Median Examples

 

Example 1: Calculate the median for the following data:

Marks	0 - 10	10 - 30	30 - 60	60 - 80	80 - 90
Number of students	6	20	37	10	7

Solution:

We need to calculate the cumulative frequencies to find the median.

Marks	Number of students	Cumulative frequency (cf)
0 - 20	6	0 + 6	6
20 - 40	20	6 + 20	26
40 - 60	37	26 + 37	63
60 - 80	10	63 + 10	73
80 - 100	7	73 + 7	80

N = sum of cf = 80, N/2 = 80/2 = 40

Since n is even, we will find the average of the n/2^th and the (n/2 +1)^th observation i.e. the cumulative frequency greater than 40 is 63 and the class is 40 - 60. Hence, the median class is 40 - 60.

l = 40, f = 37, c = 26, h = 20 

Using Median formula:

Median = l + [(n/2−c)/f] × h

= 40 + [(37 - 26)/40] × 20

= 40 + (11/40) × 20

= 40 + (220/40)

= 40 + 5.5

= 45.5

Therefore, the median is 45.5.

Example 2: A survey on the heights (in cm) of 50 girls of class X was conducted at a school and the following data was obtained:

Height (in cm)	120-130	130-140	140-150	150-160	160-170	Total
Number of girls	2	8	12	20	8	50

Find the median of the above grouped data.

Solution:

To find the median, we need cumulative frequencies.

Consider the table:

Class Intervals	No. of girls (fi)	Cumulative frequency (c)
120-130	2	2
130-140	8	2 + 8 = 10
140-150	12	10 + 12 = 22
150-160	20	22 + 20 = 42
160-170	8	42 + 8 = 50

n = 50, n/2 = 25

Median class = 150 - 160

l = 150, c = 22, f = 20, h = 10

Median = l + [(n/2−c)/f] × h = 150 + [((50/2) - 22)/20] × 10 = 150 + 1.5 = 151.5

Therefore, the Median = 151.5

 

Example 3: The following table gives the weekly expenditure of 200 families. Find the median of the weekly expenditure.

Weekly Expenditure ($)	0-1000	1000-2000	2000-3000	3000-4000	4000-5000	Total
Number of Families	34	12	43	60	51	200

Find the median of the above-grouped data.

• Solution:

To find the median, we need cumulative frequencies.

Consider the table:

Weekly Expenditure	No. of families (fi)	Cumulative frequency (c)
0 - 1000	34	34
1000 - 2000	12	34 + 12 = 46
2000 - 3000	43	46 + 43 = 89
3000 - 4000	60	89 + 60 = 149
4000 - 5000	51	159 + 51 = 200

 n = 200, n/2 = 200/2 = 100

Median Class = 3000 - 4000

l = 3000, c = 89, f = 60, h = 1000

Median = l + [(n/2−c)/f] × h = 3000 + [(200/2 - 89)/60] × 1000 = 3000 + 183 = 3183.

• Therefore, the median is 3183

 

Example 4 : The following data represents the survey regarding the heights (in cm) of 51 girls of Class x. Find the median height.

Height (in cm)	Number of Girls
Less than 140	4
Less than 145	11
Less than 150	29
Less than 155	40
Less than 160	46
Less than 165	51

 

Put your answer of Example 4 in the comment box 

 

Example 5 : Calculate the Median of Grouped Data

Suppose we have the following frequency distribution that shows the exam scored receive by 40 students in a certain class:

Put your answer of Example 5 in the comment box