1. Chapter 4
Statistics: Data and Graphs
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2. Statistics: Data and Graphs
4
Lesson 4-1 Collect and Organize Data
Lesson 4-2 Find Mode, Median, and Outliers
Lesson 4-3 Problem-Solving Strategy: Make
a Table
Lesson 4-4 Line Plots
Lesson 4-5 Bar and Double Bar Graphs
Lesson 4-6 Problem-Solving Investigation:
Choose a Strategy
Lesson 4-7 Interpret Line Graphs
Lesson 4-8 Analyze Graphs

3. 4-1 Collect and Organize Data
Five-Minute Check (over Chapter 3)
Main Idea and Vocabulary
California Standards
Example 1

4. 4-1 Collect and Organize Data
• I will take a survey, and collect and organize data.
• survey • tally chart
• data • frequency table

5. 4-1 Collect and Organize Data
Standard 4SDAP1.1 Formulate survey questions;
systematically collect and represent data on a
number line; and coordinate graphs, tables, and
charts.

6. 4-1 Collect and Organize Data
Mrs. Patel asks her students what their favorite
vegetable is. Organize the data given in a tally table
and a frequency chart.

7. 4-1 Collect and Organize Data
Step 1 Draw a table with two columns. Include a title.
Step 2 List each activity in the first column.

8. 4-1 Collect and Organize Data
Step 3 Use tally marks or numbers to record the
results.

9. 4-1 Collect and Organize Data
Tally Chart Frequency Table

10. 4-1 Collect and Organize Data
A teacher asked her students what their favorite
season of the year is. Organize the data given in a
tally table and a frequency chart.
Winter: Jessica, Adam
Spring: Xavier, Aida, Maria, Tyrone
Summer: Isi, Judy, Gabriel, Leon, Alicia
Fall: Victor, Adriana, Toru

11. 4-1 Collect and Organize Data
A teacher asked her students what their favorite
season of the year is. Organize the data given in a
tally table and a frequency chart.
A.

12. 4-1 Collect and Organize Data
A teacher asked her students what their favorite
season of the year is. Organize the data given in a
tally table and a frequency chart.
B.

13. 4-1 Collect and Organize Data
A teacher asked her students what their favorite
season of the year is. Organize the data given in a
tally table and a frequency chart.
C.

14. 4-1 Collect and Organize Data
A teacher asked her students what their favorite
season of the year is. Organize the data given in a
tally table and a frequency chart.
D.

15. 4-1 Collect and Organize Data
A teacher asked her students what their favorite
season of the year is. Organize the data given in a
tally table and a frequency chart.
D.

17. 4-2 Find Mode, Median, and Outliers
Five-Minute Check (over Lesson 4-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2

18. 4-2 Find Mode, Median, and Outliers
• I will identify the mode, median, and outliers of
a set of data.
• mode
• median
• outlier

19. 4-2 Find Mode, Median, and Outliers
Standard 4SDAP1.2 Identify the mode(s) for sets
of categorical data and the mode(s), median, and
any apparent outliers for numerical data sets.

20. 4-2 Find Mode, Median, and Outliers
Find the mode and median of the following set of
data: 8, 2, 3, 4, 9, 2, 4, 6, 5, 1, 4
To find the mode, find the number that occurs most
often.
8, 2, 3, 4, 9, 2, 4, 6, 5, 1, 4
Answer: So, the mode is 4.

21. 4-2 Find Mode, Median, and Outliers
Find the mode and median of the following set of
data: 8, 2, 3, 4, 9, 2, 4, 6, 5, 1, 4
To find the median, first arrange the numbers in
order from least to greatest. Then, find the middle
number.
1, 2, 2, 3, 4, 4, 4, 5, 6, 8, 9
Answer: So, the median is also 4.

22. 4-2 Find Mode, Median, and Outliers
Find the mode and median of the following set of
data: 6, 8, 2, 4, 5, 0, 6, 7, 5, 5, 3
A. mode = 0; median = 2
B. mode = 5; median = 5
C. mode = 6; median = 0
D. mode = 3; median = 5

23. 4-2 Find Mode, Median, and Outliers
Identify any outliers in the set of data:
12, 10, 20, 11, 9, 14, 12
Look for a number that is either much larger or much
smaller than the rest of the data items.
The number 20 is an outlier because it is much larger
than the rest of the other data items, which are between
9 and 14.

