Question

The weights (in kg) of 50 wrestlers are recorded in the following table:

Weight (in kg)	100 – 110	110 – 120	120 – 130	130 – 140	140 – 150
Number of wrestlers	4	14	21	8	3

Find the mean weight of the wrestlers.

Answer 1

We first find the class mark of each class and then proceed as follows.

Weight (in kg)	Number of wrestler `(bb(f_i))`	Class marks `(bb(x_i))`	Deviations `bb(d_i = x_i - a)`	`bb(f_i d_i)`
100 – 110	4	105	– 20	– 80
110 – 120	14	115	– 10	– 140
120 – 130	21	a = 125	0	0
130 – 140	8	135	10	80
140 – 150	3	145	20	60
	`N = sumf_i = 50`			`sumf_i d_i = -80`

∴ Assumed mean (a) = 125

Class width (h) = 10

And total observation (N) = 50

By assumed mean method,

Mean `(barx) = a + (sumf_i d_i)/(sumf_i)`

= `125 + ((-80))/50`

= 125 – 1.6

= 123.4 kg