Median of Grouped Data

Median is the middle most term of the data. Median means that when the data are arranged, the median is the middle value if the number of values is odd and the mean of the two middle values if the number of values is even. In 9th class we studied that median of ungrouped data is

1)Median for odd number of data= `(n+1)/2`, where n is the total number of data given.

Example: Find the median of 1,2,3,4,5

Median= `(n+1)/2= (5+1)/2= 3`

2)Median for even number of data

= `{(n/2)th + [(n/2)+1]th}/2`

Example: Find the median of 1,2,3,4,5,6

Median for even number of data= `{(n/2)th + [(n/2)+1]th}/2`

= `{(6/2)th + [(6/2)+1]th}/2`

= `{3rd+ 4th}/2`

= `3+4/2`

Median for even number of data= 3.5

But in this concept of class 10th we will study how to find median of grouped data. The formula to find median of grouped data is

Median= `l+ {[(N/2)- cf]/f} xx h`

l= lower limit of the median class

N= ∑fi= sum of the frequencies

cf= cumulative frequency

f= frequency of the median class

h= Class size

Example- Find the median of the following data:

Solution:

Cf of the last median class should always be equal to N

`N/2= 90/2= 45`

Median class is the class of that cf which is just more than `N/2`

therefore, Median class= 50-60, l=50,

cf is the cumulative frequency preceeding the median class

therefore, cf= 45,

f is the frequency of the median class

therefore, f=20, h=10

Median=` l+ {[(N/2)- cf]/f} xx h`

= `50+ {[45- 45]/20} xx 10`

= `50+ {0/20} xx 10`

= `50+ 0`

Median= 50

• There is a empirical relationship between the three measures of central tendency :

`3 "Median" = "Mode" + 2 "Mean"`