To find the mean hourly wage of the 45 employees, we need to follow these steps:
### Step 1: Calculate the total wages for each group of employees
First, multiply the number of employees in each group by their respective hourly wage:
- For 8 employees earning [tex]$7.00 per hour:
\[
8 \times 7.00 = 56.00 \text{ dollars}
\]
- For 13 employees earning $[/tex]8.50 per hour:
[tex]\[
13 \times 8.50 = 110.50 \text{ dollars}
\][/tex]
- For 9 employees earning [tex]$10.50 per hour:
\[
9 \times 10.50 = 94.50 \text{ dollars}
\]
- For 15 employees earning $[/tex]12.00 per hour:
[tex]\[
15 \times 12.00 = 180.00 \text{ dollars}
\][/tex]
### Step 2: Sum the total wages for all groups
Add up all the total wages calculated in step 1 to get the total wages for all employees:
[tex]\[
56.00 + 110.50 + 94.50 + 180.00 = 441.00 \text{ dollars}
\][/tex]
### Step 3: Sum the total number of employees
Add up the number of employees in all groups to get the total number of employees:
[tex]\[
8 + 13 + 9 + 15 = 45 \text{ employees}
\][/tex]
### Step 4: Calculate the mean hourly wage
The mean hourly wage can be calculated by dividing the total wages by the total number of employees:
[tex]\[
\text{Mean hourly wage} = \frac{\text{Total wages}}{\text{Total number of employees}} = \frac{441.00}{45}
\][/tex]
### Step 5: Perform the division and round the result
Perform the division:
[tex]\[
\frac{441.00}{45} = 9.80
\][/tex]
Thus, the mean hourly wage of these 45 employees, rounded to two decimal places, is:
[tex]\[
\boxed{9.80}
\][/tex]
