Organizing Data
Objective To review data landmarks and methods for
organizing data.
o
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Teaching the Lesson
Family
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Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Rounding Numbers
• Organize data using a picture, graph, line
plot, table, or list. Math Journal 1, p. 166
calculator
Students round numbers using
paper-and-pencil methods and then
explain how to round numbers using
a calculator.
[Data and Chance Goal 1]
• Identify data landmarks for data sets. [Data and Chance Goal 2]
• Compare and answer questions about
data sets and their organization. [Data and Chance Goal 2]
Key Activities
Students organize and describe previously
collected data and review the minimum,
maximum, mode, median, and mean as
data set descriptions.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes 6 1
Math Journal 1, p. 167
Students practice and maintain skills
through Math Box problems.
Study Link 6 1
Math Masters, p. 157
Students practice and maintain skills
through Study Link activities.
Use journal page 165. [Data and Chance Goals 1 and 2]
Key Vocabulary
minimum maximum mode median landmark line plot
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Reviewing Data Landmarks
Math Journal 1, p. 158
Student Reference Book, pp. 119–121
Students review definitions and strategies
for finding data landmarks.
ELL SUPPORT
Creating a Data Landmark Poster
Math Journal 1, p. 158
Differentiation Handbook, p. 143
per group: chart paper, stick-on notes,
index cards or paper, colored pencils
Students make a poster to review and
display the vocabulary for data landmarks.
EXTRA PRACTICE
5-Minute Math
5-Minute Math™, pp. 34, 116, 198
Students practice finding the median in a set
of data.
ENRICHMENT
Plotting Arm Circumference
Materials
Math Journal 1, pp. 164 and 165
Math Masters, p. 149
Class Data Pad stick-on notes calculator
Math Masters, pp. 186A and 186B
Students use fraction data to make a
line plot.
Advance Preparation
For Part 1, draw two number lines on the board and one on the Class Data Pad, labeling the points 0, 5,
and 10. Leave enough room for small stick-on notes. Use the number lines on the board to plot the
number of states students and adults have visited. The adult line may need to be longer than the student
line. Use the line on the Class Data Pad with the Math Message. For Part 2, familiarize yourself with the
rounding feature of your classroom calculators.
Teacher’s Reference Manual, Grades 4–6 pp. 160–169
378
Unit 6
Using Data; Addition and Subtraction of Fractions
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Getting Started
Mental Math and Reflexes
Math Message
Dictate the following problems. Have students use thumbs up to indicate
whether their magnitude estimate is in the tens, hundreds, or thousands. They
use thumbs down for the place values that do not apply. Suggestions:
Predict how many states
the average student has visited. Write
your prediction on a stick-on note. Be
prepared to explain the information you
used to make your prediction.
650 ÷ 6 hundreds
35 ∗ 100 thousands
103 thousands
3.5 ∗ 10 tens
7,780 ÷ 100 tens
640 ∗ 20 thousands
9.24 ∗ 1,000 thousands
24,925 ÷ 1,000 tens
35 ∗ 9.9 hundreds
1 Teaching the Lesson
▶ Math Message Follow-Up
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
WHOLE-CLASS
DISCUSSION
Have students position their stick-on notes on the Class Data Pad
number line and explain the reason why they picked that number
of states. Sample answer: I chose 2 states because the people I
know go on vacation to the same place each year. Ask volunteers
to find the minimum, maximum, mode, mean, and median for
the displayed data. Add these landmark labels and values to the
Class Data Pad.
▶ Organizing the Class Data:
States Students Have Visited
SMALL-GROUP
ACTIVITY
0
5
States Students Have Visited
10
0
5
States Adults Have Visited
10
Two number lines: one for the board, one for
the Class Data Pad
PROBLEM
PRO
P
RO
R
OB
BLE
BL
L
LE
LEM
EM
SOLVING
SO
S
OL
O
LV
VING
VIN
IIN
NG
(Math Journal 1, p. 164; Math Masters, p. 149)
Refer students to Study Link 5-10, and ask them to report the
number of states they have each visited. List these on the board or
a transparency in the order they are presented. Students should
also record these data on journal page 164.
