Answer :
Sure! Let's address each part of the question step-by-step:
(a) Determine the mean salary:
To find the mean salary, you add up all the salaries and then divide by the number of employees. Here’s the breakdown:
Salaries: \[tex]$27,000, \$[/tex]86,000, \[tex]$26,000, \$[/tex]28,000, \[tex]$31,000, \$[/tex]29,000, \[tex]$25,000, \$[/tex]73,000, \[tex]$25,000, \$[/tex]32,000.
First, add all the salaries:
[tex]\(27,000 + 86,000 + 26,000 + 28,000 + 31,000 + 29,000 + 25,000 + 73,000 + 25,000 + 32,000 = 382,000\)[/tex].
Then, divide by the number of salaries (10):
[tex]\(\frac{382,000}{10} = 38,200\)[/tex].
So, the mean salary is \[tex]$38,200.
(b) Determine the median salary:
To find the median, arrange the salaries in order and find the middle number. If there’s an even number of values, take the average of the two middle numbers.
List the sorted salaries: \$[/tex]25,000, \[tex]$25,000, \$[/tex]26,000, \[tex]$27,000, \$[/tex]28,000, \[tex]$29,000, \$[/tex]31,000, \[tex]$32,000, \$[/tex]73,000, \[tex]$86,000.
The two middle numbers are \$[/tex]28,000 and \[tex]$29,000.
Calculate their average:
\(\frac{28,000 + 29,000}{2} = 28,500\).
So, the median salary is \$[/tex]28,500.
(c) Determine the mode(s):
The mode is the salary that occurs most frequently. Look for the salary that appears the most times in the list.
From the list, \[tex]$25,000 appears three times, more than any other salary. Thus, the mode salary is \$[/tex]25,000.
(d) Determine the midrange:
The midrange is calculated by adding the smallest and largest salaries and dividing by 2.
Smallest salary: \[tex]$25,000
Largest salary: \$[/tex]86,000
Calculate the midrange:
[tex]\(\frac{25,000 + 86,000}{2} = 55,500\)[/tex].
So, the midrange salary is \[tex]$55,500.
(e) Which average to use to demonstrate the need for a raise:
Between the mean and the median:
- The mean salary is \$[/tex]38,200.
- The median salary is \$28,500.
Since the mean is higher than the median, the argument to show that salaries are lower overall would focus on the mean being higher to illustrate how a few higher salaries skew the perception. Therefore, the correct choice is:
D. The mean because it is higher.
I hope this helps! If you have any more questions, feel free to ask.
(a) Determine the mean salary:
To find the mean salary, you add up all the salaries and then divide by the number of employees. Here’s the breakdown:
Salaries: \[tex]$27,000, \$[/tex]86,000, \[tex]$26,000, \$[/tex]28,000, \[tex]$31,000, \$[/tex]29,000, \[tex]$25,000, \$[/tex]73,000, \[tex]$25,000, \$[/tex]32,000.
First, add all the salaries:
[tex]\(27,000 + 86,000 + 26,000 + 28,000 + 31,000 + 29,000 + 25,000 + 73,000 + 25,000 + 32,000 = 382,000\)[/tex].
Then, divide by the number of salaries (10):
[tex]\(\frac{382,000}{10} = 38,200\)[/tex].
So, the mean salary is \[tex]$38,200.
(b) Determine the median salary:
To find the median, arrange the salaries in order and find the middle number. If there’s an even number of values, take the average of the two middle numbers.
List the sorted salaries: \$[/tex]25,000, \[tex]$25,000, \$[/tex]26,000, \[tex]$27,000, \$[/tex]28,000, \[tex]$29,000, \$[/tex]31,000, \[tex]$32,000, \$[/tex]73,000, \[tex]$86,000.
The two middle numbers are \$[/tex]28,000 and \[tex]$29,000.
Calculate their average:
\(\frac{28,000 + 29,000}{2} = 28,500\).
So, the median salary is \$[/tex]28,500.
(c) Determine the mode(s):
The mode is the salary that occurs most frequently. Look for the salary that appears the most times in the list.
From the list, \[tex]$25,000 appears three times, more than any other salary. Thus, the mode salary is \$[/tex]25,000.
(d) Determine the midrange:
The midrange is calculated by adding the smallest and largest salaries and dividing by 2.
Smallest salary: \[tex]$25,000
Largest salary: \$[/tex]86,000
Calculate the midrange:
[tex]\(\frac{25,000 + 86,000}{2} = 55,500\)[/tex].
So, the midrange salary is \[tex]$55,500.
(e) Which average to use to demonstrate the need for a raise:
Between the mean and the median:
- The mean salary is \$[/tex]38,200.
- The median salary is \$28,500.
Since the mean is higher than the median, the argument to show that salaries are lower overall would focus on the mean being higher to illustrate how a few higher salaries skew the perception. Therefore, the correct choice is:
D. The mean because it is higher.
I hope this helps! If you have any more questions, feel free to ask.
