The mean salary of 5 employees is $34300. The median is $35500. The mode is $36200. If the median paid employee gets a $3000 raise, then what is the new mean, median, mode?
To find the new mean, median, and mode after the median paid employee gets a $3000 raise, we can follow these steps:
1. Calculate the sum of the salaries of the 5 employees. Since the mean salary is $34300, we can multiply it by the number of employees (5) to get the total sum: $34300 * 5 = $171500.
2. Find the new median: The median in this case refers to the Middle value when the salaries are arranged in increasing order. The given median is $35500, which implies that the third employee has this salary. Since the third employee gets a $3000 raise, their new salary would be $35500 + $3000 = $38500.
To find the new median, we replace the original median with the new salary of the third employee. The salaries in increasing order now become: $34300, $36200, $38500, $36200, $36200. The middle value is still $36200, so the new median is $36200.
3. Determine the new mode: The mode is the value(s) that appear most frequently in the dataset. In this case, the mode is $36200, as it appears three times. If we increase the salary of the third employee to $38500, then the new mode would be $36200, as it still appears three times.
4. Calculate the new mean: The mean is the sum of all the salaries divided by the number of employees. We already calculated the sum of the original salaries as $171500. If we increase the salary of the third employee to $38500, we also need to update the sum by subtracting the original median $35500 and adding the new median $38500. The updated sum is: $171500 - $35500 + $38500 = $176500.
Now we can find the new mean by dividing the updated sum by the number of employees (5): $176500 / 5 = $35300.
To summarize, the new mean is $35300, the new median is $36200, and the new mode is $36200.
To find the new mean, median, and mode after the median paid employee gets a $3000 raise, we need to adjust the data accordingly.
1. Finding the new mean:
- The mean salary of the employees is $34,300.
- Since the median paid employee gets a $3000 raise, we need to add $3000 to their salary in order to adjust the data.
- The new mean will be the sum of the adjusted salaries divided by 5 (the number of employees).
2. Finding the new median:
- The original median is $35,500.
- Since the median paid employee's salary increases by $3000, the new median will also increase by $3000.
3. Finding the new mode:
- The original mode is $36,200.
- The mode is not affected by increasing the salary of a single employee, so it will remain the same.
Let's proceed with the calculations:
1. New mean:
- Sum of adjusted salaries = 5 * $34,300 + $3000 = $171,500 + $3000 = $174,500
- New mean = $174,500 / 5 = $34,900
2. New median:
- New median = $35,500 + $3000 = $38,500
3. New mode:
- New mode = $36,200
Therefore, the new mean salary is $34,900, the new median salary is $38,500, and the new mode is $36,200.