Question

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Answer 1

Question:

Consider the following distribution of daily wages of 50 workers of a factory and find the mean of the daily wages.

$\displaystyle{\begin{array}{|c|c|}\cline{1-2}\bf\:Class\:(\:Daily\:wages\:in\:Rs\:) & \bf\:Frequency\\\cline{1-2}\sf\:500\:-\:520 & \sf\:12\\\cline{1-2}\sf\:520\:-\:540 & \sf\:14\\\cline{1-2}\sf\:540\:-\:560 & \sf\:8\\\cline{1-2}\sf\:560\:-\:580 & \sf\:6\\\cline{1-2}\sf\:580\:-\:600 & \sf\:10\\\cline{1-2}\end{array}}$

Answer:

The mean of the daily wages of 50 workers is 545.2 Rs.

Step-by-step-explanation:

We have given the frequency distribution of the daily wages of 50 workers.

We have to find the mean of the daily wages of those workers.

Now,

$\displaystyle{\begin{array}{|c|c|c|c|}\cline{1-4}\bf\:Class\:(\:Daily\:wages\:in\:Rs\:) & \bf\:Class\:mark\:(\:x_i\:) & \bf\:Frequency\:(\:f_i\:) & \bf\:x_i\:f_i\\\cline{1-4}\sf\:500\:-\:520 & \sf\:510 & \sf\:12 & \sf\:6120\\\cline{1-4}\sf\:520\:-\:540 & \sf\:530 & \sf\:14 & \sf\:7420\\\cline{1-4}\sf\:540\:-\:560 & \sf\:550 & \sf\:8 & \sf\:4400\\\cline{1-4}\sf\:560\:-\:580 & \sf\:570 & \sf\:6 & \sf\:3420\\\cline{1-4}\sf\:580\:-\:600 & \sf\:590 & \sf\:10 & \sf\:5900\\\cline{1-4}& & \sf\:N\:=\:\sum\:f_i\:=\:50 & \sf\:\sum\:x_i\:f_i\:=\:27260\\\cline{1-4}\end{array}}$

Now,

$\displaystyle{\pink{\sf\:Mean\:\overline{X}\:=\:\dfrac{\sum\:x_i\:f_i}{\sum\:f_i}}\sf\:\:\:-\:-\:-\:[\:Formula\:]}$

$\displaystyle{\implies\sf\:Mean\:\overline{X}\:=\:\cancel{\dfrac{27260}{50}}}$

$\displaystyle{\implies\sf\:Mean\:\overline{X}\:=\:\cancel{\dfrac{13630}{25}}}$

$\displaystyle{\implies\sf\:Mean\:\overline{X}\:=\:\cancel{\dfrac{2726}{5}}}$

$\displaystyle{\implies\boxed{\red{\sf\:Mean\:\overline{X}\:=\:545.2\:Rs}}}$

The mean of the daily wages of 50 workers is 545.2 Rs.