2}\right)^{\text {th }}$ value
If 58 is replaced by 85
Then the new values be in order are: 41, 43, 57, 61, 71, 85, 92, 99, 127
$\therefore$ New Median $=\left(\frac{\mathrm{n}+1}{2}\right)^{\text {th }}$ value
$=\left(\frac{9+1}{2}\right)^{\text {th }}$ value
$=5^{\text {th }}$ value $=71$