Question

The mean annual salary paid to all employees in a company was 1500 Kenya pounds The mean annual salaries paid to male and female employees were 1560 Kenya pounds and 1260 Kenya pounds respectively. Determine the percentages of males and females employed by the company.

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Answer 1

`Male = 80`%

`Female = 20%`%

Explanation:

Given

Annual Mean Salary = 1500

Annual Mean Salary (Male) = 1560

Annual Mean Salary (Female) = 1260

Required

Percentage of male and female employed

Represent male by m and female by 4

So, total employees = m + f

The mean of an observation is calculated as thus;

Mean = Summation of observation divided by number of observations

For Male:

Annual Mean = Total Salary/Number of males

Recall that Annual Mean = 1560

Number of males = m;

The formula becomes

`1560 = (TotalSalary)/(m)`

Multiply both sides by m

`1560 * m = (TotalSalary)/(m) * m`

`1560m = TotalSalary`

For Female:

Annual Mean = Total Salary/Number of females

Recall that Annual Mean = 1260

Number of females = f;

The formula becomes

`1260 = (TotalSalary)/(f)`

Multiply both sides by f

`1260 * f = (TotalSalary)/(f) * f`

`1260f = TotalSalary`

Total Annual Salary = Annual Salary of Male + Annual Salary of Female

Total Annual Salary = 1560m + 1260f

The mean annual salary is calculated as thus;

Mean Annual Salary = Total Annual Salary/Total Employees

Recall that Total Employees = m + f and Mean Annual Salary = 1500

So, the formula becomes

`1500 = (1560m + 1260f)/(m+f)`

Multiply both sides by m + f

`1500(m+f) = (1560m + 1260f)/(m+f) * (m+f)`

`1500(m+f) = 1560m + 1260f`

Open brackets

`1500m+1500f- = 1560m + 1260f`

Collect like terms

`1500f -1260f = 1560m - 1500m`

`240f = 60m`

Divide through by 60

`(240f)/(60) = (60m)/(60)`

`4f = m`

Reorder

`m = 4f`

At this point, the percentage male and female can be calculated;

Male = (Number of male/Total Employees) * 100%

`Male = (m)/(m+f) * 100`%

Substitute 4f for m

`Male = (4f)/(4f+f) * 100`%

`Male = (4f)/(5f) * 100`%

`Male = (4)/(5) * 100`%

`Male = 0.8 * 100`%

`Male = 80`%

If percentage of male = 80%

Percentage of Female = 100% - 80%

`Female = 20%`%