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Chapter 4Statistics: Data and Graphs
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Chapter 4Statistics: Data and Graphs
Click the mouse or press the space bar to continue.
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
44Statistics: Data and Graphs
Five-Minute Check (over Chapter 3)
Main Idea and Vocabulary
California Standards
Example 1
4-14-1 Collect and Organize Data
4-14-1 Collect and Organize Data
• I will take a survey, and collect and organize data.
• survey
• data
• tally chart
• frequency table
4-14-1 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.
Mrs. Patel asks her students what their favorite vegetable is. Organize the data given in a tally table and a frequency chart.
4-14-1 Collect and Organize Data
Step 1 Draw a table with two columns. Include a title.
Step 2 List each activity in the first column.
4-14-1 Collect and Organize Data
Step 3 Use tally marks or numbers to record the results.
4-14-1 Collect and Organize Data
4-14-1 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
4-14-1 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.
4-14-1 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.
4-14-1 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.
4-14-1 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.
4-14-1 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.
Five-Minute Check (over Lesson 4-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
4-24-2 Find Mode, Median, and Outliers
4-24-2 Find Mode, Median, and Outliers
• I will identify the mode, median, and outliers of a set of data.
• mode
• median
• outlier
4-24-2 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.
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.
4-24-2 Find Mode, Median, and Outliers
To find the median, first arrange the numbers in order from least to greatest. Then, find the middle number.
Answer: So, the median is also 4.
4-24-2 Find Mode, Median, and Outliers
1, 2, 2, 3, 4, 4, 4, 5, 6, 8, 9
Find the mode and median of the following set of data: 8, 2, 3, 4, 9, 2, 4, 6, 5, 1, 4
4-24-2 Find Mode, Median, and Outliers
A. mode = 0; median = 2
B. mode = 5; median = 5
C. mode = 6; median = 0
D. mode = 3; median = 5
Find the mode and median of the following set of data: 6, 8, 2, 4, 5, 0, 6, 7, 5, 5, 3
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.
4-24-2 Find Mode, Median, and Outliers
4-24-2 Find Mode, Median, and Outliers
A. 28
B. 30
C. 45
D. There are no outliers in this set of data.
Identify any outliers in the set of data:21, 27, 45, 25, 21, 28, 30
Five-Minute Check (over Lesson 4-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
4-34-3 Problem-Solving Strategy: Make a Table
4-34-3 Problem-Solving Strategy: Make a Table
• I will solve problems by making a table.
4-34-3 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.
4-34-3 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.
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?
4-34-3 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.
4-34-3 Problem-Solving Strategy: Make a Table
Plan
You can make a table to solve the problem.
4-34-3 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.
4-34-3 Problem-Solving Strategy: Make a Table
Check
Divide the total number of teachers by the number of teachers per group.
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.
4-34-3 Problem-Solving Strategy: Make a Table
16 ÷ 2 = 8
Five-Minute Check (over Lesson 4-3)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
4-44-4 Line Plots
4-44-4 Line Plots
• I will represent and interpret data in a line plot.
• line plot
4-44-4 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.
Organize the information from the frequency chart in a line plot.
4-44-4 Line Plots
Step 2 Mark an X above the number line to show each data item. Add a title.
4-44-4 Line Plots
4-44-4 Line Plots
Organize the information from the frequency chart in a line plot.
4-44-4 Line Plots
Organize the information from the frequency chart in a line plot.
A.
4-44-4 Line Plots
Organize the information from the frequency chart in a line plot.
B.
4-44-4 Line Plots
Organize the information from the frequency chart in a line plot.
C.
4-44-4 Line Plots
Organize the information from the frequency chart in a line plot.
D.
4-44-4 Line Plots
A.
Organize the information from the frequency chart in a line plot.
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.
4-44-4 Line Plots
Answer: So, the mode is 7, the median is 5, and 0 is an outlier.
4-44-4 Line Plots
4-44-4 Line Plots
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
Identify the mode, median, and outliers of the data shown.
Five-Minute Check (over Lesson 4-4)
Main Idea and Vocabulary
California Standards
Example 1
4-54-5 Bar and Double Bar Graphs
Make Double Bar Graphs
4-54-5 Bar and Double Bar Graphs
• I will use bar graphs to answer questions about a situation.
• double bar graph
4-54-5 Bar and Double Bar Graphs
Standard 4SDAP1.3 Interpret one- and two-variable data graphs to answer questions about a situation.
