Median is the value which occupies the middle position when all the observations are arranged in an ascending or descending order. It is a positional average.
(i) Construct the cumulative frequency distribution.
(ii) Find (N/2)th term
(iii) The class that contains the cumulative frequency N/2 is called the median class.
(iv) Find the median by using the formula:
Where l = Lower limit of the median class,
f = Frequency of the median class
c = Width of the median class,
N = The total frequency (∑f)
m = cumulative frequency of the class preceeding the median class
Example 1 :
The following are the marks scored by the students in the Summative Assessment exam.
Calculate the median.
Solution :
Median class = (N/2)th value
= (50/2)th value
= 25th value
Median class = 20 - 30
l = 20, N//2 = 25, m = 9, f = 15 and c = 10
Substitute.
Median = 20 + ([25 - 9]/15) x 10
= 20 + (16/15) x 10
= 20 + 10.6
= 30.6
≈ 31
Example 2 :
The following table gives the weekly expenditure of 200 families. Find the median of the weekly expenditure.
Solution :
Median class = (N/2)th value
= (200/2)th value
= 100th value
Median class = 2000 - 3000
l = 2000, N//2 = 100, m = 74, f = 54 and c = 1000
Substitute.
Median = 2000 + ([100 - 74]/54) x 1000
= 2000 + (26/54) x 1000
= 2000 + 481.5
= 2481.5
Example 3 :
The Median of the following data is 24. Find the value of x.
Solution :
Since the median is 24 and median class is 20 – 30.
l = 20 N = 55 + x, m = 30, c = 10, f = x
Substitute.
24 = 20 + {[(55 + x)/2 - 30] / x} ⋅ 10
4 = {[(x - 5)/2] / x} ⋅ 10
4 = {(x - 5) / 2x} ⋅ 10
4 = {(x - 5) / x} ⋅ 5
4 = (5x - 25) / x
4x = 5x - 25
25 = 5x - 4x
25 = x
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