Math Gr4 Ch4

Chapter 4
Statistics: Data and Graphs
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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

4-1 Collect and Organize Data

Five-Minute Check (over Chapter 3)
Main Idea and Vocabulary
California Standards
Example 1


• I will take a survey, and collect and organize data.

• survey • tally chart
• data • frequency table


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.


Step 1 Draw a table with two columns. Include a title.

Step 2 List each activity in the first column.


Step 3 Use tally marks or numbers to record the
results.


Tally Chart Frequency Table


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



A.



B.



C.



D.

4-2 Find Mode, Median, and Outliers

Five-Minute Check (over Lesson 4-1)
Example 1
Example 2


• I will identify the mode, median, and outliers of
a set of data.

• mode
• median
• outlier


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.


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.


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


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.


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.

4-3 Problem-Solving Strategy: Make a Table

Main Idea
Example 1: Problem-Solving Strategy


• I will solve problems by making 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.


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?


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.


Plan
You can make a table to solve the problem.


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.


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.

4-4 Line Plots

Example 1
Example 2

4-4 Line Plots

• I will represent and interpret data in a line plot.

• line plot

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.

4-4 Line Plots

Organize the information
from the frequency chart
in a line plot.

4-4 Line Plots

Step 1 Draw and label a number line.

4-4 Line Plots

Step 2 Mark an X above the number line to show each
data item. Add a title.

4-4 Line Plots

Organize the information from the frequency chart
in a line plot.

A.

4-4 Line Plots

in a line plot.

B.

4-4 Line Plots

in a line plot.

C.

4-4 Line Plots

in a line plot.

D.

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.

4-4 Line Plots

Answer: So, the mode is 7, the median is 5, and 0
is an outlier.

4-4 Line Plots

Identify the mode, median, and outliers of the
data shown.

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

4-5 Bar and Double Bar Graphs

Example 1

Make Double Bar Graphs


• I will use bar graphs to answer questions about
a situation.

• double bar graph


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?


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.


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.


On which activity does Sanji spend the least time?
How long does Sanji spend eating and practicing
sports?


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

4-6 Problem-Solving Investigation: Choose a Strategy

Main Idea
Example 1: Problem-Solving Investigation


• I will choose the best strategy to solve a problem.


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.


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.


Plan
Organize the data in a table to solve the problem.


Solve
For each round trip, the total cost increases
by $1.50.


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.


Check
Use a set of play money that is in piles of
$1.50. Add the money until you have more
than $10.

4-7 Interpret Line Graphs

Example 1
Example 2

Make a Line Graph


• I will interpret data in a line graph.

• line graph


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.


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.


Refer to the graph below. On what day were the
most tickets sold to students for the school play?


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


Refer to the line graph below. What day showed
the greatest increase of absences from the
previous day?


To find the greatest increase from one day to the next,
look for the steepest line between days.


The line from Monday to Tuesday is the steepest.

Answer: So, Tuesday shows the greatest
increase of absences from Monday.


How many more tickets were sold on Thursday
than Tuesday?


How many more tickets were sold on Thursday
than Tuesday?

A. 200

B. 150

C. 100

D. 50

4-8 Analyze Graphs

Main Idea
Example 1
Example 2
Example 3

4-8 Analyze Graphs

• I will use graphs to display different kinds of data.

4-8 Analyze Graphs

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.

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.

4-8 Analyze Graphs

To identify the three most popular granola bars, find the
three tallest stack of x’s.

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.

4-8 Analyze Graphs

Use the line plot to determine the three least
popular granola bars in Mrs. Cruz’s class.

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

4-8 Analyze Graphs

The bar graph shows the Chi family’s favorite
sports to watch. Which is the least popular?

4-8 Analyze Graphs

To determine the sport that is the least popular, find the
bar that is the lowest on the graph.

4-8 Analyze Graphs

Golf has the lowest bar on the graph.

Answer: So, golf is the least popular sport.

4-8 Analyze Graphs

sports to watch. Which is the most popular?

4-8 Analyze Graphs

sports to watch. Which is the most popular?

A. basketball

B. gymnastics

C. football

D. hockey

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?

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.

4-8 Analyze Graphs

Answer: So, a good day to recommend to visit would
be Tuesday because the park is the least
crowded.

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

4

Five-Minute Checks

Make Double Bar Graphs

Make a Line Graph

4

Lesson 4-1 (over Chapter 3)
Lesson 4-2 (over Lesson 4-1)

4
(over Chapter 3)

Tell whether each equation is balanced.
3+7=3+3+4

A. yes

B. no

4
(over Chapter 3)

22 + 13 = 22 + 7 + 4

A. yes

B. no

4
(over Chapter 3)

37 – 8 = 37 – 12 + 3

A. yes

B. no

4
(over Chapter 3)

18 – 15 = 12 + 6 – 8 – 7

A. yes

B. no

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.

4
(over Lesson 4-1)

table.

A.

4
(over Lesson 4-1)

table.

B.

4
(over Lesson 4-1)

table.

C.

4
(over Lesson 4-1)

table.

D.

4
(over Lesson 4-1)

Identify the most popular sport.

A. Baseball

B. Basketball

C. Soccer

D. Track

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

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

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

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

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

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

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

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

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

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

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

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

4
(over Lesson 4-7)

How many more students were absent on Thursday
than on Wednesday?

A. 4

B. 6

C. 5

D. 3

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Math Gr4 Ch4

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