Ask students how they might organize the class data so that the
information being presented is easy to understand. A picture,
graph, table, or list is usually easier to interpret than an
unorganized set of data.
Student Page
Date
Time
LESSON
States Students Have Visited
6 1
䉬
1.
You and your classmates counted the number of states each of you has visited.
As the counts are reported and your teacher records them, write them in the space
below. When you finish, circle your own count in the list.
Sample answer:
1 3 7 3 7 14 14 16 3 4 7 9 22
4 5 7 9 13 3 1 2 14 20 22 16 18
2.
Decide with your group how to organize the data you just listed. (For example,
you might make a line plot or a tally table.) Then organize the data and show the
results below.
1, 1, 2, 3, 3, 3, 3, 4, 4, 5, 7, 7, 7,
7, 9, 9, 13, 14, 14, 14, 16, 16, 18, 20, 22, 22
Working in small groups, students decide on a method to organize
the class data. Each student then completes Problems 2 and 3 on
journal page 164, using their group’s method. When most students
have completed Problems 2 and 3, bring the class together to
discuss the results.
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
3.
4.
Write two things that you think are important about the data.
Sample answer:
a.
The number of states visited ranges from 1 to 22.
b.
Most students have visited more than 2 states.
Compare your own count of states with those of your classmates.
Sample answer: I have visited more states than most of
my classmates.
Math Journal 1, p. 164
Lesson 6 1
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▶ Describing the Data
NOTE Students’ plots, tables, and other
ways of organizing the data should be easy to
make and easy to read. The graphs do not
have to be precisely drawn and labeled in
order to be useful for this exercise.
x
x
x x
x
x xx xx
x
x
x
x
5
0
x
x
x
x
x
x x
x
x
x
15
10
x
x
20
25
1
5
22
7
22
9
14
16
18
13 14
14 16
Ask students to share their methods for organizing the data.
Make sure several ways are presented, including a line plot. Three
methods you might expect from students are shown in the margin.
Groups may have also arranged the data in numerical order,
from smallest to largest or vice versa. Emphasize that ordering
data helps the reader recognize the data landmarks, such as the
minimum, maximum, mode, and median. To support English
language learners, ask students to describe the similarities and
differences between the median and the mode.
11
3
1
1
15
17
1 1 2 3 3
5 4 3 3
4
7
3
13
7 7 77
9 9
ELL
(Math Journal 1, p. 164)
Ask students to print their personal counts for states visited on
stick-on notes and attach them above the appropriate marks on
the number line labeled States Students Have Visited. If the
stick-on notes are carefully stacked, the result models a bar graph.
3
20
WHOLE-CLASS
ACTIVITY
0
19
2
7
3
4
3
4
5
5
14
7
9
14
16
7
9
13 14
16
10
22
18
15
20
22
20
25
States Students Have Visited
21
Ask students to compare their personal counts with the
whole-class results. Encourage students to use descriptions of the
shape of the stick-on note graph in their comparisons. Informal
terms such as bunches, bumps, and far away from most are fine.
Three ways to organize data
Have students compare the whole-class results with their
predictions of the number of states visited by an average student.
To support English language learners, discuss the meaning of the
word average in this context. Ask questions like the following:
Student Page
Date
Time
LESSON
6 1
䉬
1.
States Adults Have Visited
You and your classmates each recorded the number of states an adult has visited.
As the numbers are reported and your teacher records them, write them in the
space below.
夹
Sample answer:
1 6 14 3 7 28 30 40 22 5 8 14 18
8 10 14 18 26 30 40 2 4 6 18 40 30
2.
Draw a line plot to organize the data you just listed.
x x
x x x x x x x x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
3.
●
Do the whole-class results support the predictions?
●
What relationships can you describe between the predictions
and the results?
●
Are the shapes of the two graphs similar? Explain.
●
What do the shapes of the two graphs suggest about the data
landmarks? Do you see any connections between the shape of
the graphs and the landmarks?
Then have students complete Problem 4 on the journal page.
How does the line plot help a viewer see what is important about the data?
