The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.
Given the numbers are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30
Arranging the numbers in ascending order
27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45.
n = 15 (odd)
$\therefore$ New Median $=\left(\frac{\mathrm{n}+1}{2}\right)^{\text {th }}$ value
$=\left(\frac{15+1}{2}\right)^{\text {th }}$ value
$=8^{\text {th }}$ value $=35 \mathrm{~kg}$
If the weight 44 kg is replaced by 46 kg and 27 kg is replaced by 25 kg
Then the new values be in order are: 25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46
$\therefore$ New Median $=\left(\frac{\mathrm{n}+1}{2}\right)^{\text {th }}$ value
$=\left(\frac{15+1}{2}\right)^{\text {th }}$ value
$=8^{\text {th }}$ value $=35 \mathrm{~kg}$