Question :

Find the median of the following data set which gives the marks out of 50 of 150 students in annual examination.

Marks obtained Number of Families
20 6
29 9
31 32
33 15
42 15
19 12
35 19
43 17
39 20
25 17

 

Subject

Mathematics

Standard

Class 8

Views

138

Asked By

Knowledge

Knowledge
Answer / Solution

To find the median marks of 150 students in annual examination, first arrange the marks in ascending order, then the frequency tables as follows:

Marks Obtained Number of Students (fi) Cumulative Frequency
19 12 12
20 6 12 + 6 = 18
25 17 18 + 17 = 35
29 9 35 + 9 = 44
31 22 44 + 22 = 66
33 13 66 + 13 = 79
35 19 79 + 19 = 98
39 20 98 + 20 = 118
42 15 118 + 15 = 133
43 17 133 + 17 = 150
  ∑f = 150  

Here, Total Number of Students are 150 which is an even value. Therefore, the median will be the average of the (n/2)th observation i.e.

(n/2)th observation is = 150/2 i.e. 75th.

In the cumulative frequency table above, 75th locating in 79 i.e. whose cumulative frequency is greater than or nearest to (n/2)th term.

Thus the corresponding value of x in is a median value.

Marks Obtained Number of Students (fi) Cumulative Frequency
33 13  79

So, the median value  is 33.

 

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