Question

Shown below is a histogram representing the income of the employees of a local fortune 500 company.

Variable                N   Mean     Median TrMean       StDev  

Annual Salary           1000 101165   68734 88756       104296     

Variable                Minimum     Maximum    Q1           Q3

Annual Salary           55          812679      29194       141138

A representative of this company then released the following statement:

               “It is a great day for our company when we can finally say that more than half of our workforce is making over $100,000.00 per year. When the average salary is this high we can without reservation claim to be the greatest company to work for in this great nation.”

(a) Do you believe this statement to be an accurate representation of the statistics shown above? Explain your conclusions.

(b) How could you change this statement to accurately portray this information?

Answer 1

a) Even thought the Mean value is over 100,000 , the salary ranges from 55 to 812679.

In this case, mean doesnt accurately portray the statistic as 1st Quartile consists of more people(almost) as opposed to Q3 who have higher salaries.

Ths shows that data is skewed , it has a longer tail in one direction and not in another.

Mean can only portray accurate representations when its a bell shaped curve, which is not the case here.

b) For better representions of the statistics shown above, a more accurate representations is given by the median.
The statement can be more accturate by saying :

t is a great day for our company when we can finally say that more than half of our workforce is making over $65,000.00 per year. When the average salary is this high we can without reservation claim to be the greatest company to work for in this great nation.”