Question

Consider the following frequency distributions:
Class: 65-85 85-105 105-125 125-145 145-165 165-185 - 185-205

Frequency: 4 5 13 20 14 7 4

The difference of the upper limit of the median class and the lower limit of the modal class is
(a) 0 (b) 19 (c) 20 (d) 38

Answer 1

Class	Frequency	Cumulative frequency
65–85	4	4
85–105	5	9
105–125	13	22
125–145	20	42
145–165	14	56
165–185	7	63
185–205	4	67

Here, N = 67.
$\therefore \frac{N}{2}=33.5$, which lies in the interval 125–145.
Therefore, the lower limit of the median class is 125.
The highest frequency is 20, which lies in the interval 125–145.
Therefore, the upper limit of modal class is 145.
So, the required difference is 145 − 125 = 20.
Hence, the correct answer is option (c).