1. The following is a list of starting median salaries for college graduates by profession:
Degree
Starting Median Salary
Chemical Engineering
65,700
Finance
48,500
Economics
50,200
Statistics
48,600
Computer Science
56,400
(a) What is the average starting salary across the college degrees listed?
This is just (65
,
700 + 48
,
500 + 50
,
200 + 48
,
600 + 56
,
400)
/
5 = 53
,
880.
(b) What is the 80
th
percentile of the above sample?
Ordering the observations from smallest to largest:
{
48
,
500
,
48
,
600
,
50
,
200
,
56
,
400
,
65
,
700
}
.
The 80
th
percentile is a number “
A
” such that (#
obs
≤
“
A
”)
/
5 = 0
.
8. This implies that
(#
obs
≤
“
A
”) = 4, or equivalently that “
A
” must the be 4
th
largest observation: 56,400.
(c) Is your answer to (b) unique? Justify your answer.
It is important to notice that in fact any number “
A
” satisfying 56
,
400
≤
“
A
”
<
65
,
700 would
yield (#
obs
≤
“
A
”)
/
5 = 0
.
8. For this reason, sometimes percentiles are de±ned as the smallest
number which satis±es this property, in this case: 56
,
400.
(d) For the above sample, what is larger: the Variance or the Mean Squared Deviation?
You don’t need to do any calculations here. The variance is always larger than the mean squared
deviation, as the former divides by
N

1, while the latter divides by
N
.
(e) The Mean Absolute Deviation for the above sample is 5
,
736. What would the mean absolute
deviation be if everybody made 5,000 less dollars? Justify your answer.
Let