On which activity does Sanji spend the most time? How long does Sanji spend doing homework and reading?
4-54-5 Bar and Double Bar Graphs
4-54-5 Bar and Double Bar Graphs
Answer: Playing with friends is what Sanji spends most of his time doing.
To find which activity Sanji spends the most time doing, look for the longest bar.
4-54-5 Bar and Double Bar Graphs
40 + 50 = 90
Sanji spends 40 minutes on homework and 50 minutes on reading.
Answer: So, Sanji spends 90 minutes, or 1 hours, doing homework and reading.
12
4-54-5 Bar and Double Bar Graphs
On which activity does Sanji spend the least time? How long does Sanji spend eating and practicing sports?
4-54-5 Bar and Double Bar Graphs
A. playing with friends; 145 minutes
B. homework; 130 minutes
C. reading; 140 minutes
D. homework; 145 minutes
On which activity does Sanji spend the least time? How long does Sanji spend eating and practicing sports?
Five-Minute Check (over Lesson 4-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
4-64-6 Problem-Solving Investigation: Choose a Strategy
4-64-6 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
4-64-6 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.
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.
4-64-6 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.
4-64-6 Problem-Solving Investigation: Choose a Strategy
Plan
Organize the data in a table to solve the problem.
4-64-6 Problem-Solving Investigation: Choose a Strategy
Solve
For each round trip, the total cost increases by $1.50.
4-64-6 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.
4-64-6 Problem-Solving Investigation: Choose a Strategy
Answer: So, he can make 6 trips to school and back.
Check
Use a set of play money that is in piles of $1.50. Add the money until you have more than $10.
4-64-6 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 4-6)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
4-74-7 Interpret Line Graphs
Make a Line Graph
4-74-7 Interpret Line Graphs
• I will interpret data in a line graph.
• line graph
4-74-7 Interpret Line Graphs
Standard 4SDAP1.3 Interpret one- and two-variable data graphs to answer questions about a situation.
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.
4-74-7 Interpret Line Graphs
To find this day, find the lowest point on the line graph. Then, move down from this point. You find Thursday.
4-74-7 Interpret Line Graphs
Answer: So, the day the movie is least likely to be sold out is Thursday.
4-74-7 Interpret Line Graphs
Refer to the graph below. On what day were the most tickets sold to students for the school play?
4-74-7 Interpret Line Graphs
A. Friday
B. Thursday
C. Wednesday
D. Tuesday
Refer to the graph below. On what day were the most tickets sold to students for the school play?
Refer to the line graph below. What day showed the greatest increase of absences from the previous day?
4-74-7 Interpret Line Graphs
4-74-7 Interpret Line Graphs
To find the greatest increase from one day to the next, look for the steepest line between days.
4-74-7 Interpret Line Graphs
Answer: So, Tuesday shows the greatest increase of absences from Monday.
The line from Monday to Tuesday is the steepest.
4-74-7 Interpret Line Graphs
How many more tickets were sold on Thursday than Tuesday?
4-74-7 Interpret Line Graphs
A. 200
B. 150
C. 100
D. 50
How many more tickets were sold on Thursday than Tuesday?
Five-Minute Check (over Lesson 4-7)
Main Idea
California Standards
Example 1
Example 2
Example 3
4-84-8 Analyze Graphs
4-84-8 Analyze Graphs
• I will use graphs to display different kinds of data.
4-84-8 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.
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.
4-84-8 Analyze Graphs
4-84-8 Analyze Graphs
To identify the three most popular granola bars, find the three tallest stack of x’s.
4-84-8 Analyze Graphs
Answer: So, peanut, honey, and dried cherry are the student’s favorite types.
Peanut, honey, and dried cherry have the most x’s.
4-84-8 Analyze Graphs
Use the line plot to determine the three least popular granola bars in Mrs. Cruz’s class.
4-84-8 Analyze Graphs
A. cranberry, raisin, and strawberry
B. raisin, peanut, and oatmeal
C. cranberry, raisin, and coconut
D. peanut, honey, and dried cherry
Use the line plot to determine the three least popular granola bars in Mrs. Cruz’s class.
The bar graph shows the Chi family’s favorite sports to watch. Which is the least popular?
4-84-8 Analyze Graphs
4-84-8 Analyze Graphs
To determine the sport that is the least popular, find the bar that is the lowest on the graph.
4-84-8 Analyze Graphs
Golf has the lowest bar on the graph.
