Question

Calculate the Z-score for each data point.
Employee	Salary	Years of Employment	Z-score
Sarah	$      62,500.00	3
Amanda	$      74,250.00	5
Rachel	$      68,500.00	3
Brad	$      55,000.00	2
Josh	$      61,000.00	4
Jim	$      32,000.00	2
Cheri	$      71,500.00	2
Danuta	$      90,000.00	7
Evan	$      76,500.00	3

1.Based on the z-scores, what you say about the salaries of the employees at your company?

2. Based on the z-scores and the overall salary information, are there other criteria you would want to ask about the employees? Why would it be important to know?

3.Say you find out that Jim is the office assistant, while the other employees are all engineers. How would this change the way you look at the data?

4. Would you want to calculate the z-scores differently? Why?

5. Say you want to compare only the engineer's salaries. Calculate the z-scores below. Show your calculations. What do you notice about the new z-scores?

Answer 1

The z-score is given by z=(x-m)/s

Where x=individual salary

              m=mean salary

              s=standard deviation

here,

m=65694.44

s=15290.6

Employee	salary	z-score
Sarah	62500	-0.20892
Amanda	74250	0.559531
Rachel	68500	0.183483
Brad	55000	-0.69941
Josh	61000	-0.30701
Jim	32000	-2.2036
Cheri	71500	0.379682
Danuta	90000	1.589575
Evan	76500	0.70668

1) from the z scores I can say that 5 employee are getting more than the avg salary while the other 4 are getting paid less than the avg salary

2) Yes, I would want to know other criteria about the employee because I see some employees are getting less paid despite of more years of employment than others and vice versa.

3) Since the job of Jim is different I would not like to compare his salary and z score with others

4) Yes,I would like to calculate the z-scores differently.

5)we eliminate Jim's salary

m=69906.25 s=10167.3

Employee	salary	z-score
Sarah	62500	-0.72844
Amanda	74250	0.427227
Rachel	68500	-0.13831
Brad	55000	-1.4661
Josh	61000	-0.87597
Cheri	71500	0.156753
Danuta	90000	1.976311
Evan	76500	0.648525

Fom this we can see that Rachael also get paid below the avg salary if the salary of only engineer's is taken into account but when Jim's salary was included Rachael z-score was positive i.e, his salary was above avg salary.The z-scores of other employee also undergoes a slight change.