Chapter 2: Graphs, Charts, and Tables--Describing Your Data

54 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA
2-7. The following cumulative relative frequency distribution
summarizes data obtained in a study of the
ending overages (in dollars) for the cash register
balance at a business:
Cumulative
Relative Relative
Class Frequency Frequency Frequency
−60.00 – −40.00 2 0.04 0.04
−40.00 – −20.00 2 0.04 0.08
−20.00 – 00.00 8 0.16 0.24
00.00 – 20.00 16 0.32 0.56
20.00 – 40.00 20 0.40 0.96
40.00 – 60.00 2 0.04 1.00
a. Determine the proportion of the days in which
there were no shortages
b. Determine the proportion of the days the cash
register was less than $20 off.
c. Determine the proportion of the days in which
the cash register was less than $40 over or at
most $20 short.
2-8. You are given the following data:
6 10 6 4 9 5
5 5 5 7 6 2
5 5 5 4 5 7
6 7 8 6 8 4
7 5 5 5 5 7
8 7 6 7 5 4
6 4 4 7 4 6
6 7 8 6 7 6
7 8 5 6 5 7
3 6 4 7 4 4
a. Construct a frequency distribution for these
data.
b. Based on the frequency distribution, develop a
histogram.
c. Construct a relative frequency distribution.
d. Develop a relative frequency histogram.
e. Compare the two histograms. Why do they look
alike?
2-9. Using the data from Problem 2-8,
a. Construct a grouped data relative frequency
distribution of the data. Use the 2 k n guideline
to determine the number of classes.
b. Construct a cumulative frequency distribution
of the data.
c. Construct a relative frequency histogram.
d. Construct an ogive.
Business Applications
2-10. Wendy’s is one of the largest fast-food chains in
the world. Recently, the district manager for
Wendy’s in Las Vegas conducted a study in which
she selected a random sample of sales receipts.
She was interested in the number of line items on
the receipts. For instance, if a customer ordered
two 1 / 4 -pound hamburgers, one side of fries, and
two soft drinks, the number of line items would be
five. The following data were observed:
7 5 7 6 5 5 4 8 6 5
8 7 6 5 6 2 9 4 4 5
8 4 9 6 6 5 8 9 9 1
6 5 10 6 7 6 5 5 5 6
8 7 6 8 6 6 9 6 12 7
5 6 7 11 4 4 3 4 1 4
11 2 5 5 8 2 3 4 9 6
6 5 8 6 3 6 4 5 8 10
a. Develop a frequency distribution for these data.
Discuss briefly what the frequency distribution
tells you about these sample data.
b. Based on the results in part a, construct a frequency
histogram for these sample data.
2-11. In a survey conducted by NFO Interactive,
investors were asked to rate how knowledgeable
they felt they were as investors. Both online and
traditional investors were included in the survey.
The survey resulted in the following data:
Of the online investors, 8%, 55%, and 37%
responded they were “savvy,” “experienced,”
and “novice,” respectively.
Of the traditional investors, the percentages
were 4, 29, and 67, respectively.
Six hundred investors were surveyed, of which 200
were traditional investors.
a. Use the information to construct a joint frequency
distribution.
b. Use the information to construct a joint relative
frequency distribution.
c. Determine the proportion of investors who
were both online investors and rated themselves
experienced.
d. Calculate the proportion of investors who were
online investors.
2-12. KXGH Television, Channel 7, is the NBC affiliate
in a mid-size southeastern city. Recently, the station’s
sales manager surveyed 20 advertisers and
asked each one to rate the service of the station on
the following scale:
VERY GOOD GOOD FAIR POOR VERY POOR
1 2 3 4 5