PART I
Descriptive Statistics
M&S 55, 64-66
2.42 (5 points) A data set contains the observations 5,1,3,2,1. Find
a. ∑ x
b. ∑ x²
c. ∑ (x – 1)
d. ∑ (x-1) ²
e. (∑ x) ²
2.58 (3 points) Most powerful women in America. Fortune (Oct. 14, 2002) published a
list of the 50 most powerful women in America. The data on age (in years) and title of
each of these 50 women are stored in the WPOWER50 file.
a. Find the mean, median, and modal age of these 50 women.
b. What do the mean and median indicate about the skewness of the age
distribution?
c. Construct a relative frequency histogram for the age data. What is the modal
age class?
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Name
Carly Fiorina
Betsy Holden
Meg Whitman
Indra Nooyi
Andrea Jung
Anne Mulcahy
Karen Katen
Pat Woertz
Abigail Johnson
Oprah Winfrey
Ann Moore
Judy McGrath
Colleen Barrett
Shelly Lazarus
Pat Russo
Betsy Bernard
Amy Brinkley
Lois Juliber
Sherry Lansing
Stacey Snider
Judy Lewent
Marjorie Magner
Ann Livermore
Cathleen Black
Doreen Toben
Amy Pascal
Vivian Banta
Janet Robinson
Pam Strobel
Dina Dublon
Nancy Peretsman
Susan Arnold
Mary Kay Haben
Deb Henretta
Carole Black
Jamie Gorelick
Marce Fuller
Kathi Seifert
Anne Sweeney
Marilyn C. Nelson
Anne Stevens
Sallie Krawcheck
Carol Tome
Marion Sandler
Louise Francesconi
Vanessa Castagna
Larree Renda
Dawn Lepore
Fran Keeth
Heidi Miller
Age
48
46
46
46
44
49
53
49
40
48
52
50
58
55
50
47
46
53
58
41
53
53
44
58
52
44
52
52
50
49
48
48
46
41
59
52
42
53
44
63
53
37
45
71
49
53
44
48
56
49
Company
Hewlet-Packard
Kraft Foods
eBay
PepsiCo
Avon Products
Xerox
Pfizer
ChevronTexaco
Fidelity M&R
Harpo Entertainment
AOL Time Warner
Viacom
Southwest Airlines
Ogilvy & Mather
Lucent Tech.
AT&T
Bank of America
Colgate-Palmolive
Viacom
Vivendi Universal
Merck
Citigroup
Hewlett-Packard
Hearst Magazines
Verizon
Sony
Prudential Fin.
New York Times
Exelon
J.P. Morgan Chase
Allen & Co.
Procter & Gamble
Kraft Foods
Procter & Gamble
Lifetime Entertainment
Fannie Mae
Mirant
Kimberly-Clark
Walt Disney
Carlson Cos.
Ford Motor
Sanford Bernstein
Home Depot
Golden West Fin.
Raytheon
J.C. Penney
Safeway
Charles Schwab
Royal Dutch Petrol
Bank One
Title
CEO
CEO
CEO
CEO
CEO
CEO
EVP
EVP
President
Chairman
CEO
President
COO
CEO
CEO
CEO
CRO
COO
Chairman
Chairman
EVP
COO
President
President
EVP
Chairman
Vice Chair
SVP
EVP
EVP
EVP
President
EVP
President
CEO
Vice Chair
CEO
EVP
President
CEO
EVP
CEO
EVP
CEO
EVP
CEO
EVP
Vice Chair
CEO
EVP
2.61 (2 points) Radioactive lichen. Refer to the University of Alaska study to monitor
the level of radioactivity in lichen, Exercise 2.34 (p. 51). The amount of the radioactive
element sesium-137 (measured in microcuries per milliliter) for each of nine lichen
specimens is repeated in the table.
