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:

$41, 43, 127, 99, 61, 92, 71, 58, 57$

58 is replaced by 85

To do:

We have to find 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,

$41, 43, 57, 58, 61, 71, 92, 99, 127$

Here,

$n = 9$ which is odd

Therefore,

Median $= \frac{9+1}{2}th\ term$

$= 5$th term

$=61$  

58 is replaced by 85.

The new ascending order of the data is,

$41, 43, 57, 61, 71, 92, 92, 99, 127$

Therefore,

New median $=5th$ term

$=71$

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Updated on: 10-Oct-2022

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