GUIDED PRACTICE
✓
Concept Check ✓
Vocabulary Check
Skill Check
✓
11–16. Check plots.
11. 50, 52, 54, 60, 63, 65, 70,
74, 74, 74, 75, 78, 78
3 APPLY
1. Define the mean, the median, and the mode of a collection of numbers.
See margin.
2. Explain why you might make a stem-and-leaf plot for a data collection.
See margin.
3. Give an example in which the mean of a collection of numbers is not
Day 1: p. 371 Exs. 11–20
Day 2: pp. 371–374 Exs. 21–27,
29, 33, 36, 37, 41, 42, 44–46,
50–58 even
Sample answer: 3, 4, 5, 5, 4, 3, 2, 2, 152; the mean is 20.
4. Make a stem-and-leaf plot
22, 34, 11, 55, 13, 22,
for the data at the right.
30, 21, 39, 48, 38, 46
See margin.
Find the mean, the median, and the mode of the collection of numbers.
5. 2, 2, 2, 2, 4, 4, 5 3, 2, 2
13. 1, 2, 3, 4, 5, 20, 20, 22, 24,
26, 28, 28, 28, 30, 31, 37, 39
9. Use the stem-and-leaf plot below to order the data set.
11, 13, 13, 15, 16, 17, 18, 20, 20, 22, 25, 27, 27, 28, 31, 33, 34, 37, 38
1 6 3 8 1 7 5 3
1
2
10.
2
8 2 5 0 7 7 0
3
8 3 1 4 7
AVERAGE
6. 5, 10, 15, 1, 2, 3, 7, 8 6.375, 6, no mode
7. º4, 8, 9, º6, º2, 1 1, º}}, no mode
15. 30, 33, 37, 39, 44, 48, 52,
54, 61, 61, 62, 68, 68, 76,
76, 76, 77, 79, 80, 81, 82,
84, 86, 87, 87
BASIC
representative of a typical number in the collection.
12. 17, 18, 19, 20, 22, 23, 24,
29, 30, 39, 40, 45, 50, 51
14. 1, 9, 10, 12, 13, 15, 17, 23,
30, 31, 32, 32, 32, 38, 39,
41, 45, 46
ASSIGNMENT GUIDE
8. 6.5, 3.2, 1.7, 10.1, 3.2 4.94, 3.2, 3.2
ADVANCED
Day 1: p. 371 Exs. 11–20
Day 2: pp. 371–374 Exs. 21–27,
29, 30–34, 36, 37, 41–46,
50–58 even
Key: 3 | 8 = 38
BLOCK SCHEDULE
AGES If someone said that the mean age of everyone in your algebra
1
class is about 16ᎏᎏ years, do you think the age of the teacher was included
2
in the calculation? Explain. Sample answer: If the class is fairly large and the teacher
is very young, the teacher’s age may have been included. If the class is small and the
teacher is much older than the students, the teacher’s age was probably not included.
PRACTICE AND APPLICATIONS
STUDENT HELP
Extra Practice
to help you master
skills is on p. 802.
MAKING STEM-AND-LEAF PLOTS Make a stem-and-leaf plot for the data.
Use the result to list the data in increasing order. 11–16. See margin.
11. 60, 74, 75, 63, 78, 70, 50,
74, 52, 74, 65, 78, 54
13. 4, 31, 22, 37, 39, 24, 2, 28,
1, 26, 28, 30, 28, 3, 20, 20, 5
16. 10, 12, 13, 13, 17, 18, 19,
21, 21, 23, 25, 25, 33, 35,
40, 42, 44, 46, 48, 48, 50,
50, 57
15. 87, 61, 54, 77, 79, 86, 30, 76, 52,
44, 48, 76, 87, 68, 82, 61, 84,
33, 39, 68, 37, 80, 62, 81, 76
pp. 371–374 Exs. 11–27, 29, 33, 34,
36, 37, 41, 42, 44–46, 50–58 even
EXERCISE LEVELS
Level A: Easier
44–49
Level B: More Difficult
11–27, 29, 33–37, 41, 42, 50–59
Level C: Most Difficult
28, 30–32, 38–40, 43
12. 24, 29, 17, 50, 39, 51, 19, 22,
40, 45, 20, 18, 23, 30
14. 15, 39, 13, 31, 46, 9, 38, 17, 32,
10, 12, 45, 30, 1, 32, 23, 32, 41
16. 48, 10, 48, 25, 40, 42, 44, 23,
21, 13, 50, 17, 18, 19, 21, 57,
35, 33, 25, 50, 13, 12, 46
STUDENT HELP
FINDING MEAN, MEDIAN, AND MODE Find the mean, the median, and the
mode of the collection of numbers.
