Question

Find the mean salary of 60 workers of a factory from the following table:

Salary (in Rs.)	3000	4000	5000	6000	7000	8000	9000	10000	Total
Number of workers	16	12	10	8	6	4	3	1	60

Answer 1

We start solving the problem by recalling the definition of the weighted mean as the ratio of the weighted sum of observations to the sum of weights. We use this definition and use the formula of mean salary as $\dfrac{{\sum {{w_i}{x_i}} }}{{\sum {{x_i}} }}$. We then substitute the salary and the no. of workers in the formula and make the necessary calculations to get the required result.

Complete step-by-step solution:
According to the problem, we need to find the mean salary of the 60 workers of a factory from the following table:

Salary (in Rs.)	Number of workers
3000	16
4000	12
5000	10
6000	8
7000	6
8000	4
9000	3
10000	1
Total	60

We solve this problem by using the weighted mean formula as the number of workers is not the same for each salary.
Let us recall the definition of weighted mean. We know that the weighted mean is defined as the ratio of the weighted sum of observations to the sum of weights.
Weighted mean $= \dfrac{{\sum {{w_i}{x_i}} }}{{\sum {{w_i}} }}$
Where ${w_i} =$ the weight of the observation is related to ${x_i}$.
${x_i} =$ the value of the observation.
Now, make a table with the third column as a product of the first two columns.

Salary (in Rs.) ${w_i}$	Number of workers${x_i}$	${w_i}{x_i}$
3000	16	48000
4000	12	48000
5000	10	50000
6000	8	48000
7000	6	42000
8000	4	32000
9000	3	27000
10000	1	10000
Total	60	305000

Substitute the value in the weighted mean formula,
$\Rightarrow$Mean Salary $= \dfrac{{305000}}{{60}}$
Divide numerator by the denominator,
$\therefore$Mean Salary $= 5083.33$
Hence, the mean salary of 60 workers is Rs. 5083.33.

Note: We should not take the normal arithmetic mean for salaries in this case as the no. of workers is different for each salary. We should know that there are different types of means which will be used as per the requirement of the problem. We should not make calculation mistakes while solving this problem. We can also expect problems to find the mathematical average of salaries without giving information about the number of workers.