The mean salary of 5 employees is $34600. The median is $35700. The mode is $3700. If the highest paid employee gets a $3900 raise, then what is the new mean, median and mode?
the raise increases the mean from 34600 to 34600+3900/5 = 35380.
The median will not change, since only the highest salary has increased. The number of salaries above and below the median has not changed.
Same for the mode, since the wording of the question implies that there was a single employee with that salary.
To find the new mean, median, and mode after the highest paid employee receives a raise, we need to make the following calculations:
1) First, we find the new mean:
- The mean is the sum of salaries divided by the number of employees.
- The sum of the initial salaries is: 5 employees x $34,600 = $173,000.
- The raise for the highest paid employee is $3,900. Therefore, the new sum of salaries is: $173,000 + $3,900 = $176,900.
- Since the number of employees remains the same (5), the new mean can be calculated as: $176,900 ÷ 5 = $35,380.
2) Next, we determine the new median:
- The median is the middle value of a sorted list of numbers. We need to arrange the salaries in ascending or descending order.
- The initial median salary is given as $35,700. Since this is already the median, it remains the same even after the raise.
3) Lastly, we identify the new mode:
- The mode is the value that occurs most frequently in a dataset.
- In the initial dataset, the mode is $3,700.
- After the raise, since no other salaries change, the mode remains as $3,700.
Therefore, the new mean is $35,380, the new median is $35,700, and the new mode is still $3,700.