A corporation that operates five suppliers of athletic apparel in a region provides merchandise for a shoe company. The shoe company recently sought information from the five plants. One variable for which data were collected was the total money (in dollars) the company spent on medical support for its employees in the first three months of the year. Data on the number of employees at the plants are also shown below. Complete parts a and b.
Data:
Medical Employees
$7,773 125
$14,808 404
$12,392 253
$6,708 105
$3,532 70
a. Compute the weighted mean medical payments for these five plants using the numbers of employees as the weights. The weighted mean is (Round to the nearest dollar as needed.)
b. Explain why the shoe company would desire that a weighted average be computed in this situation rather than a simple numeric average. Choose one:
A. The weighted average takes into account the variation in the data instead of only providing a measure of central tendency.
B. The weighted average takes into account the numbers of employees and finds the average payment per employee instead of the average payment per plant.
C. The weighted average takes into account the numbers of employees and is a more reasonable measure of the average payments than would be an unweighted average.
D. The weighted average takes into account both the mean and the median of the data, instead of only providing the simpler measure of only the mean.
Suppose there is an investigation to determine whether the increased availability of generic drugs, Internet drug purchases, and cost controls have reduced out-of-pocket drug expenses. As a part of the investigation, a random sample of 196 privately insured adults with incomes above 200% of the poverty level was taken, and their 2015 out-of-pocket medical expenses for prescription drugs were collected, with the accompanying results. Complete parts a through d below.
Data:
Out-of-pocket drug expenses:
194.41 136.96 162.24 176.32 200.17 119.67 143.12 207.93 203.87 133.41 130.58 210.51 190.33 122.18 136.56 156.45 157.67 159.04 164.71 208.16 168.37 212.32 107.39 133.32 159.02 192.13 182.53 214.17 174.39 178.02 128.79 189.64 176.45 183.48 202.75 200.58 130.76 146.03 158.67 167.53 165.36 187.54 157.71 164.54 188.46 167.79 156.16 165.08 107.41 147.31 196.23 195.64 148.38 91.23 177.58 176.62 183.72 112.44 168.95 199.48 195.76 211.33 182.66 157.94 207.39 174.48 168.66 163.37 140.25 177.92 175.43 160.58 176.22 164.44 182.13 187.58 150.24 153.33 166.99 186.74 154.48 167.52 174.61 196.28 168.19 214.84 173.71 177.07 130.51 153.72 164.03 95.74 142.49 146.62 139.51 146.15 127.06 170.59 128.97 147.54 183.87 177.13 241.82 202.58 195.15 199.04 206.04 170.04 140.18 205.94 130.19 176.93 184.91 184.88 79.59 177.91 225.58 157.68 141.13 159.35 165.54 194.64 166.51 96.99 173.94 152.84 182.29 220.51 169.72 110.62 113.24 154.11 174.16 166.29 187.12 188.31 155.55 154.63 121.82 158.55 222.46 166.56 170.06 175.02 177.94 182.64 182.44 147.89 147.78 205.43 152.77 160.53 161.71 203.91 161.16 113.97 153.52 189.55 134.75 141.89 175.57 180.14 168.85 153.63 184.32 218.86 172.28 168.43 199.88 175.48 177.67 132.45 125.91 163.79 107.55 174.03 157.84 178.81 196.84 184.04 144.13 150.19 134.11 209.53 173.05 160.83 115.11 168.77 167.14 173.99 181.75 139.87 163.56 206.95 202.45 201.77
a. Calculate the mean and median for the sample data. The mean is (Type an integer or decimal rounded to the nearest cent as needed.) The median is (Type an integer or decimal rounded to the nearest cent as needed.)
b. Calculate the range, variance, standard deviation, and interquartile range for the sample data. The range is (Type an integer or decimal rounded to the nearest cent as needed.) The variance is (Type an integer or decimal rounded to two decimal places as needed.) The standard deviation is (Type an integer or decimal rounded to the nearest cent as needed.) The interquartile range is (Type an integer or decimal rounded to the nearest cent as needed.)
d. Write a short report that describes out-of-pocket drug expenses for privately insured adults whose incomes are greater than 200% of the poverty level. Choose the correct answer below.
A. Out-of-pocket drug expenses are well described by the mean and the standard deviation as there are no outliers.
B. Most adults' out-of-pocket drug expenses are close to the median, but there is at least one outlier that creates a large range.
C. Out-of-pocket drug expenses are well described by the mean and the standard deviation as the distribution of data is not roughly symmetrical.
D. Nearly all adults' out-of-pocket drug expenses are within the interquartile range.