1 Practice. Collecting and Working with Data

• • • • • • Collecting and Working with Data

1

Practice

Directions: Use the information on page 5 to help you organize the data on this page.

1. The record sheet below shows the results of a study of 20 ladybugs with the number of dots on the outer wings of each ladybug recorded.

Record Sheet for Ladybug Dots

(9, 13, 0, 13, 11, 9, 0, 13, 13, 7, 2, 13, 9, 7, 2, 13, 9, 14, 13, 13)

Complete this frequency table for Ladybug Dots using the information from the record sheet.

Dots 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Frequency

2. Teresa looked all over the house for loose change. She checked under sofas, on the floor, in drawers, and in similar places. Look at her tally sheet below. Then use the table on the right to organize her data.

Tally Sheet of Loose Coins

Pennies Nickels Dimes Quarters Half-dollars Extension

• Make a survey of all of the students in your class to determine their favorite television programming. Use the survey included here. Add other types of programming if you wish. • After you have completed the tally sheet,

complete a frequency table like the one on page 5 to organize your results.

• Create a tally sheet to survey your classmates on their favorite sports to watch or play. Then complete a frequency table to record your findings.

Table of Loose Coins Frequency

Pennies Nickels Dimes Quarters Half-dollars Tally Sheet Sports Drama Sitcoms Movies Nature/Science Science Fiction Wrestling Other

sprints relay long jump sit-ups pull-ups 6th grade boys 6th grade girls 7th grade boys 7th grade girls 8th grade boys 8th grade girls

• • • • • • • Working with Tables and Charts

Directions: Use the information on page 5 to organize the raw data from these tally sheets into tables or charts. Then answer the questions related to each set of data.

Number of Medals Awarded at Arrow Valley School “Olympics Day”

1. Make a table to organize the data on the tally sheet. 2. Which of the six groups won the most medals? ________

3. Which of the three classes was probably the most athletic? ________ 4. Which of the five activities was probably the hardest? ________ 5. How many medals did the boys win? ________

6. How many medals did the girls win? ________

Numbers Generated Rolling Two Dice 24 Times

2 3 4 5 6 7 8 9 10 11 12

7. Make a table to organize the above data. 8. Which number had no rolls? ________

9. Which four numbers combined had the same number of rolls as 6? _____ _____ _____ _____ 10. Which numbers were rolled the most often? ________ Why do you think this happened?

_______________________________________________________________________________

Extension

• Roll two dice 24 times. Keep a tally sheet to record each roll. • Make a table to organize your data.

• Compare your results to the data on this page. • Compare your table with those of your classmates.

• Create a combined table showing the results for 10 members of your class. (Include yourself.)

• • • • • • • • • • • • • • • • • • • Organizing Data

1

Practice

Directions: Use the information on page 5 to help you do this page.

This is a tally sheet indicating the number of absences during one week for 7th grade students in each homeroom.

7th Grade Arrow Valley Middle School Weekly Absence Report

Monday Tuesday Wednesday Thursday Friday

Room 12 Room 13 Room 14 Room 15 Room 16 Room 17 Room 18

1. Create a table to organize this data both by day and by weekly totals.

2. What were the total absences for the week in the 7th grade? ______________________________ 3. Which homeroom had the fewest absences? ___________________________________________ 4. Which day of the week had the best attendance? ________________________________________ 5. Which two days had the worst attendance? ____________________________________________ 6. Give a possible reason for the poor attendance on these days. _____________________________ _______________________________________________________________________________ 7. How many students were absent on Tuesday? __________________________________________ 8. Which room had the worst attendance? _______________________________________________ 9. Two students were absent the entire week in room 13. How many other absences did room

13 have? ___________________________

10. Could any one else have been absent the entire week in any room? Explain.__________________ _______________________________________________________________________________ Apple Valley Middle School has a snack table after school, which helps raise money for school projects. This tally sheet illustrates their sales for one afternoon.

Snack Table Sales for Thursday

apples juice colas candy bars chips peanuts raisins candy jellies

11. Create a table to organize this data. 12. Which product was the best seller? _____________________________ 13. Which two products were the least

popular? ______________________ 14. Did the students mainly buy healthy

snacks or sweets? _______________ 15. How many snacks were sold

altogether? ____________________ 16. If every snack sold for $0.50, how

• • • • • • • Using

Correlation,Extrapolation,

and Interpolation

• A scattergramis made by plotting two sets of data as coordinate pairs on a graph.

Students in 8th Grade

Ice Cream Sales at

The Vanilla Express

1. How long did the students with the best language arts grades (90 or above) read? ___________ 2. How long did the students with the lowest

grades (30 or below) read? ______________ 3. Is there a correlation between hours read and grades in this class? ____________________ 4. Is the correlation weak or strong? _________ 5. Is the correlation positive or negative?

_______________

6. Draw a trend line to indicate the general direction of the trend indicated on the graph. 7. Is there a correlation between the number of five-gallon tubs of ice cream consumed and the temperature? ______________________ 8. Is the correlation strong or weak? _________ 9. Is the correlation positive or negative?

____________________________________ 10. Using interpolation, make an estimate for the

number of tubs consumed on the day the temperature was 84°. __________________ 11. Using extrapolation, make an estimate for

sales on the following days if the temperature pattern remains the same. _______________

100 90 80 70 60 50 40 30 20 10 0 Gr ade P er c

entage in Language Arts

1 2 3 4 5 6 7 8 9 10

Hours Spent Reading Weekly

22 20 18 16 14 12 10 8 6 4 2 0 Numb er of F iv e-gallon T ubs of Ic e C ream C onsumed 72° 74° 76° 78° 80° 82°84° 86°88°90°92°94° 96° Trend Line

• • • • • • • • • • • • • • • • • Looking for Trends

5

Practice

Directions: Use the scattergrams below and the information on page 21 to complete the page. A basketball player graphed his shooting success from different distances from the basket. He took eight shots at each five-foot interval from the basket.

8 7 6 5 4 3 2 1 0 Numb er of Shots Made 100 90 80 70 60 50 40 30 20 10 0 S cienc e Gr ade (%) 0 1.5 3 4.5 6 7.5 9 10.5 1213.5

Distance (meters) from the Basket

0 10 20 30 40 50 60 70 80 90100

Language Arts Grade (%)

1. How many shots did the player make five feet from the basket? ________________________ 2. How many shots did the player make 25 feet

from the basket? ________________________ 3. Is there a correlation between shots made and

distance? ______________________________ 4. Is the correlation weak or strong? ___________ 5. Is the correlation positive or negative? _______ 6. Draw a trend line on the graph.

7. Extrapolating from the data given, how many of the eight shots would the player be likely to make two feet from the basket? ____________

This scattergram relates the Science and Language Arts grades of 35 students.

