Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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504 Part 6 Corporate and Special Applications
Figure 24-9 Histogram—Residential Division
60
40
20
Jan.
Dollars
(thousands)
Feb.
Solar Metals—Materials Expense
Mar.
Apr.
May
Figure 24-10 Histogram—Commercial Division
Jan.
Dollars
(thousands)
Feb.
Solar Metals — Materials Expense
Mar.
Apr.
May
60
40
20
Quarterly Home Sales
Quarter 1st 2nd 3rd 4th
Sales last year 35 85 75 62
Sales prior year 25 73 64 50
Construct two line graphs on the same grid
showing quarterly home sales for last year and
for the prior year. Make the vertical scale from
0 to 100, and mark the four quarters on the
horizontal scale.
✔
The real estate firm’s quarterly home sales for last year and the prior year are as follows.
CONCEPT CHECK 24.7
100
75
50
25
0
1
st 2nd
Quarterly Home Sales
Last Year and Prior Year
3
rd 4th
prior yearlast year
A pie chart, sometimes called a circle graph, resembles a component bar graph because
it shows how one quantity is composed of different parts. In a pie chart, however, the
parts normally are written as percents. Figure 24-11 gives the sales data breakdown for
just the Bay View location of Sosa’s Markets. (Refer back to Figures 24-3 and 24-6.) The
pie chart shown in Figure 24-12 indicates how the Bay View sales revenue for the current
year is composed of cost of goods sold, operating expenses, and net profit.
Before the pie chart is drawn, the data are changed into percents, as shown in
Figure 24-11. The size of each part of the circle can be reasonably estimated by using
the fractional equivalents of the percents. In Figure 24-12, cost of goods sold is 50%,
or , of the circle. Operating expenses make up 37.5%, or , of the circle. The remaining
represents net profit.
1
8
3
8
1
2
Chapter 24 Business Statistics 505
Constructing Pie Charts
Construct pie charts.
8
Learning Objective
Cost of
Goods
Sold
$1,000,000
50%
Operating
Expenses
$750,000
37.5%
Net
Profit
$250,000
12.5%
Bay View Market Sales Revenue—Current Year
Figure 24-12 Pie Chart
© RADIUS IMAGES/JUPITERIMAGES
Figure 24-11 Sales Revenue for Bay View Market—Current Year
Amount Percent
Cost of Goods Sold $1,000,000 50.0%
Operating Expenses 750,000 37.5%
Net Profit Last Year 1 250,000 1 12.5%
Sales Revenue $2,000,000 100.0%
$1,000,000 4 $2,000,000 5 50.0%
$750,000 4 $2,000,000 5 37.5%
$250,000 4 $2,000,000 5 12.5%
Compare the pie chart in Figure 24-12 with the Bay View part of the component bar
graph in Figure 24-6.
506 Part 6 Corporate and Special Applications
Office Homes Percent
Shopping Mall Office 150 150 4 240 5 62.5%
Downtown Office 60 60 4 240 5 25%
Mountain Office 1 30 30 4 240 5 12.5%
Total 240 240 4 240 5 100%
25% is of the circle; 12.5% is half of another quarter, or
; 62.5% is the remaining eighth plus the remaining half,
or .
COMPLETE ASSIGNMENT 24.2.
5
8
1
8
1
4
✔
The home sales by three real estate offices for the past year are shown. Calculate the percent
of the total sales for each office, and make a pie chart showing each office’s share of the
total sales.
CONCEPT CHECK 24.8
Downtown
60 homes
25%
Mountain
30 homes
12.5%
Shopping
Mall
150 homes
62.5%
Home Sales Last Year
average
bar graph
business statistics
classes of data
comparative bar graph
component bar graph
frequency
frequency table
grouped data
histogram
line graph
mean
median
mode
pie chart
statistics
ungrouped data
Chapter Terms for Review
THE BOTTOM LINE
Chapter 24 Business Statistics 507
Summary of chapter learning objectives:
Learning Objective
24.1
Compute the mean.
Example
1. Compute the mean (rounded to one decimal place) for these seven
values: 34, 26, 18, 9, 21, 24, and 15.
24.2
Determine the median.
2. Determine the median for these seven values: 15, 26, 18, 9, 21, 24,
and 15.
24.3
Determine the mode.
3. Determine the mode for these seven values: 24, 21, 17, 9, 21, 26,
and 15.
24.4
Construct a frequency table.
4. Use the following set of data to construct a frequency table. Use the
classes 0 up to 100, 100 up to 200, and so on.
150 427 134 254 75
8 134 228 317 284
347 289 129 180 125
197 27 430 246 308
210 330 297 141 182
24.5
Construct histograms.
5. Construct a histogram from the following frequency table.
Class
Fr
equency
0 up to 100 6
100 up to 200 4
200 up to 300 7
300 up to 400 5
400 up to 500 13
Total 25
Answers: 1. 21 2. 18 3. 21
4. Class Tally Frequency 5.
0 up to 100 III 3
100 up to 200 9
200 up to 300 7
300 up to 400 IIII 4
400 up to 500 II 12
Total 25
IIII
II
IIII
IIII
10
8
6
4
2
0 100 200 300 400 500 600
508 Part 6 Corporate and Special Applications
THE BOTTOM LINE
Summary of chapter learning objectives:
Learning Objective
24.6
Construct bar graphs.
