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.

Question

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.

Homi · Accepted Answer

We will find the mean daily wages using the step deviation method.

Step 1 — Prepare the table

Let's calculate the class mark ( $x_i$ ) for each interval. We use the formula $x_i = (\text{Upper limit} + \text{Lower limit}) / 2$ . The class size ( $h$ ) is $\textbf{20}$ . We take the assumed mean ( $a$ ) as $\textbf{550}$ . Then we calculate $d_i = x_i - a$ and $u_i = d_i / h$ . Finally, we find $f_i u_i$ .

| Daily wages (in ₹) | Number of workers ( $f_i$ ) | Class Mark ( $x_i$ ) | $d_i = x_i - 550$ | $u_i = d_i / 20$ | $f_i u_i$ | | :--- | :--- | :--- | :--- | :--- | :--- | | 500 - 520 | 12 | 510 | -40 | -2 | -24 | | 520 - 540 | 14 | 530 | -20 | -1 | -14 | | 540 - 560 | 8 | 550 | 0 | 0 | 0 | | 560 - 580 | 6 | 570 | 20 | 1 | 6 | | 580 - 600 | 10 | 590 | 40 | 2 | 20 | | Total | 50 | | | | -12 |

Step 2 — Calculate the mean

From the table, we have the sum of frequencies and the sum of $f_i u_i$ . The sum of frequencies is $\sum f_i = \textbf{50}$ . The sum of $f_i u_i$ is $\sum f_i u_i = \textbf{-12}$ . The assumed mean is $a = \textbf{550}$ . The class size is $h = \textbf{20}$ . We use the step deviation formula for the mean.

$\text{Mean} (\bar{x}) = a + \left( \frac{\sum f_i u_i}{\sum f_i} \right) \times h$

$= 550 + \left( \frac{-12}{50} \right) \times 20$

$= 550 + \left( \frac{-240}{50} \right)$

$= 550 - 4.8$

$\boxed{₹545.20}$

Answer

The mean daily wages of the workers of the factory is ₹545.20.

Question 2

Answer

More questions in Exercise 13.1