24. 4-2 Find Mode, Median, and Outliers
Identify any outliers in the set of data:
21, 27, 45, 25, 21, 28, 30
A. 28
B. 30
C. 45
D. There are no outliers in this set of data.

26. 4-3 Problem-Solving Strategy: Make a Table
Five-Minute Check (over Lesson 4-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy

27. 4-3 Problem-Solving Strategy: Make a Table
• I will solve problems by making a table.

28. 4-3 Problem-Solving Strategy: Make a Table
Standard 4MR2.3 Use a variety of methods, such
as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain
mathematical reasoning.

29. 4-3 Problem-Solving Strategy: Make a Table
Standard 4NS3.0 Students solve
problems involving addition, subtraction,
multiplication, and division of whole numbers
and understand the relationships among the
operations.

30. 4-3 Problem-Solving Strategy: Make a Table
The music club at Steven’s school is going to a
concert. There are 2 teachers going to the
concert for every 9 students going. If there are
16 teachers going, how many students are
going to the concert?

31. 4-3 Problem-Solving Strategy: Make a Table
Understand
What facts do you know?
• There are 2 teachers going for every 9 students
going to the concert.
• The total number of teachers going is 16.
What do you need to find?
• Find how many students are going to the
concert.

32. 4-3 Problem-Solving Strategy: Make a Table
Plan
You can make a table to solve the problem.

33. 4-3 Problem-Solving Strategy: Make a Table
Solve
Make a table to show that there are 2 teachers
going for every 9 students going.
Answer: So, 72 students are going to the concert.

34. 4-3 Problem-Solving Strategy: Make a Table
Check
Divide the total number of teachers by the
number of teachers per group.
16 ÷ 2 = 8
There are 8 groups going. There are 9 students
in each group. So, there are 8 x 9 = 72 students
going altogether. The answer is correct.

36. 4-4 Line Plots
Five-Minute Check (over Lesson 4-3)
Main Idea and Vocabulary
California Standards
Example 1
Example 2

37. 4-4 Line Plots
• I will represent and interpret data in a line plot.
• line plot

38. 4-4 Line Plots
Standard 4SDAP1.3 Interpret one- and two-
variable data graphs to answer questions about
a situation.
Standard 4SDAP1.2 Identify the mode(s) for sets
of categorical data and the mode(s), median, and
any apparent outliers for numerical data sets.

39. 4-4 Line Plots
Organize the information
from the frequency chart
in a line plot.

40. 4-4 Line Plots
Step 1 Draw and label a number line.

41. 4-4 Line Plots
Step 2 Mark an X above the number line to show each
data item. Add a title.

42. 4-4 Line Plots
Organize the information
from the frequency chart
in a line plot.

43. 4-4 Line Plots
Organize the information from the frequency chart
in a line plot.
A.

44. 4-4 Line Plots
Organize the information from the frequency chart
in a line plot.
B.

45. 4-4 Line Plots
Organize the information from the frequency chart
in a line plot.
C.

46. 4-4 Line Plots
Organize the information from the frequency chart
in a line plot.
D.

47. 4-4 Line Plots
Organize the information from the frequency chart
in a line plot.
A.

48. 4-4 Line Plots
Students in Mr. Ramos’s homeroom were asked
how many school dances they attended last year.
Identify the mode, median, and outliers of the data
shown.

49. 4-4 Line Plots
Answer: So, the mode is 7, the median is 5, and 0
is an outlier.

50. 4-4 Line Plots
Identify the mode, median, and outliers of the
data shown.

51. 4-4 Line Plots
Identify the mode, median, and outliers of the
data shown.
A. mode = 7, median = 5, outlier = 8
B. mode = 4, median = 0, outlier = 7
C. mode = 0, median = 8, outlier = 4
D. mode = 8, median = 7, outlier = 0

53. 4-5 Bar and Double Bar Graphs
Five-Minute Check (over Lesson 4-4)
Main Idea and Vocabulary
California Standards
Example 1
Make Double Bar Graphs

54. 4-5 Bar and Double Bar Graphs
• I will use bar graphs to answer questions about
a situation.
• double bar graph

55. 4-5 Bar and Double Bar Graphs
Standard 4SDAP1.3 Interpret one- and two-
variable data graphs to answer questions
about a situation.

