Chapter 3
Descriptive Statistics:
Numerical Methods
Solutions:
3.
15, 20, 25, 25, 27, 28, 30, 34
20
(8)
1.6
100
i
=
=
2nd position = 20
25
(8)
2
100
i
=
=
20
25
22.5
2
+
=
65
(8)
5.2
100
i
=
=
6th position = 28
75
(8)
6
100
i
=
=
28 30
29
2
+
=
5.
a.
3181
$159
20
i
x
x
n
Σ
=
=
=
b.
Median 10th
$160
Los Angeles
11th
$162
Seattle
Median =
160 162
$161
2
+
=
c.
Mode = $167
San Francisco and New Orleans
d.
25
20
5
100
i
=
=
5th
$134
6th
$139
1
134 139
$136.50
2
Q
+
=
=
e.
75
20
15
100
i
=
=
15th
$167
16th
$173
3
167 173
$170
2
Q
+
=
=
6.
a.
Marketing Majors
363
36.3
10
i
x
x
n
Σ
=
=
=
Data in order
28.4
30.6
34.2
34.2
35.2
35.8
37.7
39.5
42.4
45.0
Median (5
th
and 6
th
) =
35.2 35.8
35.5
2
+
=
Mode – 34.2 (2 times)
Accounting Majors
731.2
45.7
16
i
x
x
n
Σ
=
=
=
Data in order
33.5
38.0
40.2
40.8
41.1
41.7
43.5
44.2
45.2
47.8
49.1
49.7
49.9
53.9
55.5
57.1
Median (8
th
and 9
th
) =
44.2
45.2
44.7
2
+
=
There is no mode – all values occur one time.
b.
Marketing
Q
1
:
i
= .25(10) = 2.5
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Round to 3
rd
position
Q
1
= 34.2
Q
3
:
i
= .75(10) = 7.5
Round to 8
th
position
Q
3
= 39.5
Accounting
Q
1
:
i
= .25(16) = 4
Use 4
th
and 5
th
positions
Q
1
=
40.8
41.1
40.95
2
+
=
Q
3
:
i
= .75(16) = 12
Use 12
th
and 13
th
positions
Q
3
=
49.7
49.9
49.8
2
+
=
c.
The difference between the sample means is 45.7 – 36.3 = 9.4. The
difference between the sample medians is 44.7 – 35.5 = 9.2. On the
basis of both of these measures of central location, accounting
majors have an average salary that is slightly over $9,000 more per
year than marketing majors. The highest accounting major salary
was $57,1000, while the highest marketing major salary was
$45,000. The top 25% of accounting majors made $49,800 or more
per year. The top 25% of marketing majors made $39,500 or more
per year.
8.
a.
i
x
Σ
= 695
695
34.75
20
i
x
x
n
Σ
=
=
=
The modal age is 25; it appears 3 times.
b.
Median is average of 10th and 11th items.
33 36
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 Statistics, Standard Deviation, x= Σxi

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