1. Finding the Mean, Median, and Mode
LESSON 9-1
Problem of the Day
On a bus, there are three times as many children as adults and twice as many girls as boys. If there are 8 girls on the bus, how many children are there? How many passengers?
12; 16
9-1

2. Finding the Mean, Median, and Mode
LESSON 9-1
Check Skills You’ll Need
(For help, go to Lesson 1-6.)
1. Vocabulary Review What is the inverse operation
of addition?
Solve each equation.
2. a + 14 = b – 5 = 26
c = – – 48 = d – 19
Check Skills You’ll Need
9-1

3. Finding the Mean, Median, and Mode
LESSON 9-1
Check Skills You’ll Need
Solutions
1. subtraction
–41
5. –29
9-1

4. Finding the Mean, Median, and Mode
LESSON 9-1
Additional Examples
Find the mean, the median, and the mode for the values in a set of coins with 4 pennies, 2 nickels, 3 dimes, and a quarter.
Mean
Add. = 69 10
Divide.
= 6.9
The mean is 6.9¢.
Median
Order the data.
There are an even number of
data items. Find the mean of
the middle two numbers.
= 5
5 + 5 2
The median is 5¢.
9-1

5. Finding the Mean, Median, and Mode
LESSON 9-1
Additional Examples
(continued)
Mode
Use the data item(s) listed
most often. 1 is the mode.
The mode is 1¢.
Quick Check
9-1

6. Finding the Mean, Median, and Mode
LESSON 9-1
Additional Examples
Find the range for: 5, –3.2, 1.5, 4.1, –7.3, 2.8,
–5.6, 9.8, and 1.7.
9.8 – (–7.3) = 17.1
The greatest value is 9.8. The least
value is –7.3. Subtract.
The range is 17.1.
Quick Check
9-1

7. Finding the Mean, Median, and Mode
LESSON 9-1
Additional Examples
The prices of new books bought for the library are in dollars below. How does the outlier affect the mean?
7.95, 5, 12.05, 10, 6.25, 8, 56, 8.75, 9, 7
56 is an outlier because it is $43.95 away from the closest data value.
Find the mean with the outlier.
= 13
130 10
Find the mean without the outlier.
8.22 74 9
The outlier raises the mean about $4.80.
Quick Check
9-1

8. Finding the Mean, Median, and Mode
LESSON 9-1
Additional Examples
A pet store asked 12 people the number of dogs
in their household. The responses were 2, 1, 0, 5, 2, 3, 1,
1, 7, 1, 1, and 1. Which measure of central tendency
would make the number of dogs per family seem
highest?
Order the data.
The mode is 1.
The median is 1.
The mean is 25 ÷ 12  2.1.
The greatest measure is the mean, so it would make the number
of dogs per family seem highest.
Quick Check
9-1

9. Finding the Mean, Median, and Mode
LESSON 9-1
Lesson Quiz
Use the data set below for problems 1–5.
0, –2, 3, 9, 1, –2, –1, 3, –2
1. Find the mean. 2. Find the median.
3. Find the mode. 4. Find the range.
5. Find the outlier. 1 –2 11 9
6. A dance teacher advertises individual attention and small class sizes.
He is currently teaching classes of 16, 18, 22, 25, 22, and 23 students.
Which measure of central tendency would make the class size look
smallest?
mean
9-1

10. Displaying Frequency
LESSON 9-2
Problem of the Day
Lucinda buys 12 gal of gasoline at $.95 per gallon. How much does the gas cost?
$11.40
9-2

11. 1. Vocabulary Review Which is the not a measure of
Displaying Frequency
LESSON 9-2
Check Skills You’ll Need
(For help, go to Lesson 9-1.)
1. Vocabulary Review Which is the not a measure of
central tendency—mean, median, or range?
Find the mean, median, mode, and range.
2. hours driving :
3. low temperatures:
4 –2 0 –1 2 –
Check Skills You’ll Need
9-2