HOMEWORK HELP
17. 4, 2, 10, 6, 10, 7, 10 7, 7, 10
18. 1, 2, 1, 2, 1, 3, 3, 4, 3 2}2}, 2, 1 and 3
19. 8, 5, 6, 5, 6, 6 6, 6, 6
20. 4, 4, 4, 4, 4, 4 4, 4, 4
21. 5, 3, 10, 13, 8, 18, 5, 17, 2,
7, 9, 10, 4, 1 8, 7.5, 5 and 10
22. 12, 5, 6, 15, 12, 9, 13, 1, 4, 6,
8, 14, 12 9, 9, 12
23. 3.56, 4.40, 6.25, 1.20, 8.52, 1.20
4.19, 3.98, 1.2
24. 161, 146, 158, 150, 156, 150
153.5, 153, 150
Example 1: Exs. 11–16,
32–34
Example 2: Exs. 17–27
Example 3: Exs. 36, 37
Example 4: Exs. 29, 30
Day 1: p. 371 Exs. 11–20
Day 2: pp. 371–374 Exs. 21–27,
29, 33, 34, 36, 37, 41, 42,
44–46, 50–58 even
9
6.6 Stem-and-Leaf Plots and Mean, Median, and Mode
371
HOMEWORK CHECK
To quickly check student understanding of key concepts, go
over the following exercises:
Exs. 12, 18, 22, 25, 29, 36. See
also the Daily Homework Quiz:
• Blackline Master (Chapter 6
Resource Book, p. 93)
•
Transparency (p. 51)
1. Sample answer: Given a set of
n numbers, the mean is the sum of
the numbers divided by n, the
median is the middle number when
the numbers are written in order,
and the mode is the number(s) that
occurs most frequently. If n is
even, the median is the average of
the two middle numbers.
2 and 4. See Additional Answers
beginning on page AA1.
371
STUDENT HELP NOTES
Homework Help Students
can find help for Ex. 29 at
www.mcdougallittell.com.
The information can be printed
out for students who don't have
access to the Internet.
EXERCISE 32 A histogram that is
skewed slightly to the left could
represent the first set of data, with
the lower mean age. A histogram
that is skewed slightly to the right
could represent the second set of
data, with the higher mean age.
STUDENT HELP
NE
ER T
person is a multimillionaire who makes $5,000,000 per year. The mean
annual salary in the town is $74,750. Is the mean a fair measure of a typical
salary in the town? What is the mean annual salary of the other 99 adults?
HOMEWORK HELP
Visit our Web site
www.mcdougallittell.com
for help with problem
solving in Ex. 29.
See margin.
32. Sample answers: (1) 10,
12, 12, 12, 18, 18, 18, 20,
20, 20
(2) 12, 12, 15, 15, 16, 16,
18, 18, 29, 29
NUMBER OF HOUSEHOLDS The
30.
U.S. Bureau of the Census reports on the
number of households (in thousands) in
each state. Some of the data are shown in
the table. Is one measure of central
tendency the most representative of the
typical number of households in these
states? Explain your reasoning. See margin.
31. Use the data in Exercise 30. If you exclude
California from the data, is one measure of
central tendency the most representative of
the data? Explain your reasoning.
INT
31. Sample answer: The
median (619) and the
mode (619) are both
slightly more representative than the mean
(753) because they are
closer to more scores in
the lower three fourths
of the data.
