Questions: Homework for Section 3.2 A random sample of Print-O-Matic printing company's employee salaries (in dollars) are recorded in the table below. Salary 109739 76029 272500 75311 98837 74235 58456 73877 108448 52718 64553 90090 65270 57380 66346 100702 a) For the data shown above, find the following. Round the answer in the first blank to 1 decimal place(s). In the second blank put the correct units. Find the mean: Find the median: Find the range:

Solution Steps

To find the mean salary \( \mu \), we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of salaries and \( x_i \) represents each individual salary. For the given data, we have:

\[ \mu = \frac{1444491}{16} = 90280.7 \]

Thus, the mean salary is \( 90280.7 \) dollars.

To find the median salary, we first sort the data:

\[ \text{Sorted data} = [52718, 57380, 58456, 64553, 65270, 66346, 73877, 74235, 75311, 76029, 90090, 98837, 100702, 108448, 109739, 272500] \]

Since there are \( N = 16 \) salaries (an even number), the median \( Q \) is calculated using the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (16 + 1) = 8.5 \]

This indicates that the median is the average of the 8th and 9th values in the sorted list:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{74235 + 75311}{2} = 74773.0 \]

Thus, the median salary is \( 74773.0 \) dollars.

The range of the salaries is calculated as the difference between the maximum and minimum salaries:

\[ \text{Range} = \max(salaries) - \min(salaries) = 272500 - 52718 = 219782 \]

Thus, the range of the salaries is \( 219782 \) dollars.

Final Answer