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Daily wages of 110 workers, obtained in a survey, are tabulated below:

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

Find the modal daily wages of these workers.

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166.67

156.67

234.67

456.67

answer is A.

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Detailed Solution

To find the middle and frequency of the given table, assume the mean by A.

Class Interval	$f i$	$x i$	$d i = x i − A$	$u i = x i − A 20$	$f i u i$
100-120	10	110	-60	-3	-30
120-140	15	130	-40	-2	-30
140-160	20	150	-20	-1	-20
160-180	22	170	0	0	0
180-200	18	190	20	1	18
200-220	12	210	40	2	24
220-240	13	230	60	3	39

Thus, we get

∑ f i u i = 1, ∑ f i = 110

and

h = 120 − 100 = 20

.
The formula for mean is given by,

x ¯ = A + ∑ f i u i ∑ f i × h

.
Substitute the known values in the above formula, and we have

x ¯ = 170 + 1110 × 20 = 1870 + 2 11 = 170.2

The highest frequency that corresponds to class 160-180 is

f 1 = 22

. And, the previous frequencies are

f 0 = 20

and

f 2 = 18

. The lower limit of the modal class is

l = 160

.
The formula for the mode is given by,

= l + f 1 − f 0 2 f i − f 0 − f 2 × h = 160 + 22 − 20 2 (22) − (20) − (18) × 20 = 160 + 203 = 5003 = 166.67

Therefore, the modal class is 166.67.
Hence, the correct option is 1.

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