56. 4-5 Bar and Double Bar Graphs
On which activity does Sanji spend the most time?
How long does Sanji spend doing homework and
reading?

57. 4-5 Bar and Double Bar Graphs
To find which
activity Sanji
spends the most
time doing, look for
the longest bar.
Answer: Playing with friends is what Sanji spends
most of his time doing.

58. 4-5 Bar and Double Bar Graphs
Sanji spends 40
minutes on
homework and 50
minutes on reading.
40 + 50 = 90
Answer: So, Sanji spends 90 minutes, or 1 1 hours,
2
doing homework and reading.

59. 4-5 Bar and Double Bar Graphs
On which activity does Sanji spend the least time?
How long does Sanji spend eating and practicing
sports?

60. 4-5 Bar and Double Bar Graphs
On which activity does Sanji spend the least time?
How long does Sanji spend eating and practicing
sports?
A. playing with friends; 145 minutes
B. homework; 130 minutes
C. reading; 140 minutes
D. homework; 145 minutes

62. 4-6 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 4-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation

63. 4-6 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.

64. 4-6 Problem-Solving Investigation: Choose a Strategy
Standard 4MR2.3 Use a variety of methods, such
as words, numbers, symbols, chart, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
Standard 4NS2.1 Estimate and compute the sum
or difference of whole numbers and positive
decimals in two places.

65. 4-6 Problem-Solving Investigation: Choose a Strategy
TAO: I take the subway to get to
school and back. Each round trip
costs $1.50. My subway card has a
value of $10.
YOUR MISSION: Find how many round
trips Tao can make with $10.

66. 4-6 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• Each round trip costs $1.50.
• Tao’s subway card has a value of $10.
What do you need to find?
• Find out how many round trips he can make.

67. 4-6 Problem-Solving Investigation: Choose a Strategy
Plan
Organize the data in a table to solve the problem.

68. 4-6 Problem-Solving Investigation: Choose a Strategy
Solve
For each round trip, the total cost increases
by $1.50.

69. 4-6 Problem-Solving Investigation: Choose a Strategy
Solve
Tao’s card has a value of $10. He cannot
make a seventh trip because after making 6
trips he has only $1 left. This is not enough
for another trip.
Answer: So, he can make 6 trips to school
and back.

70. 4-6 Problem-Solving Investigation: Choose a Strategy
Check
Use a set of play money that is in piles of
$1.50. Add the money until you have more
than $10.

72. 4-7 Interpret Line Graphs
Five-Minute Check (over Lesson 4-6)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Make a Line Graph

73. 4-7 Interpret Line Graphs
• I will interpret data in a line graph.
• line graph

74. 4-7 Interpret Line Graphs
Standard 4SDAP1.3 Interpret one- and two-
variable data graphs to answer questions about
a situation.

75. 4-7 Interpret Line Graphs
Refer to the line graph below. On which day is the
movie least likely to be sold out?
The movie is least likely to be sold out on the day the
theater has sold the least number of tickets.

76. 4-7 Interpret Line Graphs
To find this day, find the lowest point on the line graph.
Then, move down from this point. You find Thursday.
Answer: So, the day the movie is least likely to be
sold out is Thursday.

77. 4-7 Interpret Line Graphs
Refer to the graph below. On what day were the
most tickets sold to students for the school play?

78. 4-7 Interpret Line Graphs
Refer to the graph below. On what day were the
most tickets sold to students for the school play?
A. Friday
B. Thursday
C. Wednesday
D. Tuesday

79. 4-7 Interpret Line Graphs
Refer to the line graph below. What day showed
the greatest increase of absences from the
previous day?

80. 4-7 Interpret Line Graphs
To find the greatest increase from one day to the next,
look for the steepest line between days.

81. 4-7 Interpret Line Graphs
The line from Monday to Tuesday is the steepest.
Answer: So, Tuesday shows the greatest
increase of absences from Monday.

82. 4-7 Interpret Line Graphs
How many more tickets were sold on Thursday
than Tuesday?

83. 4-7 Interpret Line Graphs
How many more tickets were sold on Thursday
than Tuesday?
A. 200
B. 150
C. 100
D. 50

85. 4-8 Analyze Graphs
Five-Minute Check (over Lesson 4-7)
Main Idea
California Standards
Example 1
Example 2
Example 3

86. 4-8 Analyze Graphs
• I will use graphs to display different kinds of data.