12. median: The middle value is 8.
Displaying Frequency
LESSON 9-2
Check Skills You’ll Need
Solutions
1. range
2. mean: =
median: The middle value is 8.
mode: 7 and 8 are listed the greatest number of times.
range: 10 – 6 = 4
3. mean: 0.875; median: 1; no mode; range: 9 9 71 9
9-2

13. Make a line plot for the number of songs on a collection of CDs.
Displaying Frequency
LESSON 9-2
Additional Examples
Make a line plot for the number of songs on a
collection of CDs.
10  11  13  8  12  11  9  15  12  11  13  15  14
Each represents one CD.
The data are from 8 to 15.
Quick Check
9-2

14. Multiply each data value by its frequency.
Displaying Frequency
LESSON 9-2
Additional Examples
Find the mean, median, and mode of the data in the line plot Example 1.
Mean
(1 • 8) + (1 • 9) + (1 • 10) + (3 • 11) + (2 • 12) + (2 • 13) + (1 • 14) + (2 • 15)
Multiply each data value
by its frequency.
Add the frequency of each item
to find the total number of items.
9-2

15. Round to the nearest tenth.
Displaying Frequency
LESSON 9-2
Additional Examples
(continued)
154 13 =
Simplify.
11.8
Round to the nearest tenth.
Median There are 13 data items. Since the data are ordered,
the median is the seventh item, which is 12.
Mode The mode is the item that occurs most often, which is 11.
Quick Check
9-2

16. Displaying Frequency
LESSON 9-2
Additional Examples
The number of goals a soccer team scored in each game of the season is shown. Make a frequency table with intervals for the data.
0  3  0  0  7  2  1  0  4  1  0  3  6  0  1
Goals Tally Frequency 0– 2– 4– 6–
The data range
from 0 to 7.
Use equal-size
intervals that
begin with
multiples of 2.
9-2

17. (continued) Quick Check Displaying Frequency Additional Examples 9-2
LESSON 9-2
Additional Examples
(continued)
Quick Check
9-2

18. 1. Make a line plot for the number of school spirit ribbons purchased.
Displaying Frequency
LESSON 9-2
Lesson Quiz
1. Make a line plot for the number of school spirit ribbons purchased.
1 3 11 2 2 10 9 1 7 6 4 3 1 1
2. Find the mean of the data in the line plot in Exercise 1.
4.4
9-2

19. 3. Make a frequency table with intervals for the data.
Displaying Frequency
LESSON 9-2
Lesson Quiz
3. Make a frequency table with intervals for the data.
1 3 11 2 2 10 9 1 7 6 4 3 1 1
Sample:
Ribbons
0–2
3–5
6–8
9–11
Tally
Freq.
|||| |
||| || 6 3 2
4. Make a histogram for the data.
1 3 11 2 2 10 9 1 7 6 4 3 1 1
9-2

20. Round each number to the underlined digit.
Venn Diagrams
LESSON 9-3
Problem of the Day
Round each number to the underlined digit.
a b. 579,122 c 90
600,000
0.8348
9-3

21. 1. Vocabulary Review Two numbers whose sum is zero are ? .
Venn Diagrams
LESSON 9-3
Check Skills You’ll Need
(For help, go to Lesson 1-3.)
1. Vocabulary Review Two numbers whose sum is zero
are ? .
Simplify.
2. 10 –(–6)
3. –4 + 3 4.
16 + (– 9)
Check Skills You’ll Need
9-3

22. Solutions 1. additive inverses 2. 16 3. –1 4. 7 Venn Diagrams
LESSON 9-3
Check Skills You’ll Need
Solutions
1. additive inverses
3. –
9-3

23. Twenty children made drawings with crayons.
Venn Diagrams
LESSON 9-3
Additional Examples
Twenty children made drawings with crayons.
Thirteen children used red crayons to color. Of those
using red crayons, 4 children used only red to color.
Twelve children used blue crayons to color. Draw a Venn
diagram to represent the situation. How many children
used both red and blue crayons?
Nine children used both red and blue crayons.
Quick Check
9-3

24. 1. Forty-two students took summer school classes.
Venn Diagrams
LESSON 9-3
Lesson Quiz
1. Forty-two students took summer school classes.
Twenty-seven students took math, 28 took science,
and 1 took math only. Draw a Venn diagram. How many
students took both math and science?
26 students
9-3

