Let's calculate the mean, median, and mode of the salary data.

Data Breakdown

Here are the groups of salaries:

• 13 employees with a salary of $20,600
• 10 employees with a salary of $23,700
• 18 employees with a salary of $25,100
• 3 employees with a salary of $30,800
• 4 employees with a salary of $39,900
• 1 employee with a salary of $147,600

Mean Salary

To calculate the mean salary, we sum all the salaries (weighted by the number of employees) and divide by the total number of employees.

1. Multiply the salary by the number of employees in each group:

   • $13 \times 20,600 = 267,800$
   • $10 \times 23,700 = 237,000$
   • $18 \times 25,100 = 451,800$
   • $3 \times 30,800 = 92,400$
   • $4 \times 39,900 = 159,600$
   • $1 \times 147,600 = 147,600$

2. Sum all the products: $267,800 + 237,000 + 451,800 + 92,400 + 159,600 + 147,600 = 1,356,200$

3. Calculate the total number of employees: $13 + 10 + 18 + 3 + 4 + 1 = 49$

4. Divide the total sum by the number of employees to get the mean salary: $\text{Mean salary} = \frac{1,356,200}{49} \approx 27,675.51$

Rounding to the nearest hundred, the mean salary is $27,700.

Median Salary

The median salary is the middle value when all salaries are arranged in ascending order.

1. List the salaries in increasing order and account for how many employees earn each salary:
   • 13 employees earn $20,600
   • 10 employees earn $23,700 (cumulative total = 23 employees)
   • 18 employees earn $25,100 (cumulative total = 41 employees)
   • 3 employees earn $30,800 (cumulative total = 44 employees)
   • 4 employees earn $39,900 (cumulative total = 48 employees)
   • 1 employee earns $147,600 (cumulative total = 49 employees)

Since there are 49 employees, the median is the salary of the 25th employee. This falls in the $25,100 group.

Thus, the median salary is $25,100.

Mode Salary

The mode is the salary that occurs most frequently.

In this case, 18 employees earn $25,100, which is more than any other group.

Therefore, the mode salary is $25,100.

Summary

• Mean salary: $27,700 (rounded to the nearest hundred)
• Median salary: $25,100
• Mode salary: $25,100

Would you like any further explanation or details?

Here are 5 related questions:

1. How does the mean salary change if the highest salary is removed?
2. What is the range of salaries in this company?
3. How does the presence of the outlier (the $147,600 salary) affect the mean salary?
4. What would the total payroll be for all employees?
5. How do you interpret the mode in this context?

Tip: The median is often a better indicator of typical salary in a dataset with outliers.