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:

Given observations are $46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33$.

92 is replaced by 99 and 41 by 43 in the above data.

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,

$33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92$

Here,

$n = 11$ which is odd

Therefore,

Median $= \frac{11+1}{2}th\ term$

$= 6$th term

$=58$  

2 is replaced by 99 and 41 by 43.

The new ascending order of the data is,

$33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99$

Therefore,

New median $=6th$ term

$=58$

Updated on: 10-Oct-2022

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