Example
6. Georgia Bailey is an automobile salesperson who sells coupes, sedans,
and sport utility vehicles. Her vehicle sales for April, May, June, and
July of this year are arranged in the table below. Also given are
Georgia’s total sales for the same four months last year.
V
ehicle Type April May June July
Coupe 9 6 9 8
Sports sedan 12 8 6 9
Sport utility vehicle 13 112 15 110
Totals this year 24 26 20 27
Totals last year 15 20 16 22
Construct a bar graph showing the four monthly totals for this year.
Make a vertical scale from 0 to 30, and mark the horizontal scale
April, May, June, and July.
7. Construct a comparative bar graph showing the four monthly totals
for this year and last year.
8. Construct a component bar graph showing car sales by model for
April through July of this year.
Answers: 6. 7.
8.
Coupe
Sedan
SUV
April May June
July
30
20
10
New Car Sales by Model
This Year
Last Year
30
20
10
New Car Sales—This Year vs. Last Year
April May June
July
30
20
10
April May
New Car Sales
June
July
.
.
.
.
.
.
.
.
.
THE BOTTOM LINE
Chapter 24 Business Statistics 509
Summary of chapter learning objectives:
Learning Objective
24.7
Construct line graphs.
Example
9. The monthly car sales for April, May, June, and July of this year and
last year for Georgia Bailey are as follows.
P
eriod A
pril May June July
This year 24 26 20 27
Last year 15 20 16 22
On one grid, construct line graphs showing her sales for these 4 months
during this year and last year.
Answers: 9. 10. 37.5%, 50%, 12.5%
Car Sales—April
coupe
37.5%
sedan
50%
sport
utility
vehicle
12.5%
30
20
10
April May June
July
New Car Sales—This Year vs. Last Year
This Year
Last Year
24.8
Construct pie charts.
10. In April of this year, Georgia Bailey sold the following numbers of
cars, arranged by type of vehicle.
V
ehicle Type Sales
Percent
Coupe 9
Sedan 12
Sport utility vehicle 1 3
Totals 24
Calculate the percent for each model. Then make a pie chart showing
Georgia’s sales for each model in April.
SELF-CHECK
Review Problems for Chapter 24
510 Part 6 Corporate and Special Applications
1 For the data 58, 65, 55, 77, 88, 58, 82, 66, 53, 58, 62, 52, 68, 58, 78, 61, 49, find (a) the mean, (b) the
median, and (c) the mode.
2 Use the data given to complete the following frequency distribution:
3 Use the frequency distributions from problem 2(a)–(d) to create the appropriate histogram. (Each vertical bar
should represent one part of the problem)
4 Kevin and Al Bianchini own two markets, Bianchini’s and Foodville. In a typical week, each store sells
approximately 2,400 lb of meat, fish, and poultry. Typical amounts are as follows:
Location Meat Fish Poultry
Bianchini’s 900 900 600
Foodville 1,200 300 900
a. Draw a comparative bar graph showing the sales of the two markets (two vertical bars for
each type of product).
b. Draw a component bar graph showing the sales of the two markets. Make one vertical bar
for each store, and each bar should show the amount of each product sold in that store.
c. Draw a pie chart for the sales for Bianchini’s market only.
86, 67, 85, 57, 72
61, 77, 53, 85, 67
69, 83, 79, 68, 71
59, 62, 88, 64, 81
Class Tally Frequency
50 up to 60 a.
60 up to 70 b.
70 up to 80 c.
80 up to 90 d.
Answers to the Self-Check can be found in Appendix B at the back of the text.
Chapter 24 Business Statistics 511
Assignment 24.1: Statistical Averages
Name
Date Score
A (52 points) Solve the following problems. (points for correct answers as marked)
1.
A department store has three local locations: Mason Plaza, Corbin Center, and Balbo Mall. The store gives
every applicant for any type of managerial job a test of basic business skills. Listed here are the scores from
the tests given to applicants at the three locations last week.
Mason Corbin Balbo
Plaza Center Mall
59 89 64
88 60 44
62 89 53
47 55 77
68 46 58
88 74 43
78 64 77
59 89 82
45 1
46 66
88 1
62
187
a. Find the mean, median, and mode for each location. (3 points for each correct answer)
Mason Corbin Balbo
Mean
Median
Mode
778988
636468
62.66869.9
626612769Sum
626612769
1
Learning Objectives
2 3 4
Mason Plaza mean
Corbin Center mean
Balbo Mall mean
Balbo Mall median 5
64 1 62
2
5
126
2
5 63
5
626
10
5 62.6
5
612
11
5 69.9
Mason Plaza: 88, 88, 88, 87, 78, 68, 62, 59, 59, 47, 45
Corbin Center: 89, 89, 89, 74, 64, 60, 55, 46, 46
Balbo Mall: 82, 77, 77, 66, 64, 62, 58, 53, 44, 43
b. Combine all the scores into one frequency
distribution with the classes as shown. (1 point
for each correct answer)
Class Tally Frequency
40 up to 50
50 up to 60
60 up to 70
70 up to 80
80 up to 90
8
IIII III
4
IIII
7
IIII II
5
IIII
6
IIII I
2. Cirano Aguilar operates a popular coffee cart from which he also sells sandwiches. He has the opportunity to
open another cart in the inner patio of a complex of office buildings, but he won’t be allowed to sell sandwiches.
