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Demonstrating the Use ofTechnology in Middle SchoolStatistics Lessons

A project forMathematics 599

Capstone

By: Robert Padian

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Lesson 1- Gathering and

Organizing Data The small keypads are designed to allow

you to interact with one another in

contributing to the progress of the lesson We will first use them to gather someinformation from you

We will then use them to help organizethat data to see what information we candraw from it

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Short Discussion

Is Information

the same

as Data?

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How to use the Keypad

The On/Off switch is at the lower left.

Slide up to turn on the device, down to turn it off

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The Enter Key

You choose your answer with the variouskeys and then they appear on the littlescreen. When you have what you want tosubmit you just press the Enter key

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Enter

Pressing the Enter Key sends whatever ison the screen.

For some questions you can submit 2answers like a max and a min value but if you press Enter twice after putting ina value, that becomes both answers.

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There are a few groups of keys thatsupport different uses, and a few functionsthat the system allows users to use.

The screen allows you to see the answersthat you type, but does not show thequestions.

For those you need to look up at the boardand listen.

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The Numeric Choices

The digits 0, 1 through 9

A decimal (.) point and a minus (-) signcomplete the numeric input choices.

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Using the pad

Turn on the Keypad

When it is finished connecting, the screenwill show Scanning Found and MyClass with a number.

Press Enter.

The screen will display ID: so enter the

last 4 digits of the long PRSRR number onthe sticker on the back of the keypad, thenpress the Enter key

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The Keypad

Alphabet choices A, B, C, D, E

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The Keypad

The True/False selections

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The Keypad

The alphabetic choices can be extended.

Press T and arrow up or down and the letters

appear in the next position in the window. Press F and the arrows scroll through the letters

at the early part of the alphabet.

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Lets collect some answers

Enter the first letter of your last name. If you need to enter A through E, F and T you

have a key just for that.

You can reach G through M from the F key andthe down arrow. You can reach N through S from T and the up

arrow. U through Z are reached from T and down

arrow. Remember to press Enter after picking your

letter!

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Getting Feedback

Answer true or false:

Boston is the capital of Massachusetts.

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Another data collection

True or false

Baltimore is the capital of Maryland.

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A bit of research

We have had a red-haired president.

T or F?

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Another poll

How many left-handed Presidents has theUnited States had?

Pick whichever number you think answersthe question.

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Presidential poll I

Thomas Jefferson had red hair.

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Presidential poll II

Lefties include1. James Garfield

2. Herbert Hoover

3. Harry Truman

4. Gerald Ford

5. Ronald Reagan

6. George H W Bush7. Bill Clinton

8. Barack Obama

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Another collecting question - Colors

Pick your favorite of the following colors byentering a choice from the letter buttonsnext to the numbers pad

Choose the letter corresponding to thecolor option

A Red B BlueC Green D Yellow

E Other

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Another Question

Pick your favorite sport

A Baseball

B BasketballC Football

D Hockey

E Soccer

F Lacrosse

G Other

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And another

Choose your favorite teams whose gameswould you most enjoy watching or attending?

Order up to 3, type the codes without spacing,

press Enter once when finished.

1 Red Sox 2 Yankees 3 Mets

4 Tigers 5 Dodgers 6 Indians

7 Patriots 8 Jets 9 Giants

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Team Favorites

Display results of 1st, 2nd, 3rd placechoices.

Save results as input to later discussion ofpreferential voting as it might change top-3winners.

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Bar Graphs

These are a simple way to visualize datathat can be counted in categories

Consider a NY Times article that repeateda survey result. They showed the numberof minutes children spend in each of 4activities each day

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NY Times Graphic

As published in the NewYork TimesMagazine, The Way

We Live Now,Kindergarten Cram

3 May 2009, p13,14

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Minutes spent each day in

These are the numbers by category

Literacy 89

Math 47 Test Prep 21

Free Play 19

REP1

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Slide 27

REP1 Robert E Padian, 5/8/2009

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What does the Times tell us?