Location
Bethel
-5.50
-5.00
Eagle Summit
-4.15
-4.85
Moose Pass
-6.05
Turnagain Pass
-5.00
Wickersham Dome
-4.10
-4.50
-4.60
a. Find the mean, median, and mode of the radioactivity levels.
b. Interpret the value of each measure of central tendency, part a.
2.65 (7 points) Children’s use of pronouns. Clinical observations suggest that
specifically language-impaired (SLI) children have a great difficulty with the proper use
of pronouns. This phenomenon was investigated and reported in the Journal of
Communication Disorders (Mar. 1995). Thirty children, all from low-income families,
participated in the study. Ten were 5-year-old SLI children, ten were younger (3-yer-old)
normally developing (YND) children, and ten were older (5-year-old) normally
developing (OND) children. The table contains the gender, deviation intelligence quotient
(DIQ), and percentage of pronoun errors observed for each of the 30 subjects.
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Gender
F
F
F
M
F
F
F
M
M
F
F
M
M
M
F
F
M
Group
YND
YND
YND
YND
YND
YND
YND
YND
TND
TND
SLI
SLI
SLI
SLI
SLI
SLI
SLI
DIQ
110
92
92
100
86
105
90
96
90
92
86
86
94
98
89
84
110
Pronoun Errors (%)
94.40
19.05
62.50
18.75
0
55.00
100.00
86.67
32.43
0
60.00
40.00
31.58
66.67
42.86
27.27
33.33
18
19
20
21
22
23
24
25
26
27
28
29
30
F
F
M
M
M
M
F
M
F
M
F
F
F
SLI
SLI
SLI
OND
OND
OND
OND
OND
OND
OND
OND
OND
OND
107
87
95
110
113
113
109
92
108
95
87
94
98
0
0
0
0
0
0
0
0
0
0
0
0
0
a. Identify the variables in the data set as quantitative or qualitative.
b. Why is it nonsensical to compute numerical descriptive measure for qualitative
variables?
c. Compute measure of central tendency for DIQ for the ten SLI children.
d. Compute measures of central tendency for DIQ for the ten YND children.
e. Compute measures of central tendency for DIQ for the ten OND children.
f. Use the results, parts c-e, to compare the DIQ central tendencies of the three
groups of children. Is it reasonable to use a single number (e.g., mean or median)
to describe the center of the DIQ distribution? Or should three “centers” be
calculated, one for each of the three groups of children? Explain.
g. Repeat parts c-f for the percentage of pronoun errors.
2.66 (5 points) Mongolian desert ants. The Journal of Biogeography (Dec. 2003)
published an article on the first comprehensive study of ants in Mongolia (Central Asia).
Botanists placed seed baits at 11 study sites and observed the ant species attracted to each
site. Some of the data recorded at each study site are provided below.
Site
Region
1
2
3
4
5
6
7
8
9
10
11
Dry Steppe
Dry Steppe
Dry Steppe
Dry Steppe
Dry Steppe
Gobi Desert
Gobi Desert
Gobi Desert
Gobi Desert
Gobi Desert
Gobi Desert
Annual
Rainfall
(mm)
196
196
179
197
149
112
125
99
125
84
115
Max. Daily
Temp. (ºC)
5.7
5.7
7.0
8.0
8.5
10.7
11.4
10.9
11.4
11.4
11.4
Total
Plant
Cover (%)
40
52
40
43
27
30
16
30
56
22
14
Number
of Ant
Species
3
3
52
7
5
49
5
4
4
5
4
Species
Diversity
Index
.89
.83
1.31
1.48
.97
.46
1.23
.76
1.26
.69
a. Find the mean, median, and mode for the number of ant species discovered at
the 11 sites. Interpret each of these values.
b. Which measures of central tendency would you recommend to describe the
center of the number of ant species distribution? Explain.
c. Find the mean, median, and mode for the total plant cover percentage at the 5
Dry Steppe sites only.
d. Find the mean, median, and mode for the total plant cover percentage at the 6
Gobi Desert sites only.
e. Based on the results, parts c and d, does the center of the total plant cover
percentage distribution appear to be different at the two regions?