87. 4-8 Analyze Graphs
Standard 4SDAP1.3 Interpret one- and two-
variable data graphs to answer questions
about a situation.
Standard 4SDAP1.1 Formulate survey questions;
systematically collect and represent data on a
number line; and coordinate graphs, tables and
charts.

88. 4-8 Analyze Graphs
Use the line plot to determine the three most
popular granola bars in Mrs. Cruz’s class. Each
student voted for his or her two favorite types.

89. 4-8 Analyze Graphs
To identify the three most popular granola bars, find the
three tallest stack of x’s.

90. 4-8 Analyze Graphs
Peanut, honey, and dried cherry have the most x’s.
Answer: So, peanut, honey, and dried cherry
are the student’s favorite types.

91. 4-8 Analyze Graphs
Use the line plot to determine the three least
popular granola bars in Mrs. Cruz’s class.

92. 4-8 Analyze Graphs
Use the line plot to determine the three least
popular granola bars in Mrs. Cruz’s class.
A. cranberry, raisin, and strawberry
B. raisin, peanut, and oatmeal
C. cranberry, raisin, and coconut
D. peanut, honey, and dried cherry

93. 4-8 Analyze Graphs
The bar graph shows the Chi family’s favorite
sports to watch. Which is the least popular?

94. 4-8 Analyze Graphs
To determine the sport that is the least popular, find the
bar that is the lowest on the graph.

95. 4-8 Analyze Graphs
Golf has the lowest bar on the graph.
Answer: So, golf is the least popular sport.

96. 4-8 Analyze Graphs
The bar graph shows the Chi family’s favorite
sports to watch. Which is the most popular?

97. 4-8 Analyze Graphs
The bar graph shows the Chi family’s favorite
sports to watch. Which is the most popular?
A. basketball
B. gymnastics
C. football
D. hockey

98. 4-8 Analyze Graphs
The Villa family is planning to go to the water park
one day next week. Based upon the information in
this line graph, what day would you recommend
they visit?

99. 4-8 Analyze Graphs
The best day to go would probably be a day when it is
the least crowded.
Tuesday has the lowest attendance out of the entire
week.

100. 4-8 Analyze Graphs
Answer: So, a good day to recommend to visit would
be Tuesday because the park is the least
crowded.

101. 4-8 Analyze Graphs
The Villa family does not like to go to the park
when there are a lot of people. Based upon the
information in this line graph, what day should
they not go to the water park?
A. Thursday
B. Friday
C. Saturday
D. Sunday

103. Statistics: Data and Graphs
4
Five-Minute Checks
Make Double Bar Graphs
Make a Line Graph

104. Statistics: Data and Graphs
4
Lesson 4-1 (over Chapter 3)
Lesson 4-2 (over Lesson 4-1)
Lesson 4-3 (over Lesson 4-2)
Lesson 4-4 (over Lesson 4-3)
Lesson 4-5 (over Lesson 4-4)
Lesson 4-6 (over Lesson 4-5)
Lesson 4-7 (over Lesson 4-6)
Lesson 4-8 (over Lesson 4-7)

105. Statistics: Data and Graphs
4
(over Chapter 3)
Tell whether each equation is balanced.
3+7=3+3+4
A. yes
B. no

106. Statistics: Data and Graphs
4
(over Chapter 3)
Tell whether each equation is balanced.
22 + 13 = 22 + 7 + 4
A. yes
B. no

107. Statistics: Data and Graphs
4
(over Chapter 3)
Tell whether each equation is balanced.
37 – 8 = 37 – 12 + 3
A. yes
B. no

108. Statistics: Data and Graphs
4
(over Chapter 3)
Tell whether each equation is balanced.
18 – 15 = 12 + 6 – 8 – 7
A. yes
B. no

109. Statistics: Data and Graphs
4
(over Lesson 4-1)
Carla took a survey to find out which sports her
friends liked best. Organize the data into a tally
table.

110. Statistics: Data and Graphs
4
(over Lesson 4-1)
Carla took a survey to find out which sports her
friends liked best. Organize the data into a tally
table.
A.

