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?

Solution

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Let XX be the hourly wage of nurse. X1X_1 is the nurse's aides, X2X_2 is the practical nurse and X3X_3 is the registered nurse.

X1=$8X_1=\$8, X2=$15X_2=\$15 and X3=$24X_3=\$24.

Let ww be the number of nurses. w1=50w_1=50, w2=50w_2=50 and w3=100w_3=100.

Weighted mean is Xˉ\bar{X}

Xˉ=ΣwXΣw=50×8+50×15+100×2450+50+100=400+750+2400200=3550200=17.75\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\$17.75.

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