8. Draw a trend line through the scattergram. 9. Is there a strong correlation, a weak

correlation, or no correlation between science and language arts grades in this group of students? _____________________________ 10. Are most students either strong in both

subjects or weak in both subjects? _________ 11. Would a student with good grades in science

be likely or unlikely to do well in language arts? _________________________________

Distanc

e Run (in met

e rs) 549 488 427 366 305 244 186 122 61 0 15 30 45 60 75 90 105120135150165180

Time (in seconds)

• • • • • • • • • • • • • Applying Data Analysis

Directions: Use the scattergrams and the information from page 21 to complete the page. An 8th grader made a graph illustrating how many feet she ran in 15-second increments.

Sheila’s Running Record

1. Draw a trend line on the graph indicating the direction of the data.

2. How many meters did Sheila run in 30 seconds? ________________________________________ 3. How many meters did Sheila run in 60 seconds? ________________________________________ 4. Using interpolation, determine about how many meters Sheila had run in 45 seconds. __________ 5. Is the correlation between the number of meters run and the time strong or weak? _____________ 6. Is the correlation between the distance run and the time spent running positive or negative?______ 7. Extrapolating from the data given, about how far will Sheila have run in 195 seconds? _________ 8. Extrapolating from the data given, about how far will Sheila have run in 210 seconds? _________

Sun _Mon. Tues. We d . T hurs. F ri. Sat . WeekOne We ek Two Numb er of Snacks 18 16 14 12 10 8 6 4 2 0

• • • • • • • • • How to Interpret Pictographs,

Histograms, and Special Graphs

3

How to

Facts to Know

Graphs are effective tools used to compare data in clear, concise, visual terms.

Three of the most common graphs are bar graphs, circle graphs (pie charts), and line graphs.

Pictograph

A pictographuses pictures or symbols to compare data. It is useful for units where smaller numbers or even blocks of data are used. A key indicates the value of each symbol. Sometimes a symbol is cut in half to indicate half of the amount.

Survey by Category of Books Read by 200 8th Grade Students

Double-Bar Graph

A double bar graphis used to compare two sets of data within a given period of time or set of circumstances.

Minutes Devoted to Music and Commercials at Radio Stations During 30-minute Programming

Multiple-line Graph

A multiple-line graphcompares two or more sets of data, which are changing over time. Two lines are usually used to compare how two events might be related to each other and affect each other over a period of time.

Number of Snacks Bought in a Ten-day Period

fantasy science fiction humor romance true life mystery Key = 10 books Numb er of Minut es 24 22 20 18 16 14 12 10 8 6 4 2 0

KBIF KLAB KMAL KCLL KBBB Radio Station

Histogram

A histogramis a diagram, which often illustrates the frequency of an event and shows how data falls into different intervals. The intervals, represented by rectangular bars, may be the same width or they may vary. Histograms are usually used with continuous data, which falls into varying intervals.

U.S. Population Density 90 86 82 78 74 70 66 62 58 54 50 19601970 1980 1990 20002010*2020* *projected Key = music = commercials

Day of the Week

P

er S

q

uar

• • • • • • • • • • • Working with Pictographs

and Histograms

A pictograph uses pictures or symbols to illustrate data comparisons. This pictograph illustrates the life span of various types of garbage.

Life Span of Garbage

cardboard boxes camera film trash bags pantyhose soft-drink cans plastic bottles coated cartons leather shoes

Directions: Use the information on page 13 and this pictograph to answer these questions.

1. How many years does it take a cardboard box to decay? __________________________________ 2. How many years does it take pantyhose to decay? _______________________________________ 3. How many more years does it take plastic bottles to decay than it takes leather shoes? __________ 4. Which two items take the longest to decay? ___________________________________________

How many years does each type take? __________

5. How long do plastic-coated cartons take to decay? ______________________________________ 6. How would this pictograph help communicate the problems of landfills and the value of recycling

in this country? __________________________________________________________________ Directions: This histogram illustrates the frequency of graduation rates in a recent year and the states where this frequency occurs.

7. How many states have between 81% and 90% of its students graduating? ____________________ 8. How many states have between 51% and 60% of its

students graduating? ____________________ 9. What percentage of students is graduating in 22

states? _______________________________ 10. How many states are represented in all?

_____________________________________ 11. About 65% of California’s public high school

students graduate. In what frequency is California recorded on the graph? __________________ 12. Vermont is the state with the highest graduation rate

(89.9%). In what frequency is Vermont included on the graph? ____________________________ 13. How might this histogram be used by public

officials? _____________________________ Numb er of Stat es 22 20 18 16 14 12 10 8 6 51-60% 61-70% 71-80% 81-90%

Percentage of Graduate Students

Key

= 5 years

= 2

1

⁄

2

years

Public High School

Graduation Rates

• • • • • • Working with Double Bar Graphs

3

Practice

A double-bar graphis used to compare two sets of data. The double bar graph shown here illustrates the percentage of male/female attendance at several major colleges in the United States.

Male/Female Attendance at Major Colleges

Directions: Use the information on page 13 and this graph to answer these questions.

1. What percentage of students at UCLA is male? ________ What percentage is female? ________ 2. What percentage of students at Yale is male? _____ What percentage of students is female? ____ 3. What percentage of students at NYU (New York University) is male? ________

What percentage is female? __________

4. In which two colleges is the percentage of male and female students almost the same? _________ 5. Which college has the greatest disparity between the percentage of male and female students?

_______________________________

6. What is the total percentage of male and female attendance at each college? ______________ Why? __________________________________________________________________________ 7. Using the graph as a representative of college attendance, are more males or more females

attending these colleges? _______________________

Directions: Study this double bar graph illustrating the points scored by two teams, the Bulldogs and the Wildcats, in the four quarters of a football game.

8. What was the Bulldogs’ best quarter? _______ 9. What was the Wildcats’ best quarter? _______ 10. How many total points did each team score in

the game? _____________________________ 11. Which team got better in the first three quarters?

_____________________________________ 12. How might a coach use this graph?

_____________________________________ _____________________________________ 60% 58% 56% 54% 52% 50% 48% 46% 44% 42% 40%

UCLA NYU USC

Michigan Stat e Y ale Harv ar d UC Irvine Pepp er dine P oints S c or ed 1 6 1 4 1 2 1 0 8 6 4 1st 2nd 3rd 4th

Key

= male

= female

Key

= bulldogs = wildcats

• • • • • Working with Multiple-line Graphs

A multiple-line graphcompares two or more sets of data, which are changing over time.

This multiple-line graph illustrates the number of novel pages read each day for one week by two language arts students, Alyssa and Greg.

Directions: Use the information on page 13 and this graph to answer the following questions. 1. How many pages did Greg read on Sunday? _________ 2. How many pages did Alyssa read on Sunday? _______ 3. How many pages did Greg read on Friday? __________ 4. How many pages did Alyssa read on Friday? ________ 5. On which day did Greg read the fewest pages? _______ 6. On which day did Alyssa read the fewest pages? _____ 7. Which student read the most pages during the week?