What does the graph tell us?

What do the numbers tell us?

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Bars

A more common representation forcomparing data by category

Useful when comparing numbers bynames data

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Another way of looking or seeing

Acti ities

iteracy Math est re ree lay

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Another way of looking at it

A ti itie

i tera y

Math

e t re

ree lay

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Horizontal or Vertical

Vertical bars are useful when thecategories are numeric ranges and can becontinuous, like 1 to 10, 11 to 20, etc.

When categories are names, either maybe used. It depends on your point of view,esthetic etc.

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Kindergarten Data

What do the numbers tell us?

What does the graph tell us?

Which representation gives a message inthe least time?

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Comparing

i

i

i

i

ra y

a

T

r p

r

!

ay

i i

i

i

ra

y

a

T

r

p

r

!

ay

T ink of R a ingup

T ink of R a ing

ou Heig or Range?

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Discussing the Graphs

Which activity used the most time?

Which used the least? Was one almost the same as another?

Were some greatly different?

"

ctivities

#

$

#

% #

& #

' #

(

#

) #

0

#

1 #

2 #

$

# #

3 iteracy 4 ath Test 5 rep 6 ree 5 lay

"

ctivities

#

$

# % # & # ' # ( # ) # 0 # 1 # 2 #

$

# #

3 iteracy

4

ath

Test5

rep

6

ree5

lay

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A Vertical Special

When the chart data displays thefrequency of occurrence of data that fallsinto continuous, non-overlappingcategories, a special vertical bar chart orHistogram is built.

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Some graphic rules

Numeric scales are regular the distancefrom an axis is directly proportional to themagnitude of the value represented.

Start scale at 0 and each increment of 10,for instance, is the same distance from thelast instance.

Leave gaps for intervals in posssibly-continuous data to keep the relative scalelooking relevant.

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More work

We will continue on how to build bargraphs next time

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Lesson 2: Organizing Data

Stem-and-Leaf TablesFrequency Tables

Histograms

By: Matt Glavin

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Investigating Data

Part I Worksheet

Assemble in small groups

Answer the questions on the worksheet Prepare to answer questions using the

PRS

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What is the lowest test score?

a. 72

b. 60

c. 52 d. 55

e. 78

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What is the highest test score?

a. 76

b. 95

c. 100 d. 98

e. 99

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Answer:

Lowest test score: 52

Highest test score: 98

How far apart are these two test scores?

Or: What is the distance between them?

Type in your answer using the PRS

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Answer:

The distance between the two scores is46.

It is found by subtraction:

98 52 = 46

46 is called the RANGE of the test score data.

The data ranges from 52 all the way up to 98.

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Range Question

What is the RANGE of the following data?:

52, 29, 60, 73, 41, 88, 35

Type in your answer using the PRS

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Answer:

88 29 = 59

Therefore, the RANGE (distance) is 59.

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Middle Score Question

Back to our original test score data

What is the middle score of all of the data?

a. 55b. 77

c. 78

d. 89e. 94

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Multiples Question

Using the PRS, list all of the test scores

that appear more than once.

A.55B.60

C.68

D.73E.76

F. 77G. 82

H. 84

I. 88J. 95

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Answer:

60, 73, 76, 77, and 84

Follow-up Question:

One of these test scores above appears more

frequently than the others.

Which test score has the greatestFREQUENCY?Type in the answer using the PRS.

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Frequency

The test score 77 has a FREQUENCY of3

The other test scores60, 73, 76, and84appeartwice, so they each have aFREQUENCY of 2.