NE
ER T
Households
Arizona
California
Colorado
Idaho
Montana
Nevada
New Mexico
Utah
Wyoming
1,687
11,101
1,502
430
341
619
619
639
184
32. CRITICAL THINKING Create two different sets of data, each having 10 ages.
Create one set so that the mean age is 16 and the median age is 18. Create the
other set so that the median age is 16 and the mean age is 18. See margin.
33.
BIRTHDAYS Use a stem-and-leaf plot (months as stems, days as leaves)
to write the birthdays in order from earliest in the year to latest (1 = January,
2 = February, and so on). Include a key with your stem-and-leaf plot.
See margin.
4–14
7–31
12–28
4–17
2–22
8–21
1–24
9–12
1–3
4–30
10–17
6–5
1–25
5–10
4–1
8–26
12–15
3–17
4–30
2–3
11–11
6–13
11–4
6–24
6–3
4–8
2–20
11–28
12–9
372
State
DATA UPDATE Visit our Web site www.mcdougallittell.com
10–11
33. See Additional Answers beginning on page AA1.
372
63
80
69
61
60
58
90
110
76
61
29. No; the mean salary of
25. Find the mean and the median for the set
the other 99 adults is
$25,000. The median and
of data. 72.8, 66
mode (both $25,000) are
much more representative 26. Write the numbers in decreasing order.
110, 90, 80, 76, 69, 63, 61, 61, 60, 58
of the “average” salary.
27. Does the set of data have a mode? If so,
30. Sample answer: The
what is it? yes; 61
median (619) and the
mode (619) are both more 28. CRITICAL THINKING What number could
representative of the data
you add to the set of data to make it have
than the mean (1902), due
more than one mode? Explain why you
to the high population in
chose the number. See margin.
䉴 Source: The Baseball Encyclopedia
California.
29.
AVERAGE SALARY A small town has an adult population of 100. One
DATA UPDATE
Updated data for Exs. 30
and 31 are available at
www.mcdougallittell.com.
APPLICATION NOTE
EXERCISE 31 If the census data
were graphed on a scatter plot, the
number of households in California
would appear as an outlier, that is,
it falls outside the overall pattern of
the graph. When outliers exist, it is
helpful also to describe the spread
of the data, using, for example,
the range.
Shutouts
Christy Mathewson
Eddie Plank
Nolan Ryan
Bert Blyleven
Don Sutton
Grover Alexander
Walter Johnson
Cy Young
Tom Seaver
allowing a run.
INT
APPLICATION NOTE
EXERCISE 29 A histogram of the
salaries would probably show most
salaries clustered around $25,000
(the mean excluding the millionaire).
The multimillionaire’s salary would
stand alone at the distant right of
the histogram. This indicates that
the millionaire’s salary pulled the
mean toward itself. Income data
are often pulled, or skewed, to the
right because there are likely to be
many moderate incomes in a group,
some large incomes, and a small
number of very large incomes.
28. You could add any of the
BASEBALL In Exercises 25–28, use the following information.
numbers (other than 61) in The table shows the number of shutouts that
Pitcher
the list. There would be ten baseball pitchers had in their careers. A
two modes, the number
Warren Spahn
shutout is a complete game pitched without
you added and 61.
Chapter 6 Solving and Graphing Linear Inequalities
34. 106, 108, 118, 126, 143,
146, 148, 158, 164, 177,
195, 206
35. 204.4, 219.3, 221.4, 221.7,
222.6, 225.2, 239.3, 247.8,
257.0, 257.4
34.
WEIGHTS The numbers shown below represent the weights (in pounds)
of twelve high school students. Use a stem-and-leaf plot to order the weights
of the students from least to greatest. (Hint: Use 17|7 = 177 for your key.)
177, 164, 108, 158, 195, 206, 106, 126, 143, 118, 148, 146 See margin for plot.
35.
ASTEROIDS The numbers below are the mean distances from the sun (in
millions of miles) of the first ten asteroids. Use a stem-and-leaf plot to order
the distances from least to greatest. (Hint: Use 25|70 = 257.0 for your key.)
257.0, 257.4, 247.8, 219.3, 239.3, 225.2, 221.4, 204.4, 221.7, 222.6
See margin for plot.
VACATIONS In Exercises 36–38, use the following information.
