99 employees in a factory earn a salary of $28,000 per year, while the CEO makes $766,000 annually. What are the mean and median salaries for all 100 people? Is the mean or the median the more appropriate measure of "center" in this case? Explain.
I have been working at this all evening and can not seem to feel comfortable with my solutions. Could some help me please and show me how the answer was found. Thank you!
See:
http://www.jiskha.com/display.cgi?id=1304259571
Median = $28,000
Mean = [(99 * 28,000) + 766,000]/100 = ?
The mean functions as a fulcrum (balance point), therefore it is most influenced by deviant scores. Compare the above value of the mean to one without the CEO's salary. Therefore the median is the best measure of central tendency with a skewed distribution.
To find the mean and median salaries for all 100 people, we need to calculate the average and sort the salaries in ascending order.
First, let's calculate the mean salary:
Total salary for 99 employees = 99 * $28,000 = $2,772,000.
Total salary for 100 employees (including the CEO) = $2,772,000 + $766,000 = $3,538,000.
Mean salary = Total salary for 100 employees / Number of employees = $3,538,000 / 100 = $35,380.
Now, let's calculate the median salary:
To find the median, we need to arrange all the salaries in ascending order.
99 employees earning $28,000 per year, and the CEO earning $766,000 per year.
Arranging the salaries in ascending order:
$28,000, $28,000, $28,000, ..., $28,000, $766,000.
To find the median, we need to find the middle value. Since there are 100 employees, the middle value will be the 50th salary when arranged in ascending order.
Since there are 99 employees earning $28,000 and 1 employee earning $766,000, the 50th salary will be $28,000.
So, the median salary for all 100 people is $28,000.
In this case, the median is the more appropriate measure of "center" because it is not influenced by extreme values, such as the CEO's salary. The mean is affected by extreme values, so in situations like this where there is a wide range of salaries, the median provides a better representation of the "center" or typical salary.