_____________________________________________ 8. How many more pages did Alyssa read than Greg on

Monday? _____________________________________ 9. On which three days did Alyssa read exactly five pages

more than Greg? _______________________________ 10. How many total pages did Alyssa read? ____________ 11. How many total pages did Greg read? ______________ 12. Which student was more consistent in doing the assigned

reading?______________________________________

13. How many minutes did Sarah practice the first week? ____________________________________________ 14. How many minutes did Catherine practice the first

week? _______________________________________ 15. How many minutes did Sarah practice for the entire six weeks? ______________________________________ 16. How many minutes did Catherine practice for the entire

six weeks? ___________________________________ 17. Which student practiced more in the sixth week?

____________________________________________ 18. Did Catherine become a better or worse piano student

during the six weeks?________ Explain.

____________________________________________ ____________________________________________ Directions: Study this graph illustrating how many minutes Sarah and Catherine practiced playing the piano in a period of six weeks. Answer the questions below.

Numb er of P ages R ead 80 70 60 50 40 30 20 10 0

Sun. Mon. Tues. We

d

.

T

hurs. Fri. _Sat

.

Pages Read per Day

for One Week

Day of the Week

Minutes of Piano Practice

Each Week for Six Weeks

Numb er of P ratic e Minut es 90 75 60 45 30 15 0 1st 2nd 3r d 4th 5th 6th Key = Alyssa = Greg Key = Sarah = Catherine Week

Facts to Know

Graphs are effective tools used to compare data in clear, concise, visual terms.

Three of the most common graphs are bar graphs, circle graphs (pie charts), and line graphs.

Graphing Terms

• The rangeis the difference between the least and the greatest values in a set of data. (2, 4, 7, 8, 10, 12)

12 – 2 = 10 The rangeis 10.

• The scaleis the set of values or numbers along the side of a graph.

• The intervalis the regular difference between each unit on the scale. The interval is always the same between each unit of the scale.

• The axesare the two labeled lines, one vertical and one horizontal, along the sides of a graph. The scale runs along one of the axes.

Single Bar Graphs

Single bar graphsoffer a clear, visual presentation

of facts. Bar graphs may be either vertical or horizontal. The names of the items being compared are listed, one in each block, along the bottom axis of the bar graph. The scale is marked in even intervals along the vertical axis.

Single Line Graphs

Single line graphsare often used to compare change

over time or the frequency of an event. The time intervals or items being compared are marked along the horizontal axis of the line graph. The scale is marked in even intervals along the vertical axis.

Circle Graphs (Pie Charts)

Circle graphs, or pie charts, demonstrate how a whole is split into individual parts.

The parts are rarely equal. The size of the angle shows how one part compares to another. They are usually expressed in percentages of the whole, based on 100%. Labels, listing names and amounts, are written on the slices of the graph.

• • • • • • • • • How to Use and Interpret Bar,

Circle, and Line Graphs

2

How to

Land Use in the United States

P

er

c

entage of Land Use

Numb er of B o oks 35 30 25 20 15 10 5 0 F armland Meadows/ Pa s t u re s F or ests/ W o o dlands Permanent Cr o p s Other 140 130 120 110 100 90 80 70 60 Sept. Oc t . Nov . De c . J an. _Feb.

Books Read by 6th Grade Students

Racial Distribution in U.S. Population

80% White 4% Other 1% Native American 3% Asian 12% African American

• • • • • • • Working with Single Bar Graphs

This single bar graph shows the number of electoral votes for each of the 10 most populated states. The states are labeled in blocks along the horizontal axis. The number of electoral votes is indicated on the vertical axis. There are 538 electoral votes distributed among the 50 states and the District of Columbia. They are elected by the people in each state to officially vote for the president of the United States. It takes 270 electoral votes to win an election. Directions: Use the information on page 9 and the graph to answer these questions.

1. How many electoral votes does California have? ____________ 2. How many electoral votes does Texas have? _______________

3. What is the interval between numbers on the scale? _____________________________________ 4. How many electoral votes does New Jersey have?_______________________________________ 5. What is the difference in the number of votes between Michigan and Illinois? ________________ 6. Which state has exactly one more electoral vote than Texas? ______________________________ 7. What is the total number of electoral votes of the 10 most populated states? __________________ 8. How many electoral votes are distributed among the remaining 40 states and the District of

Columbia? ______________________________________________________________________ 9. Why would a candidate spend more time campaigning in California than in North Carolina?

_______________________________________________________________________________ 10. How many more votes than these 10 states would be needed to win a presidential election?

_______________________________________________________________________________ 11. Which two pairs of states have the same number of electoral votes as California?

_______________________________________________________________________________ 12. Why did the intervals start with 12 votes? _____________________________________________ 13. What could be misleading about this graph? ___________________________________________

Extension

Ten students at Arrow Valley Middle School were surveyed to determine the number of times they went to a fast food restaurant in one week. This table shows the results. Use the information to create a single bar graph.

Name Frequency Name Frequency

John 3 Freddy 5

Sherry 6 Elaine 1

Jimmy 10 Ginette 4

Alex 0 Harry 3

Marianne 2 Hector 7

Number of Fast Food Visits in One Week

C alif ornia F lorida _Illinois Michigan New J ersey New Y ork North C a rolina Ohio Pennsylv ania Texas 56 52 48 44 40 36 32 28 24 20 16 12 Numb er of Elec t or al V ot es State

• • • • • • • • • • Working with Circle Graphs

2

Practice

This circle graph illustrates which elements are most abundant in the earth’s crust.

Directions: Use the information on page 9 and the circle graph to answer these questions. 1. Which is the most abundant element in the

earth’s crust? _________________________ 2. Which two elements make up three-fourth’s

of the earth’s crust? ____________________ ____________________________________ 3. Which two elements together are equal to the

amount of aluminum in the earth’s crust? ____________________________________ 4. Where would carbon, hydrogen, and sodium

be included? __________________________ 5. Which element makes up almost half of the

earth’s crust? _________________________

This circle graph illustrates the percentages of each major element in the human body. 6. Which element makes up more than half of

the human body? ______________________ 7. How much higher is the percentage of carbon than the percentage of nitrogen? __________ 8. What percentage of the human body do the

three major elements total? ______________ 9. On the graph, where do you think copper,

phosphorus, and iron are included?

____________________________________ 10. What body compound would have much of

the hydrogen and oxygen? _______________ 11. Why is this type of graph so easy to use?

____________________________________ ____________________________________ ____________________________________ 47% Oxygen 65% Oxygen 3.5% Calcium 4.5% Iron 8% Aluminum 2% Other 2% Calcium 3% Nitrogen 28% Silicon 9% Other 18% Carbon 10% Hy drogen

Elements as a

Percentage of the Earth’s Crust

Major Elements as a

Percentage of the Human Body

Extension

• Survey 10 members of your class to determine their favorite pizza topping.

Convert each topping to a percentage. (If three of the ten students prefer pepperoni, that is 30% of the total. If one student prefers cheese, that is 10% of the total.)

• • • • • • • • • • • Working with Line Graphs

The two line graphs indicate the number of hours spent on homework for two 8th grade students.

Number of Hours Spent on Homework in One Week

Carlos Janet

Days of the Week

Directions: Use the information on page 9 and the two graphs above to answer these questions.

