Question

Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, and 57. If 58 is replaced by 85, what will be the new median.

Answer 1

We will arrange this in ascending order.
So, it would be 41,43,57,58,61,71,92,99,127
There are 9 numbers, so
Median = n+1÷2th term(if n is odd)
where n= no. of observations.
Median= 9+1/2=10/2= 5th term.
In this data, 5th term is 61.
Therefore, median= 61

Now, replacing 58 by 85 we get,
41,43,57,61,71,85,92,99,127
In this data, median will be the 5th term.
Therefore median= 71
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Answer 2

Arranging the data in ascending order:

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

✪ Number of observations, n = 9 (odd)

$\therefore \: Median = ( \frac{n +1 }{2}) {}^{th} \: observation$

$= ( \frac{9 + 1}{2} ) {}^{th} \: observation$

$= ( \frac{10}{2} ) {}^{th} \: observation$

$= 5 {}^{th} \: observation$

$\star \: Value \: of \: {5}^{th} \: observations = \bold{ 61}$

If 58 is replaced by 85,

The new observations arranged in ascending order:

41, 43, 57, 61, 71, 85, 92, 99, 127

$\therefore \: New \: median = ( \frac{n + 1}{2} ) {}^{th} \: obser.$

$= ( \frac{9 + 1}{2} ) {}^{th} \: observation$

$= ( \frac{10}{2} ) {}^{th} \: observation$

$= {5}^{th} \: observation$

$\star \: Value \: of \: {5}^{th} \: observation = \bold {71}$