The distribution below gives the weight of 30 students in a class. Find the median weight of students:
Weight(in kg): 40-45 45-50 50-55 55-60 60-65 65-70 70-75
No.of students : 2 3 8 6 6 3 2
Answers
weight of no. of students
students
(Class) (frequency f) (cumulative frequency cf)
40 - 45 2 2
45 - 50 3 5
50 - 55 8 13
55 - 60 6 19
60 - 65 6 25
65 - 70 3 28
70 - 75 2 30
- N = total no. of students = ∑f = 30 N/2 = 30/2 = 15
- the cumulative frequency just greater than 15 is 19 and the corresponding class is 55 - 60 .
- therefore 55 - 60 is the median class
- l = lower limit of median class = 55
- f=frequency of the median class = 6
- F = cumulative frequency of the class preceding the median class = 13
- h = size of the median class =5
- median = l+ ( [ { (N/2) - F } /f ] * h )
= 55 + ( [ { ( 30/2 ) - 13} / 6] * 5 )
= 56.66
56.67 kg is median weight
Step-by-step explanation:
Class f cf
40-45 2 2
45-50 3 5
50-55 8 13
55-60 6 19
60-65 6 25
65-70 3 28
70-75 2 30
Total Students = 30
hence median would be Mean of 15th & 16 th students
both lies in Class 55 - 60 ( as 14 - 19 students are in that Weight range)
Median = 55 + 5 * (30/2 - 13)/6
= 55 + 5 * 2/6
= 55 + 1.67
= 56.67
56.67 kg is median weight
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