1. How many hours did Carlos spend doing homework on Tuesday? __________________________ 2. How many hours did Janet spend doing homework on Tuesday? ___________________________ 3. On which day did neither student do any homework? ____________________________________ 4. Both students had a huge science project due the Monday of next week. Which student put it off

until the end? __________________________

5. Which student is more likely to use time effectively? __________Why? _____________________ _______________________________________________________________________________ 6. How many hours did Janet spend on homework this week?________________________________ 7. How many hours did Carlos spend on homework this week? ______________________________ 8. How many hours of homework a day did Carlos average over seven days? ___________________

Extensions

• On Monday, Justin rode his scooter for 2 1_⁄

2hours. He spent the following amounts of time on his

scooter for the next six days: 3 hours, 1 1_⁄

2hours, 1⁄2hour, 2 hours, 5 1⁄2hours, and 4 hours. Make a

single line graph to illustrate how much time Justin rode each day of the week.

• Make a table estimating how many hours you slept in the last seven days. Then create a single-line graph from this table.

Numb er of Hours 8 6 5 4 3 2 1 0 Mon. Tues. We d . T hurs. F ri. Sat . Sun.

Days of the Week

Numb er of Hours 8 6 5 4 3 2 1 0 Mon. Tues. We d . T hurs. F ri. Sat . Sun.

• • • • • • • • • • • • • • • • • • • • • Answer Key

z

–

4

x

2

2

m

1. 2. 23 pennies; 9 nickels; 15 dimes; 4 quarters 0 half dollars

Answers will vary. 1.

2. 7th grade boys

3. 7th grade; The boys and girls won the most medals.

4. pull-ups; The fewest medals were awarded. 5. 54 6. 46 7. 8. 3 9. 7 10. 2, 4, 11, 12

11. 6 and 7; These combinations are the most common rolls.

Answers will vary. 1.

2.

2. 68 3. Room 14 4. Wednesday

5. Monday and Friday 6. Answers will vary. 7. 11

8. Room 13 9. 9 11. 10. Room 12 and

Room 16; There was at least one absence per day.

12. candy jellies 13. apples and raisins 14. sweets 15. 141 16. $70.50 1. 54 2. 32 3. 4 4. 15 5. 2 6. New York 7. 257 8. 281

9. There are more votes in California. 10. 13

11. Illinois and Texas; New York and Ohio

12. All states have at least 12 votes. 13. The graph can make the total of

Californiaʼs votes look many times greater than that of the smaller states. There is a distortion due to the scale. 1. oxygen 6. oxygen 2. oxygen and silicon 7. 15% 3. calcium and iron 8. 93% 4. other 9. Other 5. oxygen 10. water 11. It is visual and easy to read.

Answers will vary. 1. 3

2. 3 3. Friday 4. Carlos

5. Janet; Her work is done more regularly.

Answers will vary. 1. 20 years

2. 40 years 3. 35 years

4. cans and bottles; 85 years 5. 7 1/2 years

6. It shows how long it takes garbage to disintegrate. Answers will vary. 7. 8 states 8. 8 states 9. 71–80% 10. 50 states 11. 61-70% 12. 81-90%

13. Answers will vary. 1. 47% male; 53% female 2. 51% male; 49% female 3. 41% male; 59% female 4. USC and Yale

5. NYU

6. 100%; Students must be either male or female. 7. more females 8. 2nd quarter 9. 3rd quarter 10. Bulldogs 30; Wildcats 34 11. Wildcats

12. To see how his team played as the game progresses. (Answers will vary.) 1. 30 pages 2. 50 pages 3. 65 pages 4. 70 pages 5. Wednesday 6. Monday 7. Alyssa 8. 15 pages 9. Tuesday, Friday, and Saturday 1. (9, 12, 14, 16, 16, 19, 22, 23, 28) Mode: 16

Yes, it is in the middle and the median is the same.

Median: 16

Yes, it matches the mode and is close in value to most of the numbers.

2. (7, 9, 10, 10, 11, 14, 14, 15, 18, 20, 21, 31, 38)

Mode: 10, 14

No, the number 10 is too close to the first numbers. 14 is more representative.

Median: 14

No, there are many greater numbers after 14.

3. (19, 25, 28, 28, 32, 44, 48, 48, 51, 57, 64, 70)

Mode: 28, 48

No, 28 is too near the first numbers;

Dots 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 2 0 2 0 0 0 0 2 0 4 0 1 0 7 1 Frequency 2 2 3 3 3 3 4 4 5 5 6 7 8 9 10 11 12 1 0 1 1 1 apples 2 juice 6 colas 31 candy bar 33 chips 24 peanuts 7 raisins 3 candy jellies 35 3 5 5 2 2 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 2 4 4 4 6 2 2 0 1 0 2 2 2 2 2 0 0 0 0 0 0 11 Room 12 Room 13 Room 14 Room 15 Room 16 Room 17 Room 18

Mon. Tues. Wed. Thurs. Fri. sprints 5 5 3 3 3 3 3 3 4 4 4 1 2 2 2 2 3 3 6 6 4 4 4 3 2 2 2 2 5 5

relay long jump sit-ups pull-ups 6th grade boys 6th grade girls 7th grade boys 7th grade girls 8th grade boys 8th grade girls 10. 410 pages 11. 300 pages 12. Alyssa 13. 90 minutes 14. 45 minutes 15. 375 minutes 16. 365 minutes 17. Catherine 18. better; She practiced more regularly. 6. 16.5 hrs. 7. 17.25 hrs. 8. 2.5 hrs.

• • • • • • • • • • • • • • • • • • • • • • Answer Key

–

4

x

2

m

48 is more representative. Median: 46

Yes, it’s about in the middle of the values.

4. (31, 37, 39, 40, 40, 47, 47, 47, 48, 49, 49, 49, 61, 70)

Mode: 47 and 49

Yes, 47 is near the center. 49 is less representative because it is nearer to the end of the series. Median: 47

Yes, it is representative because it is in the center and the same as one mode.

Page 19

1. Total: 6,988 Divide by: 10 Mean: 698.8 (699)

Yes, it is representative because most of the numbers are 600s and 700s.

2. Total: 65 Divide by: 9 Mean: 7.2 (7)

No, the number of moons is very variable.

3. Total: 277 Divide by: 14 Mean: 19.8 (20)

Yes, many of the numbers are near 20.

4. Total: 1,113 Divide by: 14 Mean: 79.5 (80)

Yes, it is relatively representative of the numbers; a good average. 5. Total: 2,595

Divide by: 12 Mean: 216.3 (216)

Yes, many of the numbers are in or near the low 200s.

6. Total: 112 Divide by: 16 Mean: 7

Yes, it matches the mode and is near the center between 2 and 12. Page 20

1. Mode: 13 Median: 13 Mean: 9.6 (10)

Most representative: mode and median

Reason: They reflect the values best and are midway between high and low values.

2. Mode: 23 Median: 23 Mean: 23.3 (23) Most representative: 23 Reason: They are all the same. 3. Mode: 8 Median: 8

Mean: 8.3 (8)

Most representative: all Reason: They all are the same value.

