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

Compute the mean daily wages and modal daily wages of these workers.

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Mean daily wages = Rs 170.18 and modal daily wages = Rs 166.67.

Mean daily wages = Rs 160.18 and modal daily wages = Rs 166.67.

Mean daily wages = Rs 150.18 and modal daily wages = Rs 166.67.

Mean daily wages = Rs 170.18 and modal daily wages = Rs 156.67.

answer is A.

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Detailed Solution

Given data is,
Question Image

We know that, in direct method, we first find the class marks of the class interval.
Then these class marks would serve as the representative of the whole class and are represented by

x i

.
For each class interval, we have the frequency

f i

corresponding to the class mark

x i

. Class marks =

\frac{(lower limit + upper limit)}{2}

.
Then find the product of

f i

, &

x i

for each class interval.
To find the mean, prepare the following table.
Now, let us find the mean daily wages by using the Direct method.
Daily wages of 110 workers, obtained in a survey, are tabulated below:Compute the mean daily wages of these workers. | Snapsolve

Daily wages of 110 workers, obtained in a survey, are tabulated below:Compute the mean daily wages of these workers. | Snapsolve

From the above table

Σ f i x i

= 18720

and

Σ f i = 110

Mean = Σ f i x i Σ f i Mean = 18720110 Mean = 187211 Mean = 170.18

Hence, the mean daily wages are Rs 170.18.
Let us find mode from the given data.
Question Image

Here, maximum frequency f1 = 22.
So, the corresponding class 160 – 180 is a modal class.
We know that,

Mode = 1 + f 1 − f 0 2 f 1 − f 0 − f 2 × h

.
l = lower limit of the modal class = 160
h = size of the class intervals = 20
f1 = frequency of the modal class = 22
f0 = frequency of the class preceding the modal class = 20
f2 = frequency of the class succeeds in the modal class = 18
Now, with above values, let us find mode.
Question Image

Hence, the modal wages of workers is Rs 166.67.
The mean daily wages of workers are Rs 170.18 and the modal daily wages of workers are Rs 166.67.
The correct option is (1).

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