To find the mean hourly wage of the 22 employees, we'll follow these steps:
1. Calculate the total wages for each group of employees:
- For the first group of 3 employees with an hourly wage of \[tex]$7.50:
\[
\text{Total wages}_{1} = 3 \times 7.50 = \$[/tex]22.50
\]
- For the second group of 14 employees with an hourly wage of \[tex]$8.00:
\[
\text{Total wages}_{2} = 14 \times 8.00 = \$[/tex]112.00
\]
- For the third group of 5 employees with an hourly wage of \[tex]$9.75:
\[
\text{Total wages}_{3} = 5 \times 9.75 = \$[/tex]48.75
\]
2. Calculate the total number of employees:
[tex]\[
\text{Total number of employees} = 3 + 14 + 5 = 22
\][/tex]
3. Calculate the combined total wages for all employees:
[tex]\[
\text{Total wages} = \$22.50 + \$112.00 + \$48.75 = \$183.25
\][/tex]
4. Calculate the mean hourly wage:
[tex]\[
\text{Mean hourly wage} = \frac{\text{Total wages}}{\text{Total number of employees}} = \frac{\$183.25}{22} = \$8.33
\][/tex]
Therefore, the mean hourly wage of these 22 employees is \$8.33.
