Question

Find the median of the data 37, 63, 26, 45, 94, 87,54,77

Answer 1

Given:

Data : 37, 63, 26, 45, 94, 87,54,77

To Find:

the median of the data.

Solution:

As given data:

37, 63, 26, 45, 94, 87, 54, 77

First of all, we arrange the data in an ascending order

26, 37, 45, 54, 63, 77, 87, 94

Here observe that No of observations (n)= 8 is even.

so,

Median is an average of (n/2)​th term and (n/2​+1)th term

∴ Median =[ ( n/2 )​th term + ( n/2 ​+ 1 )th term​ ] / 2

             = [ 4th term + 5th term​ ] / 2

             = [ 54 + 63 ] / 2

             = 117/2

             = 58.5

Hence, the median of data is 58.5.

             

             

Answer 2

The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.

The given data is $37, 63, 26, 45, 94, 87,54,77$

Median of even number is

Median $=\frac{(\frac{n}{2} )^{th}term+(\frac{n}{2}+1 )^{th}term}{2}$

$n$ terms $=8$

Now, rewrite the data in ascending order

$26, 37, 45, 54, 63, 77, 87, 94$

So, $=\frac{(\frac{8}{2} )^{th}term+(\frac{8}{2}+1 )^{th}term}{2}$

$=\frac{4^{th} term+5^{th}term}{2}$

$=\frac{54+63}{2}$

$=\frac{117}{2}$

Hence, the median is $58.5$