#### Question

The Loris Healthcare System employs 200 persons on the nursing staff. Fifty are nurse’s aides, 50 are practical nurses, and 100 are registered nurses. Nurse’s aides receive $8 an hour, practical nurses$15 an hour, and registered nurses \$24 an hour. What is the weighted mean hourly wage?

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Let $X$ be the hourly wage of nurse. $X_1$ is the nurse's aides, $X_2$ is the practical nurse and $X_3$ is the registered nurse.

$X_1=\8$, $X_2=\15$ and $X_3=\24$.

Let $w$ be the number of nurses. $w_1=50$, $w_2=50$ and $w_3=100$.

Weighted mean is $\bar{X}$

\begin{align*} \bar{X}&=\frac{\Sigma wX}{\Sigma w}\\ &=\frac{50 \times 8+50 \times 15+ 100 \times 24}{50+50+100}\\ &=\frac{400+750+2400}{200}\\ &=\frac{3550}{200}\\ &=17.75 \end{align*}

Weighted mean hourly wage is $\17.75$.

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