It is easier to see the landmarks.
4.
Record landmarks for the data about adults and students in the table below.
Sample answer:
Landmark
Minimum
Maximum
Mode(s)
Median
Adults
Students
1
40
14, 18, 30, and 40
14
1
22
3 and 7
7
Math Journal 1, p. 165
380
Unit 6
Using Data; Addition and Subtraction of Fractions
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Student Page
▶ Organizing the Class Data:
PARTNER
ACTIVITY
States Adults Have Visited
PROBLEM
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SOLVING
SO
S
OL
O
LV
L
VING
VIN
V
IIN
NG
(Math Journal 1, pp. 164 and 165; Math Masters, p. 149)
Date
Time
LESSON
Models for Rounding Numbers
6 1
䉬
Rounding numbers makes mental calculations and estimates easier. The first step to
rounding to a given place is to locate the number between two consecutive numbers.
For example, what whole number comes right before 12.6? (12) What whole number
comes right after 12.6? (13)
1.
Complete the table below.
Rounding to the nearest whole number:
Refer students to Study Link 5-10 and ask them to report the
number of states visited by the adults they interviewed. As
before, list these on the board or a transparency in the order
they are presented. Students should also record these data on
journal page 165.
12.6
Is between 12 and 13
26.3
Is between
119.9
Is between
3,502
Is between
Rounding to the nearest ten:
Is between 10 and 20
26 and 27
Is between
Rounding to the nearest ten:
Is between
Is between
100 and 200
3,500 and 3,600
12
.6
15
12
12.5
10
13
20
Rounding to the nearest ten
Rounding to the nearest whole number
Numbers that are halfway between the lower number and the higher number are
rounded up to the higher number. Round . . .
Adjusting the Activity
2.
Ask several volunteers to find the mean (average) number of states
students have visited and circle this point on the displayed line plot. They should
use calculators to add the counts recorded in Problem 1 on journal page 164
and then divide by the number of counts. Ask other volunteers to find the mean
number of states adults have visited, using the counts recorded in Problem 1 on
journal page 165, and circle this point on the displayed line plot.
K I N E S T H E T I C
30
and
Next determine if the number you are rounding is closer to the lower number or to the
higher number. The models below represent different ways of thinking about making
this choice. On the number line, 12.6 is close to 13, so 12.6 rounded to the nearest
whole number is 13. If the number line were curved, 12.6 would “roll” toward 10.
12.6
20
Rounding to the nearest hundred:
110 and 120
3,500 and 3,510
Have partners complete the journal page. Circulate and assist.
A U D I T O R Y
227
T A C T I L E
4.
6.
16.4 to the nearest whole number.
7.36 to the nearest tenth.
16
7.4
3.
5.
423,897 to the nearest hundred-thousand.
500
9,300
482 to the nearest hundred.
9,282 to the nearest hundred.
400,000
30.1
7.
30.08 to the nearest tenth.
8.
Explain how you would use your calculator to round 5.3458 to the nearest hundredth.
Sample answer: I would set the Fix key to 2 decimal places,
enter the number 5.3458, and press either
or
.
Math Journal 1, p. 166
V I S U A L
When most students have finished, have them print their counts
for states visited by an adult onto stick-on notes and attach them
above the appropriate marks on the number line. For each data
set, record the data landmarks and corresponding values on the
board. Compare landmarks for the two line plots. Expect that
adults will have a larger median. Ask students why this may be
the case. Adults have lived longer and have traveled more, so
there are more values at the higher end of the scale.
Ongoing Assessment:
Recognizing Student Achievement
Journal
Page 165
Student Page
Date
Use journal page 165, to assess students’ abilities to display data on a line plot,
discuss the data’s organization, and identify minimum, maximum, mode(s), and
median for data sets. Students are making adequate progress if they have
correctly constructed the line plot and identified the landmarks. Some students
may also describe the shape of the line plot in terms of the landmarks.
Time
LESSON
Math Boxes
6 1
䉬
1.
[Data and Chance Goals 1 and 2]
Fill in the missing values on the number lines.
