Question

Daily wages of 110 workers, obtained in a survey, are tabulated below:
Compute the mean daily wages and modal daily wages of these workers.
Daily
Wages
(in Rs.)
100-120 120-140 140-160 160-180 180-200 200-220 220-240
Number
of
Workers
10 15 20 22 18 12 13

Answer 1

Answer:

Mean = 170.1818

Mode  = 166.6667

Step-by-step explanation:

The mean of the grouped frequency distribution is calculate by:

Mean is calculate by formula using:

Mean = A + $\frac{\sum fd}{n} h$

⇒ Mean = 170 + $\frac{1}{110}20$

⇒ Mean = 170.1818

and, Mode = L + $(\frac{f_1 -f_0}{2-f_1-f_0-f_2})c$

where, L = lower boundary point of mode class = 160

f₁ = frequency of the mode class = 22

f₀= frequency of the preceding class = 20

f₂= frequency of the succeeding class = 18

c = class length of mode class = 20

⇒ Mode = 160 + ($\frac{22-20}{2.22-20-18}$)20

=160+6.6667

=166.6667

Answer 2

Mean wages = Rs 170.182 and modal wages = Rs 166.667

1. Calculation of mean

Mean

Hence, mean daily wages are Rs 170.182.

2. Calculation of mode

Here, maximum frequency fm = 22. So corresponding class 160 – 180 is modal class.

L = lower boundary of modal class = 160

fm = maximum frequency = 22

f1 = frequency of pre modal class = 20

f2 = frequency of post modal class = 18

h = width of modal class = 180 – 160 = 20

= 160 + 6.67

∴ Mode = 166.67

Therefore, modal wages of workers is Rs 166.67.