25. Reading Graphs Critically
LESSON 9-4
Problem of the Day
Forty-three boys and five girls tried out for the middle school football team. One-fourth of the students were dropped after the first day. Of those who
were left, were dropped after the second day. Of those who remained,
made the team. How many students made the team? 1 6 4 5 24
9-4

26. Reading Graphs Critically
LESSON 9-4
Check Skills You’ll Need
(For help, go to the Skills Handbook page 641.)
1. Vocabulary Review What does a bar graph show?
2. The following data shows the number of students in a
class who prefer each primary color. Red: 12;Yellow: 3;
Blue: 10. Make a bar graph of this data.
Check Skills You’ll Need
9-4

27. Reading Graphs Critically
LESSON 9-4
Check Skills You’ll Need
Solutions
1. A bar graph compares amounts. 2.
9-4

28. Reading Graphs Critically
LESSON 9-4
Additional Examples
The graph makes it appear that almost twice as
much is earned on Thursday as on Monday. Explain.
The bar for Thursday appears to be twice as long as the bar for Monday because the scale on the vertical axis begins at 66 instead of 0.
Quick Check
9-4

29. Reading Graphs Critically
LESSON 9-4
Additional Examples
Using different scales, make two bar graphs for the
data. Use a break symbol in only one of the graphs.
Quarter Mile Records
Car Time(s)
Indy car
Sprint car
NASCAR stock car
Stock Bonneville
The highest time is 17 seconds.
Label the vertical axis with multiples of 5 from 0 to 20.
9-4

30. Reading Graphs Critically
LESSON 9-4
Additional Examples
(continued)
Quarter Mile Records
Car Time(s)
Indy car
Sprint car
NASCAR stock car
Stock Bonneville
The data start at 5 seconds. Label the vertical axis with multiples of 2.5,
beginning with 5. Use a break symbol.
Quick Check
9-4

31. Reading Graphs Critically
LESSON 9-4
Lesson Quiz
Use the graph for Questions 1–2.
1. The graph makes it appear that about 6 times as many
people prefer apple juice to prune juice. Explain.
The vertical scale has a break
in it, and it begins at 10.
2. How would you redraw the graph in Question 1 to more
accurately portray the data? Sketch the graph.
Sample: Use intervals of
5 from 0 to 30.
9-4

32. Stem-and-Leaf Plots
LESSON 9-5
Problem of the Day
The sum of 3 different one-digit numbers greater than 0 is 15. Two numbers are even, and one number is odd. Find all possible values for the numbers.
8, 6, 1; 8, 4, 3; 8, 2, 5; 6, 4, 5; 6, 2, 7; or 4, 2, 9
9-5

33. 1. Vocabulary Review What does a line plot display?
Stem-and-Leaf Plots
LESSON 9-5
Check Skills You’ll Need
(For help, go to Lesson 9-2.)
1. Vocabulary Review What does a line plot display?
Use the line plot for Exercises 2–4.
2. Find the mean.
3. Find the median.
4. Find the mode.
Check Skills You’ll Need
9-5

34. 1. the frequency of each data value
Stem-and-Leaf Plots
LESSON 9-5
Check Skills You’ll Need
Solutions
1. the frequency of each data value
4. 40 occurs most often.
(2 • 10) + (3 • 20) + (2 • 30) + (4 • 40) + (1 • 50)
350 12 = 2 =
9-5

35. Leaves are single digits, so use the first digits as the stems.
Stem-and-Leaf Plots
LESSON 9-5
Additional Examples
Make a stem-and-leaf plot for the data: 51, 56, 67, 44, 50, 63, 65, 58, 49, 51, 66, 59, 63, 47.
Step 1 Choose the stems. The least value is 44; the greatest value is 67.
Leaves are single digits, so use the first digits as the stems.
The stems in this case are 4, 5, and 6.
Step 2 Draw the stem-and-leaf plot.
stems leaves
The leaves are the ones place
written in increasing order.
Include a key.
The key explains what the stems and
leaves represent.
Key: 4 | 4 means 44
Quick Check
9-5