4. Mode: 46 Median: 49 Mean: 51.9 (52)

Most representative: mean and median

Reason: They are closer to the center of the numbers in terms of value.

5. Mode: 23 Median: 29.5 Mean: 32.2 (32)

Most representative: median and mean

Reason: The mode is too near the first values; The others are representative of the numbers. Page 22 1. 5 to 10 hrs. 2. 1 to 3 hrs. 3. yes 4. strong 5. positive 6. (trend line on graph) Page 23 1. 7 shots 2. 2 shots 3. yes 4. strong 5. negative

6. (trend line on graph) 7. 7 or 8 shots

8. (trend line on graph) 9. weak correlation 10. strong 11. likely Page 24 1. Page 26 1. skateboarding 4. 16.7% (17%) 2. aerobics and 5. biking; cheerleading and walking 3. 60 Page 27 1. 8

2. It should have shown the entire scale, if possible.

3. There was not enough space. 4. no

5. no

Extension: Answers will vary.

Page 28 1. (0, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 12) 2. 7 students 3. 1 student 4. 1 student 5. (0, 1, 12) 6. 7, 9 7. 7.5 8. 7 (7.1) 9. Yes

10. Yes. All of the measures are similar and close in value.

Extension: Answers will vary.

Page 30 1. 6

2. ABCD BACD CABD DABC ABDC BADC CADB DACB ACBD BCAD CBAD DBCA ACDB BCDA CBDA DBAC ADCB BDAC CDBA DCAB ADBC BDCA CDAB DCBA 3. 4! = 4 x 3 x 2 x 1; 24 4. 5! = 5 x 4 x 3 x 2 x 1; 120 5. 6! = 6 x 5 x 4 x 3 x 2 x 1; 720 6. 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1; 5,040 7. 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1; 3,628,800

• • • • • • • • • • • • • Solving Word Problems

with Data and Graphs

10

_ProblemsWord

Directions: Use the bar graph to answer these questions.

1. How many calories would you burn playing handball for one hour?_____________________ 2. Approximately how many calories would you

burn bicycling? __________________________ 3. How many more calories would you lose

running rather than playing tennis? ___________ 4. How many calories would you burn on a

2 1–

2 hour cross-country skiing trip? ___________ 5. Which two activities are almost the same in

terms of the amount of calories they burn? _______________________________________ 6. Approximately how many calories would you

burn after one hour of running and one hour of swimming?______________________________ 7. Which two activities would have to be done for

one hour each to equal one hour of cross-country skiing? _________________________________ 8. Would you burn more calories on a 3-hour walk

or a 1-hour run? __________________________ 9. Which exercise would be best for you?________

Directions: Use the histogram to answer these questions.

10. How many states have a population under a million? ________________________________ 11. How many states have a population over 10

million? ________________________________ 12. How many states have a population of 5 to 10

million? ________________________________ 13. What range of population is most common for

the states?_______________________________ 14. Name two reasons you think states have such

different population figures. ________________ 15. Which two states do you think have the most

population and the least population?__________ 16. In which category does your state fall?________ _______________________________________

Bar Graph

1,000 900 800 700 600 500 400 300 200 Calories Burned P er Hour Type of Exercise Population Running Cross-Country Skiing Swimming Bic y cling T ennis W alking Handball

Histogram

State Population (1995) Number of States 24 22 20 18 16 14 12 10 8 6 under 1 million 1–5 million 5–10 million o v er–10 million

• • • • • • • • • • • • • Solving Word Problems

with Graphs and Statistics

10

_Problems

Directions: Use the multiple-line graph to answer these questions.

1. Which day had the highest temperature of the week? _______________________________ 2. Which day had the lowest temperature that

week? _______________________________ 3. What was the usual difference between high

and low temperatures during this week? 15˚ to 20˚? __________ 25˚ to 30˚? _______ 3˚ to 4˚? __________

4. On which day were the high and low

temperatures exactly 20˚ apart? ___________ 5. On which two days were the lows 73˚?

_____________________________________ 6. On which two days were the highs 93˚?

_____________________________________ 7. On which three days were the lows 70˚?

_____________________________________ 8. What was the average high temperature for

the week? ____________________________ 9. What was the average low temperature for the week? _______________________________ 10. How does this kind of graph help you analyze the temperature data? ___________________ Directions: Use the circle graph to answer these questions.

11. Which component makes up the highest percentage of body weight?_______________ 12. Which single component on the graph has the

lowest percentage of body weight? _________ 13. What percentage of body weight do fat and

protein make up together? ________________ 14. Where do you think calcium, sodium, and

iron are included in the graph? ____________ 15. How much greater is the percentage of water

than fat? ______________________________ 16. Where do you think the water is contained in

the human body? _______________________

Multiple-Line Graph

Daily Temperatures (High and Low)

Circle Graph

Percentage of Body Weight

Monday Tu esday W ednesday Thursday Friday Saturday Sunday 100˚ 95˚ 90˚ 85˚ 80˚ 75˚ 70˚ 65˚ 60˚ Water 62% Protein 17% Fat 15% Other 3% Nitrogen 3% Day of the Week

T

• • • • • • • • • • • • • • • • • • • • • • Answer Key

6. n+ 9n+ 2n = 144 12n = 144 n = 12 Daniel has 12 stamps. Bryan has 24 stamps. George has 108 stamps. Page 36 1. n+ (n + 25) + (n + 23) = 93 3n+ 48 = 93 n = 15 Fred is 15 years old. Mom is 38 years old.

Dad is 40 years old. 2. 3n+ 220 = 310 n = 30 The skateboard is $30. The scooter is $90. The bike is $190. 3. 9n+ 6 = 3(n+ 6) n= 2 Jimmy is 2 years old. Brother is 18 years old. 4. n+ (n– 5)+ (n+ 2) + (n+ 8) = 53 4n+ 5 = 53 n= 12 Jesse is 12 years old. Maybelle is 7 years old. Ellen is 14 years old. Jeanne is 20 years old. 5. n+ (n+ 15)+ (n– 10) + (n+ 23) = 108 4n+ 28 = 108 n = 20 Joseph had $20.00. Elsa had $35.00. Julian had $10.00. Martha had $43.00. 6. n+ 2n+ 4n= 105 7n =105 n= 15 Melissa had $15.00. Christina had $30.00. Charmain had $60.00. 7. n+ 3n+ (3n– 10) = 74 7n– 10 = 74 n= 12 Kristin had $12.00. Matthew had $36.00. Joshua had $26.00. 8. n+ (n+ 8) + 3n+ (n– 5) = 63 6n+ 3 = 63 n= 10 Andrew is 10 years old. Kenneth is 18 years old. Billy is 30 years old. Cameron is 5 years old. Page 38 1. 4/7 or 4:7 4/11 or 4:11 7/4 or 7:4 7/11 or 7:11 2. 5/8 or 5:8 5/13 or 5:13 8/5 or 8:5 8/13 or 8:13 3. 6/7 or 6:7 6/13 or 6:13 7/6 or 7:6 7/13 or 7:13 4. 60/1 or 60:1 5. 55/1 or 55:1 6. 16/1 or 16:1 7. 1,200/1 or 1,200:1 8. 24/1 or 24:1 9. 60/1 or 60:1 10. 365/1 or 365:1 11. 8/100 or 8:100 Page 39 1. 2:3 :: n:18 n= 12 blocks 2. 5:3 :: n:60 n= 100 pages 3. 5:7 :: n:630 n= 450 minutes 4. 14:3 :: n:90 n= 420 gallons 5. 170:4 :: n:240 n= 10,200 gallons 6. 20:3 :: 1000:n n= 150 hours 7. 145:3 :: n:24 n= 1,160 lb. Page 40 1. 55:1 :: n:7 n= 385 miles 2. 18:1 :: n:20 n= 360 miles 3. 60:1 :: n:5.5 n= 330 minutes 4. 24:1 :: n:13.5 n= 324 hours 5. 2,000,000:1 :: n:48 n= 96,000,000 tons 6. 2,980:n :: 40:1 n= 74.5 hr. 7. 100:9 :: n:40.5 n= 450 miles 8. 16:1 :: n:45 n= 720 oz. Challenge: 86,400 sec.; 8,760 hr. Page 41 1. 600 calories 2. 650 calories 3. 400 calories 4. 2,500 calories 5. handball and bicycling 6. 1,650 calories 7. bicycling and walking 8. 3-hr. walk