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Part II Worksheet


Read and complete the first two tables

on the Part II Worksheet

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Table of Scores

Interval Scores

50-59 52, 55

60-69 60, 60, 68, 66

70-79 76, 75, 77, 72, 73, 78, 76, 77, 73, 77

80-89 85, 81, 83, 89, 84, 84, 88, 82

90-99 95, 92, 94, 90, 98

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Ordered Table of Scores

Interval Scores

50-59 52, 55

60-69 60, 60, 66, 68

70-79 72, 73, 73, 75, 76, 76, 77, 77, 77, 78

80-89 81, 82, 83, 84, 84, 85, 88, 89

90-99 90, 92, 94, 95, 98

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Stem-and-Leaf Table

Stems Leaves

5 2, 5

6

7

8

9

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Stem-and-Leaf Question:

Stem Leaves

8 5, 1, 3, 9, 4, 4

The above Stem-and-LeafTable

representssix different numbers.

Using the PRS, what integerdoes the

highlighted digit represent?

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Stem-and-Leaf Answer:

Stem Leaves

8 5, 1, 3, 9, 4, 4

Now continue completing therest of theStem-and-LeafTable

83 is the integer.

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Stem-and-Leaf Table

Stems Leaves

5 2, 56 0, 0, 8, 6

7 6, 5, 7, 2, 3, 8, 6, 7, 3, 7

8 5, 1, 3, 9, 4, 4, 8, 2

9 5, 2, 4, 0, 8

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Ordered Stem-and-Leaf Table

Stems Leaves

5 2, 56 0, 0, 6, 8

7 2, 3, 3, 5, 6, 6, 7, 7, 7, 8

8 1, 2, 3, 4, 4, 5, 8, 9

9 0, 2, 4, 5, 8

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Stem-and-Leaf Grid-Table

Stem Leaves

5 2 5

6 0 0 6 8

7 2 3 3 5 6 6 7 7 7 8

8 1 2 3 4 4 5 8 99 0 2 4 5 8

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Frequency Table

Score Absolute

Frequency

Relative

Frequency

50-59 2 2 out of 29 scores 7 %

60-69 4 4 out of 29 scores 14 %

70-79 10 10 out of 29 scores 34 %

80-89 8 8 out of 29 scores 28 %90-99 5 5 out of 29 scores 17 %

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Frequency Table

Score AbsoluteFrequency

Relative

Frequency

50-75 ___ out of 29 scores ____ %

76-100 ___ out of 29 scores ____ %

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Frequency Table Question:

Using the PRS, type in the AbsoluteFrequency for the 50-75 test score interval

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Answer:

10 is the ABSOLUTE FREQUENCY forthe 50-75 test score interval.

F T bl

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Frequency TableMultiple-Choice Question:

Using the PRS, select the Relative

Frequency of the data items in the 50-75

interval:

a. 10 %

b. 25 %

c. 34 %d. 52 %

e. 75 %

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Frequency Table

Score AbsoluteFrequency

Relative

Frequency

50-75 10 10 out of 29 scores 34 %

76-100 19 19 out of 29 scores 66 %

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Stem-and-Leaf Grid-Table

Stem Leaves

5 2 5

6 0 0 6 8

7 2 3 3 5 6 6 7 7 7 8

8 1 2 3 4 4 5 8 9

9 0 2 4 5 8

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Histograms

Difference between

Bar Graphs and Histograms

Question:

In what month is your birthday?

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Bar Graph vs. Histogram

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Histograms

Bars are contiguous (no spaces in-between)

Bars are ordered numericallyon abaseline

Height of bars indicates number of dataitems within the bars interval.

Width of bars is (generally) consistent

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Width of Bars/Intervals

Consistent width of bars/intervals isroughly found by dividing the RANGE ofthe data by the desired number of

bars/intervals.

E l D t i i B

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Example: Determining BarWidth

92 (HIGH) 37 (LOW) = 55 (RANGE)

I want (roughly) 10 Bars/Intervals

55 / 10 = 5.5 (rough) Bar/Interval Width

Thus, 5 is a good, regularwidth for the data:

12 Bars ofwidth-5from 35 up to 95

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Bar Width Question

Your data has the following characteristics:

Max value is 128

Min value is 42

I want roughly 20 intervals.

