Consider the following distribution of daily wages of 50 workers of a factory
Find the mean daily wages of the workers of the factory by using an appropriate method.
Solution:
Reasoning:
We will use Assumed Mean Method to solve this question because the data given is large.
When the numerical values of xᵢ and fᵢ are large, then finding the product of xᵢ and fᵢ becomes tedious. We can change each xᵢ to a smaller number so that our calculations become easy. Now we have to subtract a fixed number from each of these xᵢ.
- The first step is to choose one value among xᵢ as the assumed mean and denote it by ‘ a ’. Also, to further reduce our calculation work, we may take ‘ a ’ to be that xᵢ which lies in the center of x₁, x₂, . . ., xₙ. So, we can choose a.
- The second step is to find the difference ‘ dᵢ ’. That is the difference between a and each of the xᵢ. The deviation of ‘ a ’ from each of the xᵢ. i.e., dᵢ = xᵢ - a
- The third step is to find the product of dᵢ with the corresponding fᵢ. After that take the sum of all the fᵢdᵢ.
Now use the values in the below formula
Mean, (x) = a + Σfᵢdᵢ/ Σfᵢ
We know that, Class mark, xᵢ = (Upper class limit + Lower class limit )/2
Taking assumed mean, a = 550
It can be observed from the table,
Σfᵢ = 50
Σfᵢdᵢ= - 240
Mean, (x) = a + (Σfᵢdᵢ/Σfᵢ)
= 550 + (- 240/50)
= 550 - 24/5
= 550 - 4.8
= 545.2
Hence, the calculated mean daily wages of the workers of the factory is ₹ 545.20.
☛ Check: Class 10 Maths NCERT Solutions Chapter 14
Video Solution:
Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.
NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.1 Question 2
Summary:
The following distribution of daily wages of 50 workers of a factory is given. The mean daily wages of the workers of the factory having 50 workers is calculated as ₹ 545.20 using assumed mean method.
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