Answer: So, golf is the least popular sport.
4-84-8 Analyze Graphs
The bar graph shows the Chi family’s favorite sports to watch. Which is the most popular?
4-84-8 Analyze Graphs
A. basketball
B. gymnastics
C. football
D. hockey
The bar graph shows the Chi family’s favorite sports to watch. Which is the most popular?
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?
4-84-8 Analyze Graphs
The best day to go would probably be a day when it is the least crowded.
4-84-8 Analyze Graphs
Tuesday has the lowest attendance out of the entire week.
Answer: So, a good day to recommend to visit would be Tuesday because the park is the least crowded.
4-84-8 Analyze Graphs
4-84-8 Analyze Graphs
A. Thursday
B. Friday
C. Saturday
D. Sunday
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?
44Statistics: Data and Graphs
Five-Minute Checks
Make Double Bar Graphs
Make a Line Graph
44Statistics: Data and Graphs
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)
44Statistics: Data and Graphs
A. yes
B. no
(over Chapter 3)
Tell whether each equation is balanced.
3 + 7 = 3 + 3 + 4
44Statistics: Data and Graphs
A. yes
B. no
(over Chapter 3)
Tell whether each equation is balanced.
22 + 13 = 22 + 7 + 4
44Statistics: Data and Graphs
A. yes
B. no
Tell whether each equation is balanced.
37 – 8 = 37 – 12 + 3
(over Chapter 3)
44Statistics: Data and Graphs
(over Chapter 3)
A. yes
B. no
Tell whether each equation is balanced.
18 – 15 = 12 + 6 – 8 – 7
44Statistics: Data and Graphs
(over Lesson 4-1)
Carla took a survey to find out which sports her friends liked best. Organize the data into a tally table.
44Statistics: Data and Graphs
(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.
44Statistics: Data and Graphs
(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.
44Statistics: Data and Graphs
(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.
44Statistics: Data and Graphs
(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.
44Statistics: Data and Graphs
(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.
44Statistics: Data and Graphs
A. Baseball
B. Basketball
C. Soccer
D. Track
(over Lesson 4-1)
Identify the most popular sport.
44Statistics: Data and Graphs
A. media: 10; mode: 15
B. median: 12; mode: 15
C. median: 12; mode: 6
D. median: 6; mode: 10
(over Lesson 4-2)
Find the median and mode of each set of data.
1, 12, 15, 10, 6, 15
44Statistics: Data and Graphs
A. median: 5; mode: 2
B. median: 4.5; mode: 5
C. median: 5; mode: 5
D. median: 2; mode: 7
(over Lesson 4-2)
Find the median and mode of each set of data.
2, 5, 6, 4, 5, 7, 5, 2
44Statistics: Data and Graphs
A. $22
B. $46
C. $52
D. $62
(over Lesson 4-2)
Find any outlier(s) of each set of data.
Ticket prices: $52, $46, $62, $57, $22, $49
44Statistics: Data and Graphs
A. 10
B. 8
C. 20
D. 9
(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
44Statistics: Data and Graphs
A. 4 laps; 54 minutes
B. 6 laps; 32 minutes
C. 4 laps; 28 minutes
D. 6 laps; 36 minutes
(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?
44Statistics: Data and Graphs
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
(over Lesson 4-4)
Identify the mode, median and outlier for each data set.
2, 3, 3, 5, 8, 9, 22
44Statistics: Data and Graphs
(over Lesson 4-4)
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
Identify the mode, median and outlier for each data set.
0, 12, 14, 12, 15
44Statistics: Data and Graphs
A. grape
B. cranberry
C. orange
D. apple
(over Lesson 4-5)
Use the graph to answer the question. Which juice was most popular?
44Statistics: Data and Graphs
A. grapefruit
B. orange
C. apple
D. cranberry
(over Lesson 4-5)
Use the graph to answer the question. Which juice was least popular?
44Statistics: Data and Graphs
A. 9
B. 3
C. 10
D. 15
(over Lesson 4-5)
Use the graph to answer the question. How much more apple juice was sold than grape juice?
44Statistics: Data and Graphs
(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
44Statistics: Data and Graphs
(over Lesson 4-7)
A. Monday
B. Tuesday
C. Wednesday
D. Thursday
According to the graph, on which day were the fewest students absent?
44Statistics: Data and Graphs
(over Lesson 4-7)
A. 4
B. 6
C. 5
D. 3
How many more students were absent on Thursday than on Wednesday?
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