36. Basketball and Baseball Cards Basketball Baseball 9 9 8 1
Stem-and-Leaf Plots
LESSON 9-5
Additional Examples
Quick Check
Compare the number of basketball and baseball cards using the mode of each data set.
Basketball and Baseball Cards
Basketball Baseball
Key: means | 2 | means 29
The mode for basketball cards is 19 cards,
while the mode for baseball cards is 32 cards.
This measure of central tendency gives the impression that the number of baseball cards is greater than the number of basketball cards.
9-5

37. 1. Make a stem-and-leaf plot for the data. 21 39 20 22 22 31 40 33
Stem-and-Leaf Plots
LESSON 9-5
Lesson Quiz
1. Make a stem-and-leaf plot for the data.
21  39  20  22  22  31  40  33
2. Use your stem-and-leaf plot from Question 1 to find the median and mode.
median: 26.5; mode: 22
9-5

38. 3. The back-to-back stem-and-leaf plot shows the scores 16
LESSON 9-5
Lesson Quiz
3. The back-to-back stem-and-leaf plot shows the scores 16
students earned on their last math quiz. Compare each
class’s grades using the median for each group.
The median for Ms. Perez’s class is 67; the median for Mr. Harmon’s class is 45. From this data, it appears that students earned better grades on the quiz in Ms. Perez’s class compared to Mr. Harmon’s class.
9-5

39. Box-and-Whisker Plots
LESSON 9-6
Problem of the Day
Choose the symbol, <, =, or > that makes each statement true.
a   ?  b   ? 4 + 3 5 8 3 8 7 8 1 8 5 6 1 10 9 10 3 4 =
<
9-6

40. Box-and-Whisker Plots
LESSON 9-6
Check Skills You’ll Need
1. Vocabulary Review Which measure of central
tendency is the middle value of a data set?
(For help, go to Lesson 9-1.)
Find the median of each data set.
 32 24 22 25 24 35
3. 6 2 9 3 5 4 2 9 4 2 3
 95 92 91 95 96 97 98 96
Check Skills You’ll Need
9-6

41. Box-and-Whisker Plots
LESSON 9-6
Check Skills You’ll Need
Solutions
1. median
2. 22 23 24 24 25 32 35; 24 is the middle term
3. 2 2 2 3 3 4 4 5 6 9 9; 4 is the middle term
4. 90 91 92 95 95 96 96 97 98; 95 is the middle term
9-6

42. Box-and-Whisker Plots
LESSON 9-6
Additional Examples
Write a paragraph to compare the data shown in these plots.
The median attendance for football, around 1,750, is over four times
the median for soccer, 400.
The range for soccer is 2,600, which is larger than the range for footballs 900.
Attendance for football is more tightly grouped around the median than for soccer.
Quick Check
9-6

43. Box-and-Whisker Plots
LESSON 9-6
Additional Examples
Make a box-and-whisker plot for this data on study hours per week: 10, 13, 16, 17, 20, 22, 23, 24, 26, 30, 31.
Step 1 The data is in order from least to greatest. Find the median.
The median is the sixth number, 22.
Step 2 Find the lower quartile and the upper quartile. They are the
medians of the lower and upper halves.
The lower quartile is 16, and the upper quartile is 26.
9-6

44. Box-and-Whisker Plots
LESSON 9-6
Additional Examples
(continued)
Step 3 Draw a number line that spans all of the data values.
Mark points below the number line at the least and greatest values, at
the median, and at the lower and upper quartiles.
Mark the median.
Use the lower and upper quartiles to form a box.
Then draw whiskers from the box to the least and greatest values.
Quick Check
9-6

45. Box-and-Whisker Plots
LESSON 9-6
Lesson Quiz
1. Write a paragraph to describe the data in the following box-and-whisker plot.
2. Make box-and-whisker plots on a single number line to compare the
individual points scored by boys and girls.
Girls: 14, 15, 18, 20, 21, 21, 24, 24, 25, 27, 29
Boys: 8, 8, 9, 10, 14, 18, 25, 25, 28, 28, 30
3. Write a paragraph to compare the data in Question 2.
Answers will vary but should include lower quartile is 8, upper quartile is 14, median is 10, whiskers extend to 6 and 18
The range for the boys’ scores is greater than the girls’ scores. The girls’
shorter box means that their scores were more consistent. The girls’
lower quartile is equal to the boys’ median.
9-6