Vacation Travel
Number of employees
A business conducted a survey of its
employees who go on vacation every year.
Each person was asked to report the
number of miles traveled (to the nearest
hundred) on the last vacation. The
responses are shown in the histogram.
APPLICATION NOTE
EXERCISE 38 The median can
be determined in terms of the area
of a histogram: the area to the left
of the median equals the area to the
right. Adding the new data value
adds a little area to the right side of
the histogram, so the median will
shift to the right to a position that
equalizes the areas of the histogram on both sides of the median.
16
14
12
10
8
6
4
2
0
36. Find the median of the data. 300
38. Sample answer:
It would not affect either. 37. Find the mode of the data. 300
There would be 51
38. Writing Suppose a new employee
numbers in the data set
traveled 400 miles on the last
0 100 200 300 400 500 600
and the median would be
vacation. Decide whether this would
the twenty-sixth, which
Miles
would be 300. The
affect the median or the mode.
number 400 would still
Explain your thinking.
appear fewer times than
the number 300, which
EXTENSION: DOUBLE STEM-AND-LEAF PLOT In Exercises 39 and 40, use
would still be the mode.
the following information.
39. Sample answers:
Another type of visual model that you can use is a double stem-and-leaf plot.
• About half of the top
This type of visual model is used to compare two sets of data. The Stem column
17 male and female
is in the middle of the plot, so that the “stem” can apply to both sets of data.
golfers had fewer than
40 tournament wins.
The double stem-and-leaf plot below shows the number of all-time tournament
• For both males and
wins by the top 17 male and female professional golfers.
females, by far the
䉴 Source: Professional Golfers Association
most common stem
was 3, meaning
Male
Stem
Female
between 30 and 39
tournament wins.
1 8 8 2
• There were 4 male and
0 7
2 female golfers with
60 or more tournament
3 0 6
wins.
2 1 5 7 5 0
40. Sample answer:
The positions of the
0 0 4 4 2 2
stems and leaves on the
0 1 8 6 3 2 1 3 8 5 2 1 1 1
left-hand plot must be
reversed. To make
9 9 2 9 9 6
Key: 1 | 3 | 8 = 31, 38
standard ordered stemand-leaf plots, the order
39. What conclusions can be drawn from the double stem-and-leaf plot? See margin.
of the stems must be
reversed and the leaves
40. Use the data in the double stem-and-leaf plot to make two conventional stemmust be arranged in
and-leaf plots. Explain what changes you need to make. See margin for plots.
increasing order.
6.6 Stem-and-Leaf Plots and Mean, Median, and Mode
373
COMMON ERROR
EXERCISE 39 Students can easily be confused by a double stemand-leaf plot because they must
read the left side of the plot from
right to left. Remind students that
this plot has single stems, which
are shared by leaves on both sides.
34.
35.
10
11
12
13
14
15
16
17
18
19
20
6 8
8
6
20
21
22
23
24
25
44
93
14 17 26 52
93
78
Key: 2570 = 257.0
70 74
3 6 8
8
4
7
5
6
Key: 177 = 177
40. See Additional Answers beginning on page AA1.
ADDITIONAL PRACTICE
AND RETEACHING
For Lesson 6.6:
• Practice Levels A, B, and C
(Chapter 6 Resource Book, p. 82)
• Reteaching with Practice
(Chapter 6 Resource Book, p. 85)
•
See Lesson 6.6 of the
Personal Student Tutor
For more Mixed Review:
•
Search the Test and Practice
Generator for key words or
specific lessons.
373
4 ASSESS
Test
Preparation
DAILY HOMEWORK QUIZ
43. a. }}, or
Transparency Available
Make a stem-and-leaf plot of
the data. Find the mean, median,
and mode.
1. High temperatures (°F)
55 47 52 55 59 61 70
56 48 45 54 63 57 62
4
5
6
7
84 + 92 + 76 + x
4
x + 252
}}
4
x + 252
b. }} ≥ 85; 88
4
c. Sample answer: The
average of the three
tests is 84. Subtract
3 ª 84 from 4 ª 85;
the result is 88.
