I am stuck on this problem on the topic of statistics because I don't understand how these kinds of problems are solved.
If someone could explain it to me that would be a great help.
The average monthly salary paid to all employees of a company is \$5,000. Male employees receive an average of \$5,200 and female employees an average of \$4,200. Estimate the percentage of men and women working at the company.
Attempt: The total amount paid each month by the company I think it would be something like this: $X =$ amount of men, $Y =$ amount of women, then $5200X + 4200Y = 5000(X+Y)$. From that I get $X = 4Y$ but I need a second equation to substitute one of the variables, is this right or am I mistaken?
Best Answer
Let $ \$5,000$ be the average wage for this company. Denote $X$ the average salary of male employees and $Y$ the average salary of female employees. Since they all tend to the statistical average, we can write: \begin{align} 5,200 \times X + 4,200 \times Y = 5,000 \times (X+Y)\\ \implies X = 4Y \end{align} (avoided elementary number algebra, but if you are unsure I can also add that in later). Thus, the average number of males in this company is four times the number of females. In percentage style, we can write that as \begin{align} 80\% \ \text{men and} \ 20\% \ \text{women}. \end{align}