111. Statistics: Data and Graphs
4
(over Lesson 4-1)
Carla took a survey to find out which sports her
friends liked best. Organize the data into a tally
table.
B.

112. Statistics: Data and Graphs
4
(over Lesson 4-1)
Carla took a survey to find out which sports her
friends liked best. Organize the data into a tally
table.
C.

113. Statistics: Data and Graphs
4
(over Lesson 4-1)
Carla took a survey to find out which sports her
friends liked best. Organize the data into a tally
table.
D.

114. Statistics: Data and Graphs
4
(over Lesson 4-1)
Carla took a survey to find out which sports her
friends liked best. Organize the data into a tally
table.
A.

115. Statistics: Data and Graphs
4
(over Lesson 4-1)
Identify the most popular sport.
A. Baseball
B. Basketball
C. Soccer
D. Track

116. Statistics: Data and Graphs
4
(over Lesson 4-2)
Find the median and mode of each set of data.
1, 12, 15, 10, 6, 15
A. media: 10; mode: 15
B. median: 12; mode: 15
C. median: 12; mode: 6
D. median: 6; mode: 10

117. Statistics: Data and Graphs
4
(over Lesson 4-2)
Find the median and mode of each set of data.
2, 5, 6, 4, 5, 7, 5, 2
A. median: 5; mode: 2
B. median: 4.5; mode: 5
C. median: 5; mode: 5
D. median: 2; mode: 7

118. Statistics: Data and Graphs
4
(over Lesson 4-2)
Find any outlier(s) of each set of data.
Ticket prices: $52, $46, $62, $57, $22, $49
A. $22
B. $46
C. $52
D. $62

119. Statistics: Data and Graphs
4
(over Lesson 4-2)
Find any outlier(s) of each set of data.
Ages of team members: 9, 8, 10, 9, 8, 9, 20, 10, 8
A. 10
B. 8
C. 20
D. 9

120. Statistics: Data and Graphs
4
(over Lesson 4-3)
Solve. Use the Make a Table strategy. Jamilla is
running laps around a track. She runs a lap in 4
minutes. If she runs for 24 minutes, how many laps
has she run? How long would it take her to run 9
laps?
A. 4 laps; 54 minutes
B. 6 laps; 32 minutes
C. 4 laps; 28 minutes
D. 6 laps; 36 minutes

121. Statistics: Data and Graphs
4
(over Lesson 4-4)
Identify the mode, median and outlier for each data
set.
2, 3, 3, 5, 8, 9, 22
A. mode: 2; median: 5; outlier: 22
B. mode: 3; median: 5; outlier: 2
C. mode: 3; median: 5; outlier: 22
D. mode: 22; median: 5; outlier: 22

122. Statistics: Data and Graphs
4
(over Lesson 4-4)
Identify the mode, median and outlier for each data
set.
0, 12, 14, 12, 15
A. mode: 12; median: 14; outlier: 15
B. mode: 12; median: 12; outlier: 0
C. mode: 0; median: 12; outlier: 15
D. mode: 15; median: 12; outlier: 0

123. Statistics: Data and Graphs
4
(over Lesson 4-5)
Use the graph to answer the question. Which juice
was most popular?
A. grape
B. cranberry
C. orange
D. apple

124. Statistics: Data and Graphs
4
(over Lesson 4-5)
Use the graph to answer the question. Which
juice was least popular?
A. grapefruit
B. orange
C. apple
D. cranberry

125. Statistics: Data and Graphs
4
(over Lesson 4-5)
Use the graph to answer the question. How much
more apple juice was sold than grape juice?
A. 9
B. 3
C. 10
D. 15

126. Statistics: Data and Graphs
4
(over Lesson 4-6)
Make a table to solve the problem. Benji’s dad
gives him $15 each week to buy lunch at school.
He wants to save $1.50 to buy a treat at the end of
the week. If he spends $2.50 for lunch each day,
will he have enough money at the end of the week
for his treat?
A. Yes
B. No

127. Statistics: Data and Graphs
4
(over Lesson 4-7)
According to the graph, on which day were the
fewest students absent?
A. Monday
B. Tuesday
C. Wednesday
D. Thursday

128. Statistics: Data and Graphs
4
(over Lesson 4-7)
How many more students were absent on Thursday
than on Wednesday?
A. 4
B. 6
C. 5
D. 3

129. This slide is intentionally blank.