description
 Computation of Measures of Central Tendency  Median of Grouped Data
 cumulative frequency column
notes
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:
Marks 
2030 
3040 
4050 
5060 
6070 
7080 
8090 
No. of students 
5 
15 
25 
20 
7 
8 
10 
Solution:
Marks 
f 
cf 
2030 
5 
5 
3040 
15 
20 
4050 
25 
45 
5060 
20 
65 
6070 
7 
72 
7080 
8 
80 
8090 
10 
90 

N=∑fi= 90 

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= 5060, 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"`
Video Tutorials
Shaalaa.com  Statistics part 2 (Mean Median Mode)
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Related QuestionsVIEW ALL [24]
Estimate the median for the given data by drawing an ogive:
Class  010  1020  2030  3040  4050 
Frequency  4  9  15  14  8 
If the mean of the following distribution is 3, find the value of p.
x  1  2  3  5  p + 4 
f  9  6  9  3  6 