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?
Given the numbers are 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33
Arranging the numbers in ascending order
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
n = 11 (odd)
$\therefore$ Median $=\left(\frac{\mathrm{n}+1}{2}\right)^{\text {th }}$ value
$=\left(\frac{11+1}{2}\right)^{\mathrm{th}}$ value
$=6^{\text {th }}$ 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)
$\therefore$ New Median $=\left(\frac{\mathrm{n}+1}{2}\right)^{\text {th }}$ value
$=\left(\frac{11+1}{2}\right)^{\text {th }}$ value
$=6^{\text {th }}$ value $=58$