Type in your response to the following question:

What is a good, regularwidth for my bars?

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Answer:

128 (HIGH) 42 (LOW) = 86 (RANGE)

86/20 (Desired number of intervals) = 4.3

Thus, 4, or even 5, would be good regular

widths for the bars used to display mydata.

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Histogram Worksheet Part V


and Complete the Worksheet

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Bar Width Considerations

Too narrow: Too many similar-height bars

Too wide: Too few choppy bars

Goldilocks Just-Right Width: Difference

in heights of consecutive bars is smallenough to suggest curve of data results.

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Discussion Wrap-up Questions

How are Stem-and-Leaf Tables better atdisplaying data than Histograms?

How are Histograms better at displayingdata than Stem-and-leaf Tables?

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Lesson 3: Circle Graphs

By: Wing Leung

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Out of a class of 30 students:

Number ofSiblings Frequency

0 81 7

2 9

3 5

4 1

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# of

Siblings Freq.0 8

1 7

2 93 5

4 1

5 0

1

sibling

23%

3siblings

17%

2

siblings

30%

4

siblings3%

0

siblings

27%

Circle Graph

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Out of a class of 30 students, whatpercentage of students have 0 siblings?

0 siblings

siblings

3

siblings

30

3 siblings

sibling

3

0 siblings

siblings3

siblings30

3 siblings

sibling3

0 siblings

siblings3

siblings30

3 siblings

sibling3

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Out of a class of 30 students, what percentageof students have more than 3 siblings?

0 siblings

siblings

3

siblings

30

3 siblings

sibling

3

0 siblings

siblings3

siblings30

3 siblings

sibling3

0 siblings

siblings3

siblings30

3 siblings

sibling3

O t f l f 30 t d t h t

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Out of a class of 30 students, whatpercentage of students have at least 2

siblings but less than 4?

sibling23

3

siblings2

siblings

30

4siblings

3

0siblings

2

A.30

B.C.4D.5E.None of the

above

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True or False:More students have 3 siblings than 0 siblings.

0 siblings

siblings

3

siblings

30

3 siblings

siblings

3

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Out of a class of 30 students, how manystudents have 2 siblings?

0 siblings

2

siblings

3

2 siblings

30

3 siblings

siblings

23

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Out of a class of 30 students, how many studentshave 2 siblings?

siblings23

3 siblings

2

siblings

30%

siblings

3

0 siblings2

Percentage Number ofPeople

30% out of the 30 students

=

0.30 x 30 students = 9 students

M k i l h

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Ice Cream Flavor Frequency

Vanilla 6

Chocolate 3Strawberry 4

Cookies & Cream 6

Mint Chip 2

Other 9

Make your own circle graph

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Out of a class of 30 students:

Vanilla:

30x = 600

x = 600/30 = 20%

Chocolate:

30x = 300x = 300/30 = 10%

Ice CreamFlavor Frequency

Vanilla 6

Chocolate 3

Strawberry 4

Cookies &Cream 6

Mint Chip 2Other 9

6

30 100

x

!

3

30 100

x

!

Wh t t f t d t f Oth ?

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What percentage of students prefer Other?


Vanilla 6


Cookies &Cream 6

Mint Chip 2

Other 9

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Put the percentages from least to greatest:

A.StrawberryB.Other

C.ChocolateD.VanillaE.Mint Chip


Vanilla 6

Chocolate 3

Strawberry 4

Cookies &Cream 6

Mint Chip 2Other 9

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Which two percentages are the same?

A.StrawberryB.Other

C.ChocolateD.VanillaE.Mint ChipF.Cookies & Cream


Vanilla 6


Cookies &Cream 6

Mint Chip 2

Other 9

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Favorite Ice Cream Flavor

Chocolate10%

Strawberry13%

Other30%

Cook es

Cream

20%

Mint Chip

7%

Vanilla

20%

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What you should know:

1. Read a circle graph

2. Convert percentages to number of people3. Convert number of people to percentages

4. Create a circle graph

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Wrap Up:

Circle graphs are normally represented by:

A.FractionsB.DecimalsC.PercentagesD.Number of People

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Wrap Up:

40 people were surveyed on favorite color.10% of them said blue.How many people chose blue?