29
36
43
50
57
64
71
19
36
53
70
87
104
121
230–233
2.
Make up a set of at least twelve numbers that have the following landmarks.
Sample answer:
2 Ongoing Learning & Practice
▶ Rounding Numbers
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 166)
Students practice rounding numbers using paper-and-pencil
methods. Then they explain how to round numbers using a
calculator. Any calculator with the fix feature can be used with
this activity.
Students
minimum: 2
maximum: 11
median: 6
mode: 6
2, 2, 3, 4, 5, 6,
6, 6, 7,7, 8, 11
Make a bar graph for this set of numbers.
5
4
3
2
1
0
Students’ Cousins
2 3 4 5 6 7 8 9 10 11
Cousins
119 122
3.
Write 3 equivalent fractions for each
fraction.
4.
Sample answers:
80
ᎏ
a. ᎏ
100
2
b. ᎏ3ᎏ
⫽
36
c. ᎏ9ᎏ
3
ᎏ
d. ᎏ
24
3
e. ᎏ8ᎏ
⫽
⫽
⫽
⫽
Write each number in standard notation.
8 4 20
ᎏᎏ, ᎏᎏ, ᎏᎏ
10 5 25
4 6 20
ᎏᎏ, ᎏᎏ, ᎏᎏ
6 9 30
a.
33 ⫽
b.
103 ⫽
c.
63 ⫽
4 12 72
ᎏᎏ, ᎏᎏ, ᎏᎏ
1 3 18
d.
4 ⴱ 103
e.
72 ⫽
1
ᎏᎏ,
8
6
ᎏᎏ,
16
6
ᎏᎏ,
48
9
ᎏᎏ,
24
9
ᎏᎏ
72
12
ᎏᎏ
32
27
1,000
216
4,000
⫽
49
6 8
59
Math Journal 1, p. 167
Lesson 6 1
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12/9/10 9:12 AM
Student Link Master
Name
Date
STUDY LINK
Time
䉬
1.
35
33
33
52
48
33
33
29
48
59
35
59
27
48
55
37
43
42
117–122
24
42
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 6-3. The skill in Problem 4 previews
Unit 7 content.
Organize these data on the line plot below.
x
x
x x
x x x
x
x
x xx x
20
2.
27
26
25
30
x
x
x
x
xx
40
35
x
x
x
50
45
55
x
x
Writing/Reasoning Have students respond to the
following: If you extended the top number line in Problem
1, would 100 be one of the missing numbers? Explain.
No, each number increases by 7. If I add 7 to 71 four more times,
the answer is 99, which is 1 less than 100.
60
Standing Long Jump
Make a bar graph for these data.
Number of Students
4
3
2
1
0
20–24 25–29 30–34 35–39 40–44 45–49 50–54 55–59
Length of Long Jump (inches)
3.
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 167)
Ms. Perez’s physical education class participated in the standing long jump.
Following are the results rounded to the nearest inch.
24
55
▶ Math Boxes 6 1
The Standing Long Jump
61
Find the following landmarks for the standing long jump data:
59 in.
33 in.
Mean (average): 39.5
24
36
a.
Maximum:
b.
Minimum:
c.
Mode:
d.
Median:
in.
e.
in. (Use a calculator. Add the distances and
divide the sum by the number of jumps. Round to the nearest tenth.)
in.
▶ Study Link 6 1
INDEPENDENT
ACTIVITY
(Math Masters, p. 157)
Practice
4.
48 ⴱ 29 6.
24冄3
苶8
苶4
苶
1,392
98.25
79.82
5.
Home Connection Students construct a line plot and a
bar graph from a set of given data. Then students identify
the landmarks.
18.43
16
767.5 30.82 7.
798.32
157
Math Masters, p. 157
3 Differentiation Options
READINESS
▶ Reviewing Data Landmarks
WHOLE-CLASS
ACTIVITY
15–30 Min
(Math Journal 1, p. 158; Student Reference
Book, pp. 119–121)
To provide experience with the definitions of and methods for
finding data landmarks, have students analyze the snack-survey
data on journal page 158. Use pages 119–121 in the Student
Reference Book.