46. Making Predictions From Scatter Plots
LESSON 9-7
Problem of the Day
Suzanne saw six animals. Some were mice; two were doves; and the rest were rabbits. In all there were 20 legs. What different combinations of mice, doves, and rabbits might there be?
3 mice, 2 doves, 1 rabbit; or 2 mice, 2 doves, 2 rabbits; or 1 mouse,
2 doves, 3 rabbits
9-7

47. Making Predictions From Scatter Plots
LESSON 9-7
Check Skills You’ll Need
(For help, go to Lesson 3-4.)
1. Vocabulary Review What is an ordered pair ?
Graph each point on the same coordinate plane.
2. A(1, –2)
3. B(–3, 5)
Check Skills You’ll Need
9-7

48. Making Predictions From Scatter Plots
LESSON 9-7
Check Skills You’ll Need
Solutions
1. It identifies the location of a point.
2–3.
9-7

49. Making Predictions From Scatter Plots
LESSON 9-7
Additional Examples
Make a scatter plot for the data.
Miles Traveled and Gas Used
Step 1 Choose a scale along the x-axis to show the gallons of gas
used. The y-axis scale will represent the number of miles.
Step 2 (5, 150) represents a data pair. Plot each data pair.
Gas (gal) Miles
Quick Check
9-7

50. Making Predictions From Scatter Plots
LESSON 9-7
Additional Examples
Describe the trend of the data in the scatter plot
in Example 1 and draw a trend line. Then predict the
miles for 6 gallons of gas.
Step 1 Determine the type of trend.
The type of trend tells you the direction and
slope of the trend line. This scatter plot
shows a positive trend.
Step 2 Draw a line with a positive slope.
Make sure there are about as many points
above the line as there are below it.
9-7

51. Making Predictions From Scatter Plots
LESSON 9-7
Additional Examples
(continued)
Step 3 Find 6 gal along the horizontal axis. At 6 gal, the
trend line seems to go through the 185 miles mark. The miles
for 6 gallons of gas should be near 185 miles.
Quick Check
9-7

52. Making Predictions From Scatter Plots
LESSON 9-7
Lesson Quiz
The following data give the high temperatures for the first week in June.
Use this data to answer the questions.
(1, 68), (2, 70), (3, 65), (4, 67), (5, 71), (6, 75), (7, 74)
1. Make a scatter plot 2. Draw a trend line for the data in the
for the data. scatter plot in Question 1. Describe
the trend of the data.
positive trend
3. Predict what will happen to the high temperature in June
if the trend continues.
Sample: High temperatures will continue to rise.
9-7

53. Order from greatest to least: 0.677, 0.855, 0.760, 0.078, 0.541.
Circle Graphs
LESSON 9-8
Problem of the Day
Order from greatest to least: 0.677, 0.855, 0.760, 0.078,
0.855, 0.760, 0.677, 0.541, 0.078
9-8

54. 1. Vocabulary Review How are ratios and proportions related?
Circle Graphs
LESSON 9-8
Check Skills You’ll Need
(For help, go to Lesson 4-3.)
1. Vocabulary Review How are ratios and proportions
related?
Solve each proportion.
2. = = = = 2 3 16 y s 12 5 2 7 3 r 12 25 p 75
125
Check Skills You’ll Need
9-8

55. 1. A proportion is an equation stating that two ratios are equal.
Circle Graphs
LESSON 9-8
Check Skills You’ll Need
Solutions
1. A proportion is an equation stating that two ratios are equal.
2. 2y = 3 • s = 12 • r = 7 • 12
2y = 48 2s = r = 84
y s r
5. 75p = 3,125; p = = 41 2y 2 48 2 2s 2 60 2 3r 3 84 3 = = = = = =
3,125 75 2 3
9-8

