Question

use the salaries of employees of the moe d. lawn landscaping company to answer the question.
salary | frequency
$22,000 | 4
$27,000 | 3
$30,000 | 2
$45,000 | 1
what is the median?
$ blank

Explanation:

Step1: Calculate total number of employees

First, we sum up the frequencies. The frequencies are 4, 3, 2, and 1. So total number of employees \( n = 4 + 3 + 2 + 1 = 10 \).

Step2: Determine the position of the median

For a dataset with \( n \) values, if \( n \) is even, the median is the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th values when the data is ordered. Here, \( n = 10 \), so \( \frac{n}{2}=5 \) and \( \frac{n}{2}+1 = 6 \). We need the 5th and 6th values.

Step3: Order the salaries by frequency

We list the salaries in order (from lowest to highest) with their frequencies:

• \( \$22,000 \) (4 times: positions 1 - 4)
• \( \$27,000 \) (3 times: positions 5 - 7)
• \( \$30,000 \) (2 times: positions 8 - 9)
• \( \$45,000 \) (1 time: position 10)

So the 5th value is \( \$27,000 \) and the 6th value is also \( \$27,000 \).

Step4: Calculate the median

The median is the average of the 5th and 6th values. Since both are \( \$27,000 \), the median is \( \frac{27000 + 27000}{2}=27000 \).

Answer:

\( 27000 \)