Student Page
Date
LESSON
5 11
䉬
Time
Making Circle Graphs: Snack Survey
Your class recently made a survey
of favorite snacks. As your teacher
tells you the percent of votes each
snack received, record the data in
the table at the right. Make a circle
graph of the snack-survey data in
the circle below. Remember to
label each piece of the graph and
give it a title.
Explain the following prominent features of a data set:
Votes
Snack
Other
8
4
10
2
1
Total
25
Cookies
Granola Bar
Candy Bar
Fruit
Sample answers:
Number
Fraction
ᎏ8ᎏ
25
ᎏ4ᎏ
25
1ᎏ
0
ᎏ
25
ᎏ2ᎏ
25
ᎏ1ᎏ
25
2ᎏ
5
ᎏ
25
Percent
32%
16%
40%
8%
4%
About 100%
minimum—smallest value
maximum—largest value
range—difference between the minimum and the maximum
mode—most frequent value or values
Favorite-Snack Survey Results
median—middle value
other
fruit
cookies
candy bar
granola
bar
mean (average)—quotient of the sum of the data set divided by
the number of values in the set
Discuss the examples in the Student Reference Book, and have
students find each landmark using the snack-survey data.
Math Journal 1, p. 158
382
Unit 6
Using Data; Addition and Subtraction of Fractions
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Teaching Master
ELL SUPPORT
▶ Creating a Data Landmark
SMALL-GROUP
ACTIVITY
15–30 Min
Poster
Name
Date
LESSON
6 1
Sometimes measurements need to be very precise. When a blood pressure
reading is taken, it is important that the proper cuff size is used. Blood pressure
cuffs come in different sizes and are adjustable. Using a blood pressure cuff
that is too small or too large can lead to inaccurate results. Before doing a blood
pressure screening of the members of the fifth-grade running club, the school
nurse measured the circumference of each student’s upper arm to the nearest
_1 inch. Measurements are shown in the table below.
8
(Math Journal 1, p. 158; Differentiation Handbook, p. 143)
Upper Arm
Circumference (to
1
the nearest _8 in.)
Student
To complete the poster, ask students to discuss, find, and label
the landmarks on the line plot with the cards or strips of paper.
Consider having students use the Word Bank Template found
on Differentiation Handbook, page 143. Ask students to write
the terms minimum, maximum, range, mode, median, mean,
and outlier; to draw a picture relating to each term; and to
write other related words. See the Differentiation Handbook for
more information.
EXTRA PRACTICE
▶ 5-Minute Math
Upper Arm
Circumference (to
1
the nearest _8 in.)
Student
Jason
1
5_4
Robin
3
6_8
Mike
1
6_8
Javon
6
Kylie
1
6_2
Beatrice
1
5_4
Peter
1
6_8
Charlie
1
6_8
Diego
5
Shawn
3
6_8
Juan Carlos
6
India
6
Lisa
1
5_2
Katy
3
6_8
Pamela
7
Make a line plot in the grid below to display the arm circumference measurements.
Begin by completing the labeling of the x-axis. Use these data and the completed
line plot to answer the questions on the next page.
Upper Arm Circumference
Number of Students
To provide a visual reference for data landmark words, have
students create a line plot poster using the snack-survey data
from journal page 158. As a group, make a line plot of the
snack-survey data using chart paper and stick-on notes. Assign
students the data landmark words to write on an index card or
strips of paper, using a different-colored pencil for each word.
Time
Arm Circumference Data
X
X
X
5 18
5
5 14
X X
X X
X X
X
3
8
1
2
5
8
3
4
7
8
X
X
X X
1
8
1
4
3
8
1
2
X
5
8
3
4
7
8
5 5 5 5 5 6 6 6 6 6 6 6 6 7
Circumference (inches)
Math Masters, p. 186A
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SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with finding the median in a
set of data, see 5-Minute Math, pages 34, 116 and 198.
