How to Find Decimal Median

Introduction to how to find decimal median:

Statistically median is defined as a measure of central tendency which gives the value of the middle-most observation in the data. Of course the median can be a decimal. Decimal median is the median of set of decimal numbers and when the set of observations are even and the middle two values are 1odd and 1 even then the median of that set will be decimal median. . This article deals how to find decimal median with example problems and its solutions.


Formula to find decimal median


To find the decimal median we need to arrange the given list of data in ascending order.

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 }


Find decimal median Example problems:
Example 1:

Find the decimal median of the given observations 5.2, 12.5, 1.0, 2.1, 5.6, 2.4, 17.5

Solution:

Ascending order of given data,

1.0, 2.1, 2.4, 5.2, 5.6, 12.5, 17.5

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 5. 2.

Example 2:

Find the decimal median of the given observations 20, 7, 9, 12, 7, 8, 5,3,15, 15

Solution:

Ascending order of given data,

3, 5, 7, 7, 8, 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) th data)) / 2

Note: Here the two middle numbers is 1 odd and another 1 is even So the median will be decimal median

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

=` (8+9)/2`

= `17/2`

= 8.5

Hence the median is 8.5.

Example 3:

Find the decimal median of this observation 2.0, 2.9, 2.8, 3.3, 4.2, 3.8, 4.3, 2.5?

Solution:

Ascending order of given data,

2.0, 2.5, 2.8, 2.9, 3.3, 3.8, 4.2, 4.3

Number of observation = n= 8

N= even,

Median = Average of middle two values

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

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

= `(2.9+3.3)/2`

= 3.1

Hence the median is 3.1.

Example 4:

Find the median of the observation 6, 2.8, 2.4, 1.5, 5.4

Solution:

Ascending order of given data,

1.5, 2.4, 2.8, 5.4, 6

Here the number of observations = 5

n= 5 (odd)

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

= `(5+1)/2`

= `6/2`

= 3

Median is the 3rd observation.

Hence median = 2.8 .