Question

The salaries of seven employees of a small company are $38,000, $47,000, $35,000, $36,500, $47,000, $39,500, and $50,000. Each of the employees receives a 6% raise. What are the mean, median, mode, and range of their new salaries?

Answer 1

The mean of the new salaries is $44,354.29, the median is $41,770, there is no mode, and the range is $15,900.

Step-by-step explanation:

To find the new salaries after a 6% raise, we need to calculate the raise amount for each employee and add it to their original salary.

1. Employee 1: $38,000 + ($38,000 x 6%) = $40,280
2. Employee 2: $47,000 + ($47,000 x 6%) = $49,820
3. Employee 3: $35,000 + ($35,000 x 6%) = $37,100
4. Employee 4: $36,500 + ($36,500 x 6%) = $38,690
5. Employee 5: $47,000 + ($47,000 x 6%) = $49,820
6. Employee 6: $39,500 + ($39,500 x 6%) = $41,770
7. Employee 7: $50,000 + ($50,000 x 6%) = $53,000

The mean is the average of all the new salaries. Add up all the new salaries and divide by the number of employees (7).

Total new salaries = $40,280 + $49,820 + $37,100 + $38,690 + $49,820 + $41,770 + $53,000 = $310,480
Mean = $310,480 / 7 = $44,354.29

The median is the middle value when the salaries are arranged in order. In this case, there are 7 salaries, so the median is the 4th value.
Arranging the salaries in ascending order: $37,100, $38,690, $40,280, $41,770, $49,820, $49,820, $53,000
Median = $41,770

There is no mode because no salary appears more than once.

The range is the difference between the highest and lowest salaries.
Highest salary = $53,000
Lowest salary = $37,100
Range = $53,000 - $37,100 = $15,900