Question

The annual rainfall record of a city for 66 days is given in the following table:

Rainfall (in cm):	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50	50 − 60
Number of days :	22	10	8	15	5	6

The difference of upper limits of modal and median classes is ______.

विकल्प

• 10

• 15

• 20

• 30

Answer 1

The annual rainfall record of a city for 66 days is given in the following table:

Rainfall (in cm):	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50	50 − 60
Number of days :	22	10	8	15	5	6

The difference of upper limits of modal and median classes is 20.

Explanation:

Modal class is the one having the highest frequency.

Here, the highest frequency = 22 days

So modal class = 0 − 10

Now, Cumulative frequency table is:

Class − Interval	Frequency	Cumulative Frequency
0 − 10	22	22
10 − 20	10	32
20 − 30	8	40
30 − 40	15	55
40 − 50	5	60
50 − 60	6	66

Since total frequency is 66.

`N/2 = 33`

And cumulative frequency greater than or equal to 33 lies in class 20 − 30.

So, median class is 20 − 30.

∴ Upper limit of median class is 30

Thus, difference between upper limits of modal and median classes is

= 30 − 10 = 20.