Perform a statistical analysis on Cirano’s sales receipts for nonsandwich items for the first 15 work days of May
and September. (3 points for each correct answer)
May September
$430 $470 $450 $200 $320 $430
240 350 240 340 240 295
280 260 340 280 230 360
305 360 370 290 370 420
325 190 250 220 250 180
a. Find the mean for May.
b. Find the mean for September.
c. Find the median for May.
d. Find the median for September.
e. Find the combined mean for all 30 days.
(Hint: Add the two sums and divide by 30.)
$309.50
$290
$325
$295
$324
May sum 5 $4,860; May mean 5
May: 470, 450, 430, 370, 360, 350, 340, 325, 305, 280, 260, 250, 240, 240, 190
$4,860
15
5 $324
B (48 points) Solve the following problems. (points for correct answers as marked)
3. La Morra Bank & Trust Co. has several retail branches. Bank management wants to compare the ages of
personal banking customers at two specific branches—the Financial District Branch, downtown, and the
University Branch, located in a residential area between the local university and a retirement community.
The bank’s analyst randomly selects 30 personal banking customers from each bank and writes down their
ages. The following two tables show the results.
Financial District Branch University Branch
43 30 43 51 60 74 82 46 19 20
68 32 72 52 27 21 36 73 57 18
28 73 43 19 64 54 17 18 75 84
70 35 56 55 31 76 22 24 19 68
63 24 47 44 34 27 21 75 34 18
52 61 66 57 58 81 64 22 60 70
a. Compute the mean age of the group of customers from the Financial District Branch. (8 points)
b. Compute the mean age of the group of customers from the University Branch. (8 points)
c. Make two frequency tables of customer ages, one for the Financial District Branch and one for the University
Branch. For each table, use frequency classes 10 up to 20, 20 up to 30, . . . , 80 up to 90. (2 points for each correct
row in each table)
Financial District Branch University Branch
Class Tally Frequency Class Tally Frequency
Mean 5 1,375 4 30 5 45.8
45.8
Mean 5 1,458 4 30 5 48.6
48.6
1,3752782642582423331,458274278327255324
297294
175212
209247
248227
205251
241227
512 Part 6 Corporate and Special Applications
Assignment 24.1 Continued
May median is $325
Sept. sum 5 $4,425; Sept. mean 5
Sept.: 430, 420, 370, 360, 340, 320, 295, 290, 280, 250, 240, 230, 220, 200, 180
Sept. median is $290
Combined mean 5
$4,860 1 $4,425
30
5
$9,285
30
5 $309.50
$4,425
15
5 $295
10 up to 20 I 1 10 up to 20 I 6
20 up to 30 III 3 20 up to 30 II 7
30 up to 40 5 30 up to 40 II 2
40 up to 50 5 40 up to 50 I 1
50 up to 60 II 7 50 up to 60 II 2
60 up to 70 I 6 60 up to 70 III 3
70 up to 80 III 3 70 up to 80 IIII I 6
80 up to 90 10 80 up to 90 III 13
Total 30 Total 30
IIII
IIII
IIII
IIII
IIII
IIII
Score for B (48)
Score for A (52)
Chapter 24 Business Statistics 513
Assignment 24.2: Graphs and Charts
Name
Date Score
A (18 points) Complete the following problem as directed. (9 points for each correct graph)
1. After doing the initial research in problem 3 of Assignment 24.1, the analyst from La Morra Bank randomly
selected 100 customers from the Financial District Branch and 100 customers from the University Branch.
She found the age of each customer and summarized the data in the following two frequency tables.
Financial District Branch University Branch
Class Frequency Class Frequency
10 up to 20 5 10 up to 20 20
20 up to 30 10 20 up to 30 21
30 up to 40 15 30 up to 40 10
40 up to 50 21 40 up to 50 9
50 up to 60 18 50 up to 60 5
60 up to 70 16 60 up to 70 7
70 up to 80 12 70 up to 80 15
80 up to 90 1 3 80 up to 90 113
Total 100 Total 100
5
Learning Objectives
6 7 8
a. Draw a histogram for the Financial District
Branch. Label each axis, and write a title under
the graph.
b. Draw a histogram for the University Branch.
Label each axis, and write a title under the graph.
Score for A (18)
20
20
15
10
5
10
Number of
Customers
Age
University Branch Customers
4030 6050 80 9070
20
20
15
10
5
10
Number of
Customers
Age
Financial District Customers
4030 6050 80 9070