Question

Brainstorm an example of a skewed data distribution relating to something in real life.

For your example would the median be a better description of the center of the distribution, why or why not? What could be the ramifications of the MEAN being communicated to the audience instead of the median? Can you think of any situations where the data may be skewed and the mean communicated not the median?

Textbook : Garfunkel, S. (2016). For all practical purposes: Mathematical literacy in today's world (10th ed).

Answer 1

An example of a skewed data distribution relating to something in real life:

Suppose a company has 5 employees and one CEO.

Their salary is given below:

Employee No 1 : $15,000

Employee No. 2: $18,000

Employee No.3: $18,000

Employee No. 4: $19,000

Employee No. 5: $19,000

Employee No. 6: $20,000

CEO: $100,000

The Mean Salary is given by:

xbar = 209000/7 = 29857.14

Arranging data in ascending order, we get:

15,000,   18,000, 18,000, 19,000, 19,000, 20,000, 100,000

n = 7

Median =(7+1)/2th item = 4th item = 18,000

Here, the distribution is skewed because of the salary of CEO = $100,000 which very much higher than the remaining 6 Employees. So, Mean Salary = $29,857.14 does not give the realistic picture of the average salary of the company.

The Median = $18,000, which is not affected by the presence of extreme value = $100,000 gives the realistic value of the average salary of the company.