Problem

The salaries of 10 employees of a small company are listed. Complete parts (a) through (f) below.
\begin{tabular}{rc}
$\$ 30000$ & $\$ 66000$ \\
25000 & 27000 \\
31000 & 32000 \\
26000 & 60000 \\
26000 & 28000
\end{tabular}
a) Uetermine the mean.

The mean salary is $\$ \square$
(Simplify your answer.)
b) Determine the median

The median salary is $\$ \square$.
(Simplify your answer.)
c) Determine the mode(s). Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The mode salary/salaries is/are $\$$
(Use a comma to separate answers, but do not use commas in any individual numbers.)
B. There is no mode.

Answer

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Answer

The mode salary is \(\boxed{26000}\).

Steps

Step 1 :First, we calculate the mean by adding up all the salaries and dividing by the number of salaries. The total sum of the salaries is \(30000 + 66000 + 25000 + 27000 + 31000 + 32000 + 26000 + 60000 + 26000 + 28000 = 356000\). There are 10 salaries, so the mean is \(356000 \div 10 = 35600\).

Step 2 :The mean salary is \(\boxed{35600}\).

Step 3 :Next, we determine the median by listing the salaries in numerical order and finding the middle value. If there are two middle values, we take their average. The ordered list of salaries is \(25000, 26000, 26000, 27000, 28000, 30000, 31000, 32000, 60000, 66000\). There are 10 salaries, so the two middle values are the 5th and 6th salaries, which are 28000 and 30000. The median is the average of these two values: \((28000 + 30000) \div 2 = 29000\).

Step 4 :The median salary is \(\boxed{29000}\).

Step 5 :Finally, the mode is the salary that appears most frequently. Looking at the list of salaries, we can see that \$26000 appears twice. No other salary appears more than once, so the mode is \$26000.

Step 6 :The mode salary is \(\boxed{26000}\).

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