What is Median in Math

Introduction to what is median in math:

Let us see what is median in math. In general, median in math is the middle value in a set of data. Statistically median is defined as a measure of central tendency which gives the value of the middle-most observation in the data. The median in math is obtained by arranging the given list of data in ascending order. Median separates the higher value and lower vale. This article deals with what is median in math and how to find median with examples.


How to find median in math:


To find median initially we have to arrange the data values of the observations in ascending order. Then,

If n = odd {n= number of data} ,

Median = `(n+1)/2` th observation

If n= even,

Median = `(((n/2)th data ) + ((n/2) +1)th data) / 2 ` {which means average of ((n/2) + (n/2)+1)th data }


Example Problems to find median in math:

Example 1:

What is the median of the given observations 50, 125, 10, 210, 50, 24, 175

Solution:

Ascending order of given data,

10,24,50,50,125,175,210

Here the number of observations= n= 7

n= odd,

Median = `(n+1)/2 ` th observation

= `(7+1)/2`

=` 8/2`

= 4th observation

Hence median is 50.

Example 2:

Find the median of the given observations 20, 7, 9, 12, 7, 9, 5,3,15, 15

Solution:

Ascending order of given data,

3, 5, 7, 7, 9,9,12,15,15,20

Here n= 10 (even) ,

Median = `(((n/2)^(th) data) + ((n/2) +1^(th) data)) / 2`



=   ((10/2)th data) + ((10/2)+1) thdata)) / 2

= `(5^(th) data + 6^(th) data) / 2`

= `(9+9 )/ 2`

= `18/2`

= 9

Hence the median is 9.

Example 3:

What is the median of this observation 20, 29, 28, 33, 42, 38, 43, 25?

Solution:

Ascending order of given data,

20, 25, 28, 29, 33, 38, 43, 42.

Number of observation = n= 8

N= even ,

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Median = `(((n/2)th data ) + ((n/2) +1)th data) / 2 `

=((8/2)th data +(8/2)+1 th data )/2

= `(4^(th) data + 5^(th) data) / 2`

= `(29+33)/2`

= 31.

Hence the median is 31.

Example 4:

Find the median of the observation 6 ,28, 24, 15, 2, 4, 1 ,20,5

Solution:

Ascending order of given data,

1,2,4,5, 6, 15,20,24,28

Here the number of observations = 9

n= 9 (odd)

Median =`(n+1)/2` th observation

= `(9+1)/2`

= `10/2`

= 5

Median is the 5th observation.

Hence median = 6.