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?
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 $=71$
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