A.4B.5

C.6D.10E.None of the above

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Wrap Up:

40 people were surveyed on favorite color.5 of them said green.What percentage of people chose green?

A. 5%B. 40%

C. 10%D. 12.5%E. 8%

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Wrap Up:

40 people were surveyed on favorite color.25% of them said yellow.

How portion of the circle graph is yellow?A.1/2B.1/3

C.1/25D.1/40E.1/4

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Wrap Up:

40 people were surveyed on favorite color.25% of them said yellow.

How portion of the circle graph is not yellow?A.15B.25/40

C.15/40D.1/4E.3/4

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Homework:

1. Survey 20 people about Month of Birth.2. Create a frequency table.3. Convert all frequencies to percentages.4. Create circle graph.5. Make sure to label graph appropriately.

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Exploring Measures of Center

Mode, Median, and Mean

By Ben Rockoff

M d

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Mode

The data value or category occurring with thegreatest frequency (appears the most).

Ex. 4, 5, 4, 6, 3, 7, 4, 5, 4, 4- rearrange numbers from least to greatest

- 3, 4, 4, 4, 4, 4, 5, 5, 6, 7

Mode = 4

M di

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Median

The median is the midpoint of adistribution; that is, 50% of values arelower than or equal to the median and

50% are higher than or equal to themedian.

The middle number in an ordered set ofnumerical data.

The location of the Median

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The location of the Median The median of an odd number of data values

is located in the position (n+1)/2.

The median of an even number of values isdefined to be the average (mean) of themiddle two values, on either side of position(n+1)/2.

(n+1) / 2 when n = 7= (7+1) / 2= 8 / 2= 4

(n+1) / 2 when n = 8

= (8+1) / 2= 9 / 2= 4.5 so avg location 4 and 5

Pictorially the median divides

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Pictorially, the median divides

the distribution into two equalareas.

median median median

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What is the mode of this data

set?[ 8, 3, 5, 8, 7, 3, 8 ]

3, 3, 5, 7, 8, 8, 8

Number 8 occurs 3 times,

Number 3 occurs 2 times,

Number 5 occurs 1 time,

Number 7 occurs 1 time

Mode is 8

True / False

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It is possible to have more than one

mode for a set of data?

0

1

2

3

5

6

78

9

10

2 3 5 6 7

Frequency

Two Modes: 3 and 6BimodalTrue

Which of the following statements

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is true?

45, 37, 48, 27, 31, 35, 42, 30A) The set is bimodal

B) The mode is 27

C) The mode is 45

D) This data set has no mode

Each number only appearsonce

A group of students were asked to

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identify how many siblings they have.

Here are the results.0 siblings

1 sibling

2 siblings

3 siblings

4 siblings

more than 4siblings

Which statement is true?

A) This data set has nomode

B) Mode is 0C) Mode is 2

D) Most of of the studentshave more than 4

siblingsNote - there is a difference between having no mode and having amode of zero

Mode is the best (only) measure

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of central tendency for which type

of data?Enter

C for categorical data

N for numerical data(quantitative)

There is no middle regarding something such as

favorite ice cream and you certainly cannotaverage categorical data

What is the median for the

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following set of data?

12, 9, 15, 9, 7, 13, 16 Step 1 - rearrange data from least to greatest

7, 9, 9, 12, 13, 15, 16

Step 2 - count the number of elements within the set,7 numbers in the distribution - note 7 is odd

Step 3 - locate middle

(n+1) / 2 (7+1) / 2 = 4The number at the 4th position is 12

Median = 12

What is the median of thef ?

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following numbers?

