A group of recent marketing graduates from a small liberal arts university have

Question

A group of recent marketing graduates from a small liberal arts university have jobs ranging from selling shoes at $18,000/yr. to playing professional basketball at $1.5 million/yr. Current salaries for the 22 graduates are (in $000): 24, 20, 32, 36, 18, 28, 42, 37, 20, 27, 52, 31, 45, 33, 20, 1500, 23, 38, 27, 31, 36, 40.

What is the mean salary for these graduates?

Suppose the university wished to publish a brochure for prospective students, and include some indication of the average salary of recent graduates in various disciplines. Compute the average that best represents the central tendency of the data on marketing graduates.

Explain your choice of one average over other averages for the data.

Is the distribution symmetrical? Why or why not?

Explanation / Answer

a) What is the mean salary for these graduates?

Getting the mean, X,  
  
X = Sum(x) / n  
Summing the items, Sum(x) =    2163
As n =    22
Thus,  
X =    98.31818182 [ANSWER]

***********************

b) Suppose the university wished to publish a brochure for prospective students, and include some indication of the average salary of recent graduates in various disciplines. Compute the average that best represents the central tendency of the data on marketing graduates.

Explain your choice of one average over other averages for the data.

There is an outlier, 1500, which greatly affects the mean, so it is not a good measure of central tendency.

There is also no prominent mode, so we do not use it as well.

Hence, we use the median.

As there are 22 entries, the median is the average of the 11th and 12th smallest entries.

18
20
20
20
23
24
27
27
28
31
31
33
35
36
36
37
38
40
42
45
52
1500

Hence,

Median = (31+33)/2 = 32 [ANSWER]

*********************

It is not symmetrical, as we can see, there is already an outlier far to the right, which is 1500.

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