Question

Given below is the distribution of total household expenditure of 200 manual workers in a city:

Expenditure (in Rs)	1000 – 1500	1500 – 2000	2000 – 2500	2500 – 3000	3000 – 3500	3500 – 4000	4000 – 4500	4500 – 5000
Number of manual workers	24	40	31	28	32	23	17	5

Find the average expenditure done by maximum number of manual workers.

Answer 1

As the class 1500-2000 has the maximum frequency, it is the modal class.
Now, `x_k = 1500, h = 500, f_k = 40, f_k-1 = 24, f_k+1 = 31`

∴ Mode, `M_0 = x_k + {ℎ ×((f_k− f_k−1))/((2f_k− f_k−1−f_k+1))}`

 = 1500 + `{500 xx ((40-24))/((2 xx40-24-31))}`

 = `1500 + {500xx 16/25}`

= (1500 + 320)

= 1820

Hence, mode = Rs 1820