9. Answers will vary. 10. 8 states

11. 7 states 12. 12 states 13. 1 to 5 million

14. Answers will vary. 15. California has the

most.

Wyoming has the least.

16. Answers will vary.

Page 42 1. Friday 2. Thursday 3. 15˚ to 20˚ 4. Monday 5. Wednesday and Friday 6. Tuesday and Saturday 7. Monday, Saturday, and Sunday 8. 91.7˚ or 92˚ 9. 71.7˚ or 72˚ 10. Answers will vary. 11. water

12. nitrogen 13. 32%

14. other category 15. 47%

16. Answers will vary.

Page 43 1. +2 – 12 = -10 You owe $10.00. 2. 32 – 40 = -8 8 below 0 3. -4 + -11 + -6 = -21 21 below par 4. -$1000 + $750 = $250 $250 owed 5. -600 + 200 + 100 + 150 = -150 He needed 150 points to get to 0. 6. -69 + 35 = -34˚ F 7. -129 – (+)136 = -265 265˚ difference 8. -80 – (+)134 = -214 214˚ difference ? ? ?

22

Practice 19

This single bar graph illustrates the life spans of various animals. Study the graph and use the information to answer the questions below.

Life Spans of Animals

d o g c a t c a m e l m o u s e ra b b it re d fo x c h ip m u n k lio n p o la r b e a r le o p a rd g ir a ff e p ig o p o s s u m b la c k b e a r

1. Which animal on the graph has the longest life span? _________________ 2. Which four animals live about 12 years? _________________

3. How many more years does a polar bear live than a black bear? _________________ 4. Which animal lives as long as a giraffe? _________________

5. How much longer does a leopard live than a mouse? _________________ 6. How long does a lion live? _________________

7. How much longer does a red fox live than a chipmunk? _________________ 8. How much longer does a cat live than a mouse? _________________

9. The average life span of an American is about 75 years. How much longer does a person live than a polar bear? _________________

10. How much longer does a person live than a rabbit? _________________

Animals 22 20 18 16 14 12 10 8 6 4 2 0 N u m b e r o f Y e a rs

Practice 20

This double bar graph illustrates a survey of the relative popularity of soccer and football as participant sports for boys in the third through the eighth grade.

Single Bar and Double Bar Graphs

3rd 4th 5th 6th 7th 8th

1. What percentage of third grade boys preferred to play football? _________________

2. In which two grades do boys like to play soccer and football equally well? _________________ 3. What percentage of boys in the fourth grade prefer soccer? _________________

4. Is there any grade in which more boys prefer football? _________________ 5. What percentage of boys prefer football in the sixth grade? _________________ 6. What percentage of boys prefer football in the seventh grade? _________________

Popularity Survey: Soccer vs. Football

100 90 80 70 60 50 40 30 20 10 0

P

e

rc

e

n

ta

g

e

o

f

S

tu

d

e

n

ts

■

■

_football

■

■

_soccer

Grade Level

24

Practice 21

7 8 9 10 11 12 13 14 15 16 This single line graph illustrates the percentage of

children in the general population from 1950 until 2000. Study the graph and use the information to answer the questions below.

This double line graph shows the average heights of boys and girls by age from 7 through 16. Study the graph and answer the questions below.

1. In which year did children comprise 36% of the population? ____________

2. In which years were only 26% of the population children? ____________ 3. What year saw the highest percentage of

children? ____________

4. In which ten-year period did the number of children as a percentage of the population rise? ____________

5. In which years are children just about one-fourth of the population? ____________ 6. In which ten-year period did the greatest

drop occur? ____________

7. In which two ten-year periods were children more than one third of the population? ____________

8. Does the most recent trend seem to be rising, falling or staying the same? ____________

9. At which two ages do boys and girls average the same heights? ____________

10. At which two ages are girls on average taller than boys? ____________

11. At what age do boys average 4 inches taller than girls? ____________

12. At what three ages do boys and girls grow at about the same amount before the girls catch up to boys? ____________

13. Are sixth grade girls usually taller or shorter than boys? ____________

14. At what age do boys catch up and pass girls? ____________ 40 38 36 34 32 30 28 26 24 22

Population of Children in the U.S. Average Heights of Children

P e rc e n ta g e o f C h il d re n 70 68 66 64 62 60 58 56 54 52 50 48 H e ig h t in I n c h e s Year Age 1 9 5 0 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 Boys Girl s

