Question

Compare the modal ages of two groups of students appearing for an entrance test:

Age (in years):	16-18	18-20	20-22	22-24	24-26
Group A:	50	78	46	28	23
Group B:	54	89	40	25	17

Answer 1

Age (in years)	Group ‘A’	Group ‘B’
16–18	50	54
18–20	78	89
20–22	46	40
22–24	28	25
24–25	23	17

For group “A”

The maximum frequency is 78 so the modal class is 18–20.

Therefore,

l = 18

h = 2

f = 78

f1 = 50

f2 = 46

Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`

`=18+(78-50)/(156-50-46)xx2`

`=18+28/60xx2`

`=18+14/15`

= 18 + 0.93

= 18.93

For group “B”

The maximum frequency 89 so modal class 18–20.

Therefore,

l = 18

h = 2

f = 89

f1 = 54

f2 = 40

Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`

`=18+(89-54)/(178-54-40)xx2`

`=18+35/84xx2`

`=18+35/42`

`=18+5/6`

= 18 + 0.83

= 18.83

Thus, the modal age of group A is 18.93 years whereas the modal age of group B is 18.83 years.