Question

the union negotiators counter that the “average” employee misses only 3 days of work each year. explain how both sides might be correct, identifying the measure of center you think each side is using and why the difference might exist.

1. payroll a small warehouse employs a supervisor at $1200 a week, an inventory manager at $700 a week, six stock boys at $400 a week, and four drivers at $500 a week.

a) find the mean and median wage.
b) how many employees earn more than the mean wage?
c) which measure of center best describes a typical wage at this company: the mean or the median?
d) which measure of spread would best describe the payroll: the range, the iqr, or the standard deviation? why?

1. singers the frequency table shows the heights (in inches) of 130 members of a choir.

height count height count
60 2 69 5
61 6 70 11

Explanation:

Step1: Calculate the total number of employees

There is 1 supervisor, 1 inventory - manager, 6 stock - boys, and 4 drivers. So the total number of employees $n=1 + 1+6 + 4=12$.

Step2: Calculate the total wage

The supervisor earns $1200$ a week, the inventory - manager earns $700$ a week, 6 stock - boys earn $400$ each a week, and 4 drivers earn $500$ each a week. The total wage $T=1200\times1 + 700\times1+400\times6 + 500\times4=1200 + 700+2400 + 2000=6300$.

Step3: Calculate the mean wage

The mean wage $\bar{x}=\frac{T}{n}=\frac{6300}{12}=525$.

Step4: Arrange the wages in ascending order

The wages are: 400, 400, 400, 400, 400, 400, 500, 500, 500, 500, 700, 1200. Since $n = 12$ (an even - numbered data set), the median is the average of the 6th and 7th ordered values. The median $M=\frac{400 + 500}{2}=450$.

Step5: Count the number of employees earning more than the mean wage

The supervisor ($1200$) and the inventory - manager ($700$) earn more than the mean wage of $525$. So 2 employees earn more than the mean wage.

Step6: Determine the best measure of center

The median best describes a typical wage at this company because the mean is affected by the relatively high - wage supervisor. The supervisor's wage is an outlier, and the median is less sensitive to outliers.

Step7: Determine the best measure of spread

The IQR (Inter - Quartile Range) would best describe the payroll. The range is affected by the outlier (the supervisor's wage). The standard deviation is also affected by outliers. The IQR is less sensitive to outliers and gives a better measure of the spread of the middle 50% of the data.

Answer:

a) Mean wage: $525$, Median wage: $450$.
b) 2 employees.
c) Median.
d) IQR, because it is less sensitive to outliers.