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 weights (in kg) of 15 students are : 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. 

The weight 44 kg is replaced by 46 kg and 27 kg by 25 kg.

To do:

We have to find the median and the new median.

Solution:

We know that,

Median $= \frac{1}{2}[\frac{n}{2}th\ term+(\frac{n}{2}+1)th\ term]$  (when $n$ is even)

$=\frac{n+1}{2}th\ term$    (when $n$ is odd)

Arranging the data in ascending order, we get,

$27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45$

Here,

$n = 15$ which is odd

Therefore,

Median $= \frac{15+1}{2}th\ term$

$= 8$th term

$=35$  

44 kg is replaced by 46 kg and 27 kg by 25 kg.

The new ascending order of the data is,

$25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46$

Therefore,

New median $=8th$ term

$=35$ 

The original median and the new median both are equal to $35\ kg$.

Updated on: 10-Oct-2022

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