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 value of x and the mean mass of the apples.

Answer 1

Given, total number of apples = 250

∴ 20 + 60 + 70 + x + 60 = 250

`\implies` x = 250 – 210 = 40

Mass (in grams) C.I.	Number apples (f)	Mid value (x)	d = (xi – A)	f × d
80 – 100	20	90	–40	–800
100 – 120	60	110	–20	–1200
120 – 140	70	130(A)	0	0
140 – 160	40	150	20	800
160 – 180	60	170	40	2400
	`sumf` = 250			`sumfd` = 1200

Now, mean `overlinex = A + (sumfd)/(sumf)`

= `130 + 1200/250`

= `130 + 24/5`

= 130 + 4.8

= 134.8