Question

250 apples of a box were weighed and the distribution of masses of the apples is given in the following table:

Mass (in grams)	80 – 100	100 – 120	120 – 140	140 – 160	160 – 180
Number of apples	20	60	70	x	60

Find the modal mass of the apples.

Answer 1

Mode = `l + (f_1 - f_0)/(2f_1 - f_0 - f_2) xx h`  ...(1)

Where l = lower class limit of modal class = 12

Modal class is (120 – 140), Since it consists highest frequency

∴ l = 120

h = class size = 20

f₁ = frequency of modal class = 70

f₀ = frequency of class preceding the modal class = 60

f₂ = frequency of class succeeding the modal class = 40

On putting these values in (1), we get

Modal mass or mode

= `120 + ((70 - 60)/(2 xx 70 - 60 - 40)) xx 20`

= `120 + 10/40 xx 20`

= `120 + 10/2`

= 120 + 5

= 125