Question

calculate the range of marks obtained by middle 50% of the students from the following data:
marks:
0-10,10-20,20-30,30-40,40-50
no. of students: 5,8,12,8,7
​

Answer 1

Class 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80

Frequency 2 5

8

16

9

5

3

2

Cumulative Frequency 2

7

15

31

40

45

48

50

Total number of students=n=50

2

n

=

2

50

=25

As 25<31 so 30−40 is the median class.

l is the lower limit of median class, so l=30

h is the size of class interval, so h=40−30=10

f is the frequency of median class, so f=16

F is the cumulative frequency of class preceding the median class, so F=15

Median=l+(

f

2

n

−F

)×h

Median=30+(

16

2

50

−15

)×10

Median=30+(

16

10

)×10

Median=30+(

16

100

)

Median=36.25

Hence the median =36.25