9, 11, 1, 14, 14, 6 Step 1 - rearrange from least to greatest1, 6, 9, 11, 14, 14

Step 2 - count the number of elements

6 numbers in the distribution - note 6 is even Step 3 - locate middle

(n+1) / 2 (6+1) / 2 = 3.5Numbers located at position 3 (9) and 4 (11) need to averaged

(9+11) / 2 = 10

Median = 10

Given the following stem and

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gleaf plot?

What is the mode?

16

Given the following stem and

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gleaf plot?

What is the median?

26

7 8 10 24 25 30

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7, 8, 10, 24, 25, 30

The median is 17

Please enter one new number, so that thenumber which you enter becomes the new

median.

10 new number 24

7 8 10 24 25 30

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7, 8, 10, 24, 25, 30

If you were to add a number less than 10to the above set, what will the new medianbe?

Adjusted Median = 10

7 8 10 24 25 30

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7, 8, 10, 24, 25, 30

If you were to add a number greater than24, what would the new median be?

Adjusted median = 24

7 8 10 24 25 30

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7, 8, 10, 24, 25, 30

If you want to increase your median, thenew piece of data should be?

A) Less than the original median (17)

B) Greater than the original median (17)

C) Between 10 and 24

D) Must be the largest value in set

E) Equal to original median (17)

A statistic is called resistant if it ist t l i fl d b

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not strongly influenced by

extreme values (outliers)

Choose one of the following

- median- mean

The __________ is resistant to outliers.

The median of the data sets 1,2,3,4,5 and 1,2,3,4,100 arethe same.

Will adding a new data point (15) to

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these distributions have the same

effect on the medians (Yes/No)?

Median for bothis 8 prior toentering newdata point

Adjusted median = 12

Adjusted median = 8

No

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Assessment:

MCAS Review

1. Sharon took 24 nighttime photographs.Th ti i d f h

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The exposure times, in seconds, for herphotographs are represented in the stem-

and-leaf plot below.

What is the median exposure time forher photographs?

A. 24 seconds

B. 25 secondsC. 27 secondsD. 28 seconds

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Davis is on the high school track team. The table below showsthe number of laps he ran around the schools track each day

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the number of laps he ran around the school s track each dayfor 7 consecutive days.

Number of Laps Each Day

Day Mon Tues Wed Thu Fri Sat Sun

Number ofLaps

8 11 7 9 10 11 12

What is the mode of this set of data?

The box-and-whisker plot below shows the distribution of the dailyhigh temperatures, in degrees Fahrenheit, in the town of Clifton

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g p , g ,during the year 2004. Based on the box-and-whisker plot, in whichof the following intervals of temperatures is it most likely that exactly50% of the daily high temperatures are located?

A. 38F to 54F

B. 38F to 81F

C. 54F to 72F

D. 54F to 81F

A contest is being held at a school fair for fifth-grade and sixth-gradestudents.

5

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There are 40 fifth-grade students at the fair. There are 30 sixth-grade students at the fair.

Each students name was written on one card and placed into a box.The principal will reach into the box and pick one card withoutlooking. The student named on the card will be the winner of thecontest.

What is the probability that the winner of the contest will be a sixth-grade student?

1

2

3

4

3

71

30

C.

D.

A.

B.

Jeremy calculates his cars gas mileage every time he buys gas

for his car The chart below shows the data from the last5 times

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for his car. The chart below shows the data from the last5 times

he bought gas.

Gas Mileage forJeremys Car

MilesGallons of Gas GasMileage

(miles per gallon)

370 11.3 32.74352 9.5 37.05

303 8.9 34.04

298 9.7 30.72

398 11.2 35.54

Based on the data in the chart, what is the range of gas mileage

forJeremys car?

Nick has the following items in a bag:7.

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1 red pencil,1 yellow pencil,1 green eraser,1 blueeraser

Nick will randomly select one pencil and one eraser from thebag. Both pencils are the same size and shape. Both erasers arethe same size and shape. The tree diagram below shows all thepossible combinations Nick can select.

