The mean salary of 5 employees is 33700 The median is 34800

The mean salary of 5 employees is $33700. The median is $34800. The mode is $36100. If the highest paid employee gets a $3100 raise, then ...
Hint: It will help to write down what salaries you know of the five a) What is the new mean? Write your work and explanation in the box below.

Solution

The total salary of the 5 employees is 5 * $ 33700 = $ 168500. Since the median is $ 34800, 2 employees get a salary less than $ 34800 and 2 employees get salary more than $ 34800. Also, the 5^th employee gets a salary of $ 34800.The mode is the number that is repeated more often than any other so that at least 2 employees get a salary of $ 36100 each. Therefore, the total salary of the remaining 2 employees is $ ( 168500 – 34800 – 2* 36100) = $ 61500. Since the salary of the 2 employees in the upper half (more than the median i.e. $ 34800) is $ 36100 each, therefore, the 2 employees in the lower half (less than the median i.e. $ 34800) together is $ 61500. The highest paid employee i.e. the employee drawing a salary of $ 36100 gets a raise of $ 3100 so that the new salary is $ 36100 + 3100 = $ 39200.

Thus, the total salary of the 5 employees now will be $ ( 61500 + 34800 + 2 * 39200 ) = $ 174700. Then, the new mean salary will be $ 174700/5 = $ 34940.