100 students were randomly picked up from a class and the frequency distribution of the number of hours per week they spent playing outdoor games was obtained as follows:

No. of hours per week

1-4

4-7

7-10

10-13

13-16

16-19

No. of students

6

30

40

16

4

4

Determine the median number of hours spent by the students playing in a week.

Asked by Topperlearning User | 10th Apr, 2014, 01:52: PM

Expert Answer:

We can find cumulative frequencies with their respective class intervals as below: 

 

No. of hours per week 

Number of students

(fi)

Cumulative frequency

1 - 4

6

6

4 - 7

30

30 + 6 = 36

7 - 10

40

36 + 40 = 76

10 - 13

16

76 + 16 = 92

13 - 16

4

92 + 4 = 96

16 - 19

4

96 + 4 = 100

 

Total (n) = 100

 

 

 

Now we may observe that cumulative frequency just greater than is 76 belonging to class interval 7 - 10.

Median class = 7 - 10

Lower limit (l) of median class = 7

Cumulative frequency (cf) of class preceding median class = 36

Frequency (f) of median class = 40

Class size (h) = 3

Median

          

           = 8.05


Answered by  | 10th Apr, 2014, 03:52: PM