Name: ___________________________________________________________ Date: ______________
Statistics Problem Packet
1. The test grades for a certain class were entered into a Minitab worksheet, and then “Descriptive Statistics”
were requested. The results were:
MTB > Describe 'Grades'.
Grades
N
28
MEAN
74.71
MEDIAN
76.00
Grades
MIN
35.00
MAX
94.00
Q1
68.00
STDEV
12.61
Q3
84.00
You happened to see, on a scrap of paper, that the lowest grades were 35, 57, 59, 60, . . . but you don’t know
what the other individual grades are. Nevertheless, a knowledgeable user of statistics can tell a lot about the
dataset simply by studying the set of descriptive statistics above.
(a)




Write a brief description of what the results tell you about the distribution of grades. Be sure to address:
the general shape of the distribution
unusual features, including possible outliers
the middle 50% of the data
any significance in the difference between the mean and the median. Why might the mean be lower?
(b) Construct a box and whisker plot for these data.
2. The following table gives the Nielsen ratings for the top 50 prime-time television shows for the first half of
the 1994-95 viewing season. Each ratings point represents 954,000 households.
Show
Home Improvement
Grace Under Fire
Seinfeld
E.R.
NYPD Blue
60 Minutes
Monday Night Football
Roseanne
Murder, She Wrote
Ellen
Frasier
Mad About You
Murphy Brown
CBS Sunday Movie
Madman of the People
NBC Monday Movie
Friends
Dave’s World
20/20
Me and the Boys
Full House
Law and Order
Love and War
Northern Exposure
The Nanny
Network
ABC
ABC
NBC
NBC
ABC
CBS
ABC
ABC
CBS
ABC
NBC
NBC
CBS
CBS
NBC
NBC
NBC
CBS
ABC
ABC
ABC
NBC
CBS
CBS
CBS
Rating
20.8
20.0
19.7
18.5
18.1
17.9
17.4
17.3
16.2
15.5
15.0
14.8
14.8
14.7
14.6
14.1
13.9
13.8
13.7
13.5
13.0
12.9
12.8
12.8
12.8
Show
ABC Sunday Movie
Wings
NBC Sunday Movie
Step by Step
Beverly Hills, 90210
Walker, Texas Ranger
Dr. Quinn, Med. Woman
Family Matters
Dateline NBC Tuesday
CBS Tuesday Movie
Boy Meets World
John Larroquette Show
Hangin’ with Mr. Cooper
Turning Point
Earth 2
Due South
Rescue 911
Chicago Hope
Fresh Prince of Bel-Air
Blossom
All-American Girl
Diagnosis Murder
The Cosby Mysteries
Picket Fences
SeaQuest DSV
Network
ABC
NBC
NBC
ABC
FOX
CBS
CBS
ABC
NBC
CBS
ABC
NBC
ABC
ABC
NBC
CBS
CBS
CBS
NBC
NBC
ABC
CBS
NBC
CBS
NBC
Rating
12.8
12.6
12.0
11.7
11.6
11.6
11.5
11.5
11.5
11.4
11.4
11.4
11.3
11.2
10.9
10.9
10.9
10.7
10.6
10.6
10.5
10.5
10.5
10.3
10.2
(a) Make a stem and leaf plot of the ratings for the 16 programs that were broadcast by ABC and the 17 by
NBC.
(b) How does ABC compare with NBC in the race for high ratings? Give appropriate graphical (dotplot or
steam and leaf) and numerical evidence to support your answer. As long as you can defend your answer
with math, your answer is right.
3. We all “know” that the body temperature of a healthy person is 98.6°F. In reality, the actual body
temperature of individuals varies. Here is a back-to-back stemplot of the body temperatures of 130 healthy
individuals (65 males and 65 females).
(a) Here are boxplots, produced by Minitab, for these distributions. Label both boxplots with the fivenumber summary values.
Males
Females
96
97
98
99
100
101
(b) Determine whether the 3 points graphed by the + symbol are indeed outliers by our defined criteria.
(c) Write a few sentences comparing the body temperatures of adult males and females.
4. The following data represent scores of 50 students on a calculus test.
72
57
74
71
65
72
67
76
53
51
93
72
79
67
75
70
57
72
65
68
59
83
61
100
75
78
76
72
83
66
74
74
73
69
77
65
56
76
61
61
73
68
67
72
64
80
67
49
68
74
(a) Construct a histogram for this data set.
(b) Describe the shape, center, and spread of the distribution of test scores.
(c) Would the mean and standard deviation be appropriate measures of center and spread for these test
scores? Explain.