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Find the mean of the following distribution.The daily wages of 50 employees in an organization are given below:Daily wages (in $)100 - 150150 - 200200 - 250250 - 300Number of Workers1213178Find the mean daily wages.

Question

Find the mean of the following distribution.The daily wages of 50 employees in an organization are given below:Daily wages (in $)100 - 150150 - 200200 - 250250 - 300Number of Workers1213178Find the mean daily wages.

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Solution

To find the mean of the distribution, we need to follow these steps:

  1. Find the midpoint of each wage range. This is done by adding the lower limit to the upper limit and dividing by 2.

    For the wage range 100−100 - 150, the midpoint is $125.

    For the wage range 150−150 - 200, the midpoint is $175.

    For the wage range 200−200 - 250, the midpoint is $225.

    For the wage range 250−250 - 300, the midpoint is $275.

  2. Multiply the midpoint of each wage range by the number of workers earning within that range.

    For the wage range 100−100 - 150, the total wage is 12 * 125=125 = 1500.

    For the wage range 150−150 - 200, the total wage is 13 * 175=175 = 2275.

    For the wage range 200−200 - 250, the total wage is 17 * 225=225 = 3825.

    For the wage range 250−250 - 300, the total wage is 8 * 275=275 = 2200.

  3. Add up all the total wages to get the sum of wages.

    Sum of wages = 1500+1500 + 2275 + 3825+3825 + 2200 = $9800.

  4. Divide the sum of wages by the total number of workers to get the mean wage.

    Mean wage = Sum of wages / Total number of workers = 9800/50=9800 / 50 = 196.

So, the mean daily wage of the 50 employees is $196.

This problem has been solved

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