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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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