ENRICHMENT
▶ Plotting Arm Circumference
INDEPENDENT
ACTIVITY
15–30 Min
(Math Masters, pp. 186A and 186B)
To apply students’ understanding of line plots, have them create a
line plot with measurements in fractions of a unit. When students
have completed the line plot on Math Masters, page 186A, ask
them to solve the problems on Math Masters, page 186B using the
data in the line plot.
Teaching Master
Name
Date
LESSON
6 1
Time
Arm Circumference Data
continued
Use the line plot on Math Masters, page 186A to answer the questions.
1.
What is the minimum arm circumference of the students in the fifth-grade
5
running club?
2.
_1
2
maximum?
3.
in.
How much smaller is Kylie’s upper arm circumference than the club’s
in.
What is the range in arm circumference of the members of the fifth-grade
running club?
4. a.
b.
2
in.
What is the median of the data set?
6_18
in.
How much greater is the median arm circumference than the minimum arm
circumference?
1_18
in.
5.
What is the mode (or modes) for the data set?
6.
What is the mean arm circumference measurement?
7.
On the day of the blood pressure screening, the nurse brought a cuff that is
3
1
made for people with arm circumferences between 5_8 in. and 6_4 in. What
fraction of the fifth-grade running club was able to use that cuff?
6 in., 6_18 in., and 6_38 in.
13
__
15
8.
6
in.
of the club
Suppose a new member, Denise, joins the club. The circumference of her
1
upper arm is 6_2 in. Tell whether each of these club’s landmarks will increase,
decrease, or stay the same. Determine your answers without doing any
calculations.
a.
Mean:
b.
Median:
c.
Mode:
increase
Stay the same
Stay the same
Math Masters, p. 186B
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Lesson 6 1
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2/14/11 1:38 PM
Name
Date
LESSON
Time
Arm Circumference Data
6 1
Sometimes measurements need to be very precise. When a blood pressure
reading is taken, it is important that the proper cuff size is used. Blood pressure
cuffs come in different sizes and are adjustable. Using a blood pressure cuff
that is too small or too large can lead to inaccurate results. Before doing a blood
pressure screening of the members of the fifth-grade running club, the school
nurse measured the circumference of each student’s upper arm to the nearest
_1 inch. Measurements are shown in the table below.
8
Upper Arm
Circumference (to
1
the nearest _8 in.)
Student
Jason
1
5_4
Robin
3
6_8
Mike
1
6_8
Javon
6
Kylie
1
6_2
Beatrice
1
5_4
Peter
1
6_8
Charlie
1
6_8
Diego
5
Shawn
3
6_8
Juan Carlos
6
India
6
Lisa
1
5_2
Katy
3
6_8
Pamela
7
Make a line plot in the grid below to display the arm circumference measurements.
Begin by completing the labeling of the x-axis. Use these data and the completed
line plot to answer the questions on the next page.
Upper Arm Circumference
Number of Students
Copyright © Wright Group/McGraw-Hill
Student
Upper Arm
Circumference (to
1
the nearest _8 in.)
5
5 18
5 14
Circumference (inches)
186A
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Name
Date
LESSON
6 1
Time
Arm Circumference Data
continued
Use the line plot on Math Masters, page 186A to answer the questions.
1.
What is the minimum arm circumference of the students in the fifth-grade
in.
running club?
2.
How much smaller is Kylie’s upper arm circumference than the club’s
maximum?
3.
in.
What is the range in arm circumference of the members of the fifth-grade
running club?
4. a.
b.
in.
What is the median of the data set?
in.
How much greater is the median arm circumference than the minimum arm
circumference?
in.
5.
What is the mode (or modes) for the data set?
6.
What is the mean arm circumference measurement?
7.
On the day of the blood pressure screening, the nurse brought a cuff that is
3
1
made for people with arm circumferences between 5_8 in. and 6_4 in. What
fraction of the fifth-grade running club was able to use that cuff?
8.
Suppose a new member, Denise, joins the club. The circumference of her
1
upper arm is 6_2 in. Tell whether each of these club’s landmarks will increase,
decrease, or stay the same. Determine your answers without doing any
calculations.
Mean:
b.
Median:
c.
Mode:
Copyright © Wright Group/McGraw-Hill
a.
in.
186B
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