What is the probability that Nickwill select a red pencil and a blueeraser?

A

B

C

D

The bar graph below shows the attendance at each of fivebasketball games.

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g

Which of the following is closest to the difference between the

least and the greatest attendance for the five basketballgames?

A. 35B. 55

C. 70

D. 125

The histogram below shows the scores for all the students who9.

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The histogram below shows thescores for all the students who took amathematics quiz.

took a mathematics quiz.

What percent of the students received a score of 80 or above?

A. 55%

B. 40%

C. 25%

D. 11%

The circle graph below shows the percent of students enrolled ineach of four foreign language classes being offered at a school.

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each of four foreign language classes being offered at a school.

No student is enrolled in more than one foreign language class.

The number of students enrolled in Italian is 36.

Based on the graph and the given data, what is the total numberof students enrolled in foreign language classes?

A. 72

B. 100

C. 116D. 180

Alecia surveyed some elementary schoolstudents about the methods they use to get to

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Based on Alecias results, what fractional part of thegirls surveyed ride the bus?

A) 7/13B) 2/5

C) 7/20

D) 1/5

students about the methods they use to get toschool each morning. Her resultsare shown in

the table below.

Transportation to School

Method Boys Girls

bus 24 28

car 18 30walk 10 16

bicycle 8 6

The list below shows the number of miles12

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The list below shows the number of milesSophie hiked on each of the 7 days.

What was the mean number of miles she hiked

each day?A) 1.5 miles

B) 1.6 miles

C) 1.8 miles

D) 2.0 miles

1.6, 3.1, 1.5, 2.0, 1.1, 1.8, 1.5

12

To order a burrito from Teresas Burrito Shop,

Jim always chooses 1 item from each column in

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Jim always chooses 1 item from each column in

the table below.Burrito Choices

Wrap Filling Topping

-plain -beans -sour cream

-wheat -beef -guacamole

-chickenWhat is the total number of ways that Jim can order a

burrito at Teresas Burrito Shop by choosing

1 wrap, 1 filling, and 1 topping?

A) 6B) 7

C) 10

D) 12

Ms. Ortega recorded the number of siblings(brothers and sisters) each student in her classh H d i h h li l b l

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has. Her data is shown on the line plot below.

Number of Siblings of Students in Ms. Ortegas Class

What is the total number of students in Ms. Ortegas class

who have 2 or fewersiblings?

A) 3 C) 20

B) 5 D) 12

Mr. Chang surveyed the fifth-grade students aboutwhere they would most like to go for a field trip.

The res lts of the s r e are sho n in the graph

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The results of the survey are shown in the graphbelow.

Based on the graph, where

would the greatest number

of fifth-grade students mostlike to go for a field trip?

A) Zoo

B) Museum

C) Farm

D) Other

The tally chart below shows the different ways the24 students in Ms. Mitchells class get to school.

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24 students in Ms. Mitchell s class get to school.

Which circle graph

best represents the

information in the

tally chart?

A

B

C

D

Erin recorded the height of a tomato plant

each week for four weeks Which of the

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each week for four weeks. Which of the

following would be best for Erin to use todisplay the change in the height of the

tomato plant?

A) A line graph

B) A pictograph

C) A circle graph

D) A Venn diagram

Jamie made the line graph below to show howmuch money he earned shoveling snow each

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y gweek for five weeks.

Based on the information in the graph,

which of the following statements is

true?

A) Most weeks Jamie earned moremoney than the week before.

B) Each week Jamie earned moremoney than the week before.

C) Most weeks Jamie earned less

money than the week before.D) Each week Jamie earned less

money than the week before.

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The heights, in inches, of the members of asoccer team are listed below

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soccer team are listed below.

Which is the outlier(s)?A) 50

B) 80

C) Both 50 and 80D) None of the above

50, 66, 61, 71, 62, 64, 70, 64, 63, 80, 72, 68

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