# 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 x_{i} and f_{i} are large, then finding the product of x_{i} and fi becomes tedious. we can change each x_{i} to a smaller number so that our calculations become easy. Now we have to subtract a fixed number from each of these x_{i}.

The first step is to choose one among the x_{i} as the assumed mean and denote it by ‘ a ’. Also, to further reduce our calculation work, we may take ‘ a ’ to be that x_{i} which lies in the center of x_{1}, x_{2}, . . ., x_{n}. So, we can choose a.

The second step is to find the difference ‘ d_{i} ’. That is the difference between a and each of the x_{i. }The deviation of ‘ a ’ from each of the x_{i}. i.e., d_{i} = x_{i} - a

The third step is to find the product of d_{i} with the corresponding f_{i.} After that take the sum of all the f_{i}d_{i}.

Now use the values in the below formula

Mean, (x) = a + Σf_{i}d_{i}/ Σf_{i}

We know that, Class mark, x_{i} = (Upper class limit + Lower class limit )/2

Taking assumed mean, a = 550

It can be observed from the table,

Σf_{i} = 50

Σf_{i}d_{i}= - 240

Mean, (x) = a + (Σf_{i}d_{i}/Σf_{i})

= 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.

**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:

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

The mean daily wages of the workers of the factory having 50 workers is ₹ 545.20