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 46kg and 27kg by 25kg, find the new median.

Explanation

by arranging the weights in increasing order, we get : 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45
Total number of observations = 15 (odd)
Required median`=((n+1)/2)`th value
`= ((15+1)/2)` th value
`16/2=8` th value
`therefore Median =35` kg
If 44kg is replaced by 46kg and 27kg by 25 kg
then the new ascending order of data is :
25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46
no. of terms=15(odd)
`therefore` new median =`((n+1)/2)`th value
`= ((15+1)/2)` th value
`16/2=8` th value
`therefore "New Median" =35` kg