Question

According to the Bureau of Labor Statistics (as of May 2016), the mean annual wage for criminal justice and law enforcement professors is $67,040. The median annual wage is $59,590. Explain how each would be calculated and the advantages to using each over the other to characterize the typical annual salary. As a professor, which should I view as more accurate/appropriate? Explain your position.

Answer 1

Question: Explain how each would be calculated

Mean = $67,040 is calculated by dividing the total annual wage for criminal justice and law enforcement professors by the total number of professors

Median = $59,590 is calculated as follows: First arrange in ascending order the annual wage for criminal justice and law enforcement professors. Then choose the middle of the values as the median.

Question: the advantages to using each over the other to characterize the typical annual salary.

Answer: Mean is better than the median to present the measure of central tendency in case of nearly symmetrical distribution without any outliers due to its mathematical tractability and amenability for generalization in hypothesis testing and confidence level estimation. Median is preferable to mean for distributions which are skewed and have outliers because median is not affected by outliers whereas mean is affected by outliers.

Question: As a professor, which should I view as more accurate/appropriate?

Answer: Since the annual wages of professors are not nearly symmetrical with some professors having cmparatively larger annual wage as compared to junior professors whose annual wage will not be that mush and since the data has outliers, I view median as more accurate/appropriate since median is not affected by outliers.