Question

In the following table, the toll (in ₹) paid by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method.

Toll (Rupees)	300 - 400	400 - 500	500 - 600	600 - 700	700 - 800
No. of vehicles	80	110	120	70	40

Answer 1

Class (Toll in ₹)	Class Mark xi	Deviations di = xi − A di = xi − 550	Frequency (Number of vehicles fi)	Frequency × deviation fi × di
300-400	350	−200	80	−16000
400-500	450	−100	110	−11000
500-600	550 = A	0	120	0
600-700	650	100	70	7000
700-800	750	200	40	8000
			∑fi = 420	∑fidi = −12000

Here, ∑f_id_i = −12000, ∑f_i = 420

`bard = (sumf_i d_i)/(sumf_i) = (-12000)/420 = -28.57`

Mean `(bar"X") = "A" + bar"d"`

= 550 + (−28.57)

= 521.43

Hence, the mean of the toll is Rs 521.43.