Question

10. The median class of the following data is:
Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
No. of students 8 10 12 22 30 18
(a) 20 – 30 (b) 30 – 40 (c) 40 – 50 (d) 50 – 60

Answer 1

Answer:

b 30 -40

after calculating cumulative frequency

use the formula N/2 =100/2 =50

find the class with respective cumulative frequency equal or greater than 50

hence the median class is 30-40

Answer 2

The 52nd observation lies in the class interval 30 – 40, which means that the median class is (b) 30 – 40.

To find the median class of the given data, we need to first find the cumulative frequency of each class interval.

Marks  No. of students Cumulative frequency

0 – 10              8                      8

10 – 20             10              18

20 – 30             12             30

30 – 40            22             52

40 – 50            30             82

50 – 60            18                    100

The total number of students is 100.

The median is the middle value of the data when arranged in ascending or descending order.

To find the median class, we need to first find the cumulative frequency just greater than 50 (which is half of 100).

From the above table, we see that the cumulative frequency just greater than 50 is 52.

Therefore, the median class is the class interval in which the 52nd observation lies.

The 52nd observation lies in the class interval 30 – 40, which means that the median class is (b) 30 – 40.

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