Impact of Salary Raise on Mean and Median Salary

What is the impact of giving the lowest paid employee a raise on the mean and median salary of the employees?

If the lowest paid employee receives a raise of $53,500, their new salary would be $29,000 + $53,500 = $82,500.

Detailed Explanation:

To determine the impact of this raise on the mean and median salaries of the 5 employees, we can calculate the new values:

Mean Salary: The mean salary is the sum of all salaries divided by the number of employees. Initially, the sum of the salaries is $42,500 * 5 = $212,500. After the raise, the new sum of salaries becomes $212,500 + $53,500 = $266,000. The new mean salary is then $266,000 / 5 = $53,200.

Median Salary: The median is the middle value when the salaries are arranged in ascending order. Initially, the median salary is $40,700. After the raise, the new salaries are $29,000, $40,700, $42,500, $42,500, and $82,500. The new median remains the same at $42,500 since the lowest paid employee's raise does not affect the relative position of the other salaries.

Therefore, after the lowest paid employee receives a $53,500 raise, the mean salary increases to $53,200, while the median salary remains at $42,500.

When the lowest paid employee receives a significant raise, it impacts both the mean and median salary of the employees. While the mean salary increases due to the overall raise in total salary amount, the median salary remains the same as it is not affected by the raise in the lowest paid employee's salary.

This highlights the importance of understanding the difference between mean and median when analyzing salary data and the effects of individual salary adjustments on these measures.