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 |
Mathematics
Class 8
990
Knowledge
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.