Page 4 1. 279 marbles 2. 146 marbles 3. 188 marbles 4. 55 marbles 5. 1,316 marbles 6. 37 marbles 7. 96 marbles 8. 222 marbles 9. 245 marbles 10. 468 marbles 11. 71 marbles 12 marbles 12. 444 marbles Page 5 1. addition 19,056 bases 2. subtraction 1,689 at bats 3. addition 2,129 home runs 4. division 177 hits 5. multiplication 3,928,500 tickets 6. subtraction 1,578 strike outs 7. division 2,800 groups 8. subtraction 329 walks 9. division 175 hits (174 R13) 10. division .600 or 60% Page 6 1. subtraction 37,036 people 2. subtraction 14,443 people 3. addition 132,118 fans 4. addition 35,292 fans 5. division 860 packages 6. division 2,000 packages 7. subtraction 28,538 fans 8. division 8,250 packages 9. multiplication 601,536 fans 10. multiplication 3,649,050 tickets Page 7 1. 7/12 lb. 2. 1 5/12 lb. 3. 1/8 lb. 4. 1/12 lb. 5. 5 lb. 6. 1/4 feet 7. 1 7/10 lb. 8. 11/24 feet 9. 6 cups 10. 1 19/30 lb. Page 8 1. 15 ounces 2. 24 3/4 ounces 3. 21/40 ounces 4. 25 students 5. 14 students 6. 1/12 ounces 7. 1 7/10 ounces 8. 27 1/5 ounces 9. 9 3/8 ounces 10. 8 3/4 lb. 11. 1 1/2 ounces 12. 28 cups Page 9 1. 10 3/8 inches 2. 32 3/4 inches 3. 7/8 inches 4. 51 5/8 inches 5. 83 7/8 inches 6. 3 1/4 lb. 7. 20 1/4 lb. 8. 24 1/6 inches 9. 14 1/8 ounces 10. 20 3/8 inches Page 10 1. 76 inches 2. 52 1/5 inches 3. 10 prints 4. 8 prints 5. 150 inches 6. 355 inches 7. 23 1/3 inches 8. 7 prints 9. 451 inches 10. 8 prints Page 11 1. 2 1/4 feet 2. 9 5/6 feet 3. 17 3/4 feet 4. 3 1/8 feet 5. 2 1/3 feet 6. 6 2/5 times 7. 12 lengths 8. 6 1/12 feet 9. 5 1/2 feet 10. 14 7/12 feet Page 12 1. $5.04 2. $0.56 3. $63.68 4. $43.45 5. $5.51 6. $5.04 7. $29.25 8. $0.96 9. $10.13 10. $20.15 11. $18.35 12. $17.10 Page 13 1. 7.9 centimeters 2. 87.6 centimeters 3. 30.25 centimeters 4. 220.89 centimeters 5. 204.26 centimeters 6. 347.863 centimeters 7. 24.99 centimeters 8. 1.201 centimeters 9. 56.899 centimeters 10. 59.663 centimeters 11. 26.989 centimeters 12. 181.91 centimeters Page 14 1. 0.21 lb. 2. 100.2 ounces 3. 1.09 ounces 4. 10.2 candies 5. 45.1 lb. 6. 80.5 ants 7. 969.624 ounces 8. $0.23 9. $0.38 10. 157.68 lb. Page 15 1. 75% 6. 80% 2. 72% 7. 64% 3. 75% 8. 67% 4. 60% 9. 70% 5. 75% 10. 82% Page 16 1. $34.00 2. $4.00 3. $1.32 4. $9.52 5. $7.00 6. $2.48 7. $22.80 8. $4.00 9. $18.00 $42.00 10. $5.24 $29.71 Page 17 1. 467.476 mi. 2. 2,246.8 mi. 3. 32.422 feet 4. 94.14 mi. 5. 15.23 mi. 6. 44.636 mi. 7. 177.813 m.p.h. 8. 3,030.957 lb. 9. 91.05 mi. 10. 880.431 mi. Page 18 1. 60 m.p.h. 2. 50 m.p.h. 3. 30 m.p.h. 4. 60 m.p.h. 5. 50 m.p.h. 6. 55 m.p.h. 7. 52 m.p.h. 8. 40 m.p.h. 9. 40 m.p.h. 10. 80 m.p.h. Page 19 1. 3,200 feet 2. 40 min. 3. 10,000 feet 4. 7,128 feet 5. 396 min. 6. 7,740 feet 7. 24,000 feet 8. 503 min. 9. 410 min. 10. 30,400 feet Page 20 1. $1 2. $1 3. $11 4. 7 5. $21 6. 2 7. -$6 8. -24 9. 17 10. -72 11. -32 12. $226 Page 21 1. -$12 2. -$20 3. +42 4. -$7 5. -9 6. +10 7. $270 8. +156 9. 64 10. +5 11. -$5 12. +20 Page 22 1. polar bear 2. leopard/camel dog/cat 3. 2 yr. 4. pig 5. 9 yr. 6. 15 yr.. 7. 1 yr. 8. 9 yr. 9. 55 yr. 10. 70 yr. Page 23 1. 30% 2. 5th/8th 3. 60% 4. no 5. 45% 6. 40% Page 24 1. 1960 2. 1990–2000 3. 1960 4. 1950–1960 5. 1990–2000 6. 1970–1980 7. 1960–1970 8. the same 9. 10/11 10. 12/13 11. 16 12. 7/8/9 13. taller 14. 14 Page 25 1. 12 Frequency 2. 1 Cat 8 3. 4 Dog 12 4. 2 Snake 2 5. 2 Bird 3 6. 12 Mouse 3 7. 18 Hamster 4 8. 1 Fish 6 9. 4 Other 3 10. dog 11. snake 12. 5 13. 41 14. 27 Page 26 1. 10 m.p.h.

2. the scale starts at 20 rather than 0

103

Interpreting Data

7.12

Name _______________________________________________ Date _______________________

You and your family wish to plan a winter and a summer vacation. You look forward to skiing, sledding, skating, and warming your feet by an indoor fire during your winter trip, and swimming, boating, biking, and roasting marshmallows by the campfire during your summer trip.

Climate and Precipitation Data from Around the United States

Directions: Use the data from the chart above to answer the following questions. 1. In which city would you have the least probability of being rained out in July?

______________________________________________________________________ 2. What can you say about the rainfall in July in Houston compared to that in Denver? ___ ______________________________________________________________________ 3. Describe how you might pack differently if you plan to camp in Anchorage in July

compared to camping in Washington, D.C., in July. _____________________________ ______________________________________________________________________ 4. Which city do you think would make the best location for your family’s summer vacation? Why? _________________________________________________________________ 5. In which city would you have the least probability of being snowed (or rained) out in

January? ______________________________________________________________ 6. Based on the daily average temperature, which city has the least probability of snow in

January? ______________________________________________________________ 7. How does the January snowfall/rainfall in Burlington compare to that in Chicago?

______________________________________________________________________ 8. Which city do you think would make the best location for your family’s winter vacation? Why? _________________________________________________________________ ______________________________________________________________________

City Average High/Low (in ˚F) Average Precipitation Average Number of

(snow or rain, in inches) Snow or Rain Days

January July January July January July

Anchorage, AK 21/8 65/52 0.79 1.71 8 12 Burlington, VT 25/8 81/60 1.82 3.65 14 12 Chicago, IL 29/13 84/63 1.53 3.66 11 10 Denver, CO 43/16 88/59 0.50 1.91 6 9 Houston, TX 61/40 93/72 3.29 3.29 11 10 Washington, D.C. 42/27 89/71 2.70 3.80 10 10

Sunflower Competition

1.2

Name _________________________________________ Date ___________________ The Hexford Gardening Society holds a sunflower competition every year. To reach the finals in the competition, the sunflower must reach a qualifying height, which is kept secret until the day of the competition. This year 20 people have entered the competition. (Hint: This year’s qualifying height is 70 inches.)

Name Inches P. Jones 1 R. Smith 4 A. Junor 8 L. Solby 5 D. Malik -2 R. Blundell 6 P. S. Foster 0 V. Lapwood -3 J. Vickers -4 F. Clark -8 T. Lindus -5 S. P. Carroll 2 K. Tanner -1 J. S. Camp 3 R. T. Formoy -6 L. Godfrey -7 J. Penney -10 M. Moore -9 K. L. Lilley -11 T. R. Foot 10

The chart on the left shows how much above or below the qualifying height each sunflower is.