56. How many students are there in the eighth grade?
Circle Graphs
LESSON 9-8
Additional Examples
Use this circle graph for a school with a total enrollment of 1,308 students.
How many students are there in the eighth grade?
1,308 • 36.4% = 1,
There are about 476 students enrolled in the eighth grade.
Quick Check
9-8

57. Favorite Season Number Spring 20 Summer 53 Fall 28 Winter 19
Circle Graphs
LESSON 9-8
Additional Examples
Make a circle graph for the results of a survey of students’ favorite season.
Favorite Season Number
Spring
Summer
Fall
Winter
Step 1 Add each number of responses
to find the total number of people in
the survey.
= 120
Step 2 Use proportions to find the measures of the central angles. 20
120
= a = 60° a
360° 28
= c = 84° c 53
= b = 159° b 19
= d = 57° d
9-8

58. Step 3 Use a compass to draw a circle.
Circle Graphs
LESSON 9-8
Additional Examples
(continued)
Step 3 Use a compass to draw a circle.
Mark the center of the circle and draw
a radius. Construct a central angle
with a protractor.
Step 4 Construct the other central angles using a protractor.
Step 5 Label each sector and title your graph.
Set up a key to make the graph easier to read.
Quick Check
9-8

59. The circle graph shows the survey results of 400 students.
LESSON 9-8
Lesson Quiz
The circle graph shows the survey results of 400 students.
1. What percent exercise 3–5 times each week?
2. How many exercise 6–8 times each week?
37%
68 students
3. A fruit seller has the following amounts of
fruit at his stand. Make a circle graph using
these data.
Mango, 33.3%; Banana 37.5%; Pear 16.7%;
Papaya 12.5%.
9-8

60. Choosing an Appropriate Graph
LESSON 9-9
Problem of the Day
Find the total cost of a shirt if the price marked is $23.69 and the tax rate is 6.3%.
$25.18
9-9

61. Choosing an Appropriate Graph
LESSON 9-9
Check Skills You’ll Need
(For help, go to Lesson 9-2.)
1. Vocabulary Review What do you call the number of
times a data item occurs?
2. Make a frequency table for the data set:
2, 0, 8, 3, 4, 1, 2.5, 0, 3, 1.5, 4, 8, 7, 2, 0, 3.5, 6.5
Check Skills You’ll Need
9-9

62. Choosing an Appropriate Graph
LESSON 9-9
Check Skills You’ll Need
Solutions
1. frequency 2.
Hours
Tally
Frequency
0–1.9
|||| 5
2–3.9
|||| | 6
4–5.9 || 2
6–7.9 || 2
8–9.9 || 2
9-9

63. Choosing an Appropriate Graph
LESSON 9-9
Additional Examples
Choose the appropriate graph to display the data about a survey of students’ favorite type of music. Explain your choice.
A stem-and-leaf plot is used to compare and find patterns in data that
all measure the same thing, which is not the case here.
The limited number of categories and the percents in the survey adding up to 100% make the circle graph a good choice.
Quick Check
9-9

64. Choosing an Appropriate Graph
LESSON 9-9
Additional Examples
This table shows membership in the Computer Club over several years. Decide which type of graph would be most appropriate. Explain your choice and draw the graph.
Since the data show a change
over time, a line graph
is appropriate.
Year Number of
Members
Quick Check
9-9

65. Choosing an Appropriate Graph
LESSON 9-9
Lesson Quiz
1. Which type of graph would be appropriate to show the
daily high temperatures for May? Explain your choice.
Sample: line graph shows changes during the month
2. Five students in a sixth-grade class are surveyed about
the number of hours they watched television and the
number of hours they worked on homework one Sunday.
Decide which type of graph would be most appropriate. Explain your choice.
Scatter plot; there are two pieces of data for each person, which can be
expressed as an ordered pair. You can look for a relationship between
the number of hours of television-watching and the number of hours of homework.
9-9

66. Choosing an Appropriate Graph
LESSON 9-9
Lesson Quiz
3. Draw the graph of the data in Question 2.
9-9