Question

Consider the data:

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:

Options

• 0

• 19

• 20

• 38

Answer 1

20

Explanation:

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

Here, `N/2 = 67/2 = 33.5`, which lies in the interval 125 – 145.

Hence, upper limit of median class is 145.

Here, we see that the highest frequency is 20, which lies in 125 – 145.

Hence, the lower limit of modal class is 125.

∴ Required difference

= Upper limit of median class – Lower limit of modal class

= 145 – 125

= 20