5 7 8
2 4 5 5 6 7 9
1 2 3
0
Key: 61 = 61
★ Challenge
QUANTITATIVE COMPARISON In Exercises 41 and 42, choose the statement
below that is true about the given numbers.
A
¡
B
¡
C
¡
D
¡
11.1
11.2
11.3
11.4
11.5
11.6
9
8
5
2
6
1
11.49, 11.56, 11.56
The two numbers are equal.
The relationship cannot be determined from the given information.
Column B
41.
The mean of 1, 2, 3, 4, 5, 5, 10
The mean of 2, 3, 4, 5, 5, 10, 11
B
42.
The mode of º2, º2, º2, 4
The mode of º2, º2, º3, º3, º3
A
43.
TEST SCORES You have test scores of 84, 92, and 76. There will be one
more test in the marking period. You want your mean test score for the
marking period to be 85 or higher. See margin.
a. Let x represent your last test score. Write an expression for the mean of
your test scores for the marking period.
b. Write and solve an inequality to find what you must score on the last test.
EXTRA CHALLENGE
c. Solve the problem without using algebra. Describe your method. Do your
answers agree?
www.mcdougallittell.com
7 9
8
6 7 8
2 7 9 Key: 11.56 = 11.56
The number in column B is greater.
Column A
56, 55.5, 55
2. 100 meter race results (sec)
11.35 11.42 11.19 11.56 11.69
11.61 11.56 11.58 11.48 11.28
11.62 11.67 11.57 11.39 11.37
The number in column A is greater.
MIXED REVIEW
EVALUATING EXPRESSIONS Evaluate the expression. (Review 1.3 for 6.7)
44. 35 + 40 ÷ 2 55
EXTRA CHALLENGE NOTE
47. x + 5 > 11; 6 not a solution
49.
46. 237 º 188 ÷ 4
190
48. 2z º 3 < 4; 4 not a solution
1
ROAD TRIP You and two friends each agree to drive ᎏᎏ of a 75-mile trip.
3
Which equation would you use to find the number of miles each of you must
drive? (Review 1.5) A
ADDITIONAL TEST
PREPARATION
1. WRITING Explain how you can
use a stem-and-leaf plot to determine the median of a set of data.
1
B. ᎏᎏx = 75
3
A. 3x = 75
FINDING SLOPE Find the slope of the graph of the linear function ƒ.
(Review 4.8)
See sample answer below.
2. OPEN ENDED Describe a
real-life situation in which the
mean is lower than the median.
50. ƒ(2) = º1, ƒ(5) = 5 2
51. ƒ(0) = 5, ƒ(5) = 0 º1
52. ƒ(º3) = º12, ƒ(3) = 12 4
53. ƒ(0) = 1, ƒ(4) = º1 º}}
1
2
SOLVING INEQUALITIES Solve the inequality and graph the solution.
(Review 6.2–6.4) 54–59. See margin for graphs.
Sample answer: You just bought
5 CDs, four that cost $14.99 and
one that was on sale for $5. The
mean price of the CDs is lower
than the median price.
374
358
CHECKING SOLUTIONS Check whether the given number is a solution of
the inequality. (Review 1.4)
Challenge problems for
Lesson 6.6 are available in
blackline format in the Chapter 6
Resource Book, p. 90 and at
www.mcdougallittell.com.
54–59. See Additional Answers
beginning on page AA1.
45. 120 ª 3 º 2
54. ºx + 7 > 13 x < º6 55. 16 º x ≤ 7 x ≥ 9
57. 7 < 3 º 2x ≤ 19
º8 ≤ x < º2
374
58. |x º 3| < 12
º9 < x < 15
56. º4 < x + 3 < 7
º7 < x < 4
59. |x + 16| ≥ 9
x ≤ º25 or x ≥ º7
Chapter 6 Solving and Graphing Linear Inequalities
Additional Test Preparation Sample answer:
1. Create an ordered stem-and-leaf plot for the data.
Count either from the top or the bottom to locate the
middle number in the leaves if there is an odd number
of data values. Read this leaf with its stem. This is the
median. If there is an even number of data values,
locate the middle two numbers in the leaves and find
their mean. This number with its stem is the median.