Question

In the following data, find the values of p and q. Also, find the median class and modal class.

Class	Frequency (f)	Cumulative frequency (cf)
100−200	11	11
200−300	12	p
300−400	10	33
400−500	q	46
500−600	20	66
600−700	14	80

Answer 1

Here, p = 11 + 12 = 23

and 33 + q = 46 ⇒ q = 46 − 33 = 13

Thus, p is 23 and q is 13.

Now,

Here the maximum class frequency is 20, and the class corresponding to this frequency is 500−600.

So, the modal class is 500−600.

Also, ∑ f = N = 80 $\Rightarrow \frac{N}{2}=40.$

The cumulative frequency just greater than 40 is 46, and the corresponding class is 400−500.

Thus, the median class is 400−500.