1. The following is a list of starting median salaries for college graduates by profession:
Degree
Starting Median Salary
Education
36,200
Horticulture
37,200
Music
34,000
Social Work
33,400
Theology
34,800
(a) What is the average starting salary across the college degrees listed?
This is just (36
,
200 + 37
,
200 + 34
,
000 + 33
,
400 + 34
,
800)
/
5 = 35
,
120.
(b) What is the median starting salary among the college degrees listed?
Ordering the data from smaller to larger, we get :
{
33
,
400
,
34
,
000
,
34
,
800
,
36
,
200
,
37
,
200
}
.
The median is the smallest number whose percentile is still larger than 50
th
. Here the answer
is the middle observation: 34
,
800.
(c) Suppose that to the above list you add the starting salary for Economics majors, which is 50,200.
What is the average then? How about the median?
The average is now (36
,
200 + 37
,
200 + 34
,
000 + 33
,
400 + 34
,
800 + 50
,
200)
/
6 = 37
,
633, while
the median is still given by 34
,
800. Any number who is the 50
th
percentile (not necessarily the
smallest such number) is also an acceptable answer. In this case, any number greater than or
equal to 34
,
800 but strictly smaller than 36
,
200.
(d) Compare your answer to (c) with what you found in (a) and (b).
Does adding the starting
salary for Economics majors affect the mean and the median in the same way? Which one is
more affected by adding this new observation? Why? Justify your answer.
They mean changes by more than the median. This is an accordance to the mean being more
sensitive to changes in the tails of the distribution than the mean.
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 Spring '10
 M.Abajian
 Econometrics, Normal Distribution, Probability, Standard Deviation, Probability theory, Usain Bolt

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