1. Who has the shortest sunflower?

_______________________________________ 2. Who has the tallest sunflower?

_______________________________________ 3. Whose sunflower was exactly the qualifying

height? _________________________________ 4. What is the range of heights of sunflowers? _______________________________________ 5. Write the names of the competitors in ascending

order by the heights of their sunflowers.

_______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________

109

Page 21

1. mode 9, median 7, range 8 2. mode 2, median 3, range 5 3. mode 1, median 5/5, range 5 5/6 4. mode (none), median $1.90, range

$1.50

5. mode 65, median 72, range 26 6. Answers will vary.

Page 27

1. finding the most frequently occurring data.

2. finding the point that shows half the population above and half the population below.

3. finding the difference between the highest and lowest data.

4. finding the average of the data.

5. Christopher 18.8, Yolanda 16.7, Ryan 11.3, Sandy 18, Mark 17, Cody 10.7 6. mode 3 kg, median 2.5 kg, range 3

kg, mean 2.6 kg

Page 33

1. a. 1/2 b. 1/4 c. 1/8 d. 1/3 e. 1/6 2. 5 3. a. 5 b. 5 c. 10

Page 34

1. The pie chart tells how many students (30) watched cartoons, dramas,

and comedies: cartoons 1/3 or 10, dramas 1/6 or 5, comedies 1/2 or 15. 2. a. 14 b. 7 c. 28 3.

Page 41

1. 25% 2. 62.5% 3. 12.5% 4. transportation $35, accommodations $87.50, meals $17.50 5. a. $1,050 b. $2,625 c. $525 6. $4,200 saved 10 magazines 20 saved and spent 10 movies 5 candy 5

Answer Key

Student Pages

Page 95

1.

2. Answers will vary. 3.

If Arthur takes a green marble, there will be only 5 green left, along with the 4 red. If he takes a red marble, there will be only 3 red ones left, along with the 6 green.

Page 103

1. Anchorage

2. Houston gets twice as much rain as Denver in the same amount of time. 3. Anchorage—clothes for cooler

climate; Washington—clothes for warmer climate.

4. Answers will vary. 5. Denver

6. Houston

7. They have similar amounts of snow or rain in a similar amount of time.

• • • • • • • • • Collect, Organize, Represent,

and Interpret Your Data

Facts to Know

Data is all around you—in the classroom, on the playing field, at home, in every store, and many other places as well.

Collecting Data

• Use tally sheets, record sheets, or lists of data to record your information.

• Use almanacs, field guides, encyclopedias, or textbooks to find data on history or science.

• Use magazines, newspapers, or television news programs to find up-to-the-minute data about daily life.

Data Ideas

• passing percentages • calories taken in/expended • student food preferences • hitting/baseball • basketball shooting scored • time expended on . . . • grades/scores • heights or weights • comparative prices • store sales

Organizing Data

• Use tables and charts to group your data according to size, time periods, amounts, or some other numerical pattern.

Representing Data

• Choose the best type of graph to represent your data in a clear, visual, and effective way. Bar Graph compares data in numerical chunks

Circle Graph shows percentages of 100; parts of a whole

Line Graph compares change over a period of time

Pictograph symbols used to compare data

Histogram compares data in varying intervals

Double Bar Graph compares sets of related data

Multiple-line Graph compares how two or more related sets of data change over a period of time

Scattergram shows how pieces of data are related

Interpreting Data

• Use the measures of central tendency to determine various averages for sets of data. Mode—most frequently occurring number

Median—the middle number in a set of data arranged from least to greatest Mean—the sum of the values divided by the number of values

• Look for the trend lineor line of best fit.

• Use interpolationto find an unknown value within or between known pieces of data. • Use extrapolationto find data beyond the values listed in a set of data.

• Look for positive or negative correlationto determine if two sets of data are actually related to each other.

Recognizing Misleading Statistics

• Study graphs to determine if they are truncated or designed to distort data.

• • • • • • • • • • • • Collecting and Recording

Your Own Data

6

Practice

Directions: This bar graph illustrates the results of one 6th grade class survey of favorite exercises. Use the information on page 25 and the graph to answer these questions.

1. Which exercise was the most favorite? ________________________________________________ 2. Which two exercises together were as popular as skateboarding? ___________________________ 3. How many students were surveyed altogether? _________________________________________ 4. What percentage of the total did not do any exercise? ____________________________________ 5. Fill in the circle graph above with the same information. The lines are already drawn for you. Directions: Write down an estimate of the number of

hours you spent watching television in the last seven days. Round each number off to the nearest half-hour. Use the line graph below to illustrate your findings.

Then do the following activities.

1. Describe how your television habits changed over time, the course of one week. Explain why some days had more or less hours than others.

__________________________________________ __________________________________________ 2. Make this a multiple-line graph by recording your

television watching for another seven days. Compare your results. Are the patterns similar or is there a large difference? ____________________________ Numb er of Hours 5 4 3 2 1 0 1st 2nd 3rd 4th 5th 6th 7th Day

Television Viewing Time

Favorite Exercises

Numb er of Students Type of Excercise 14 12 10 8 6 4 2 0 W alking Running _Aer obics Skat eb o ar ding Cheerleading

52 50 48 46 44 42 40 38 36 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 _{60 61 62 63 64 65 66 67 68 69 70 71}

Height (in inches)

• • • • • • • • • • • • • • • Correctly Interpreting

Your Own Data

Both the bar graph and the scattergram are misleading and can lead to misunderstanding the data. National League Home Run

Leader Totals 1965–1974

6th Period History Grades

Gr ade (%) Numb er of Home Runs 100 90 80 70 60 50 40 30 20 10 0

Directions: Use the information on page 25 and your careful examination of the graphs to answer these questions.

1. The graph makes it look as if the 1965 leader hit twice as many home runs as the 1966 leader. What is the actual difference? _______________________________________________________ 2. The information on the home run scale is truncated. It begins with 36 home runs. How should

the graph have been arranged? ______________________________________________________ 3. Why do you think the scale was truncated? ____________________________________________ 4. Is there likely to be any relationship between height and history grades? _____________________ 5. Is there any trend line on the scattergram? _____________________________________________

Extension

• Survey the height (in inches) of 20 or more students.

• Survey each student’s arm span from fingertip to fingertip (to the nearest inch). • Record each student’s information on a record sheet.

• Create a scattergram and graph the data on it (a dot for each individual). Use the vertical axis for the height and the horizontal axis for the arm span.

• Draw a trend line on your scattergram.

• Interpret your data by answering the following questions: What is the correlation between arm span and height? Why is there a correlation between arm span and height?

• • • • • • • • • • • Analyze and Interpret Data

5

How to

Facts to Know

Here are some special tools for analyzing and interpreting the meaning of data, which has been organized into tables or plotted on a graph.

Trends

• A trendindicates the direction of the data. A trend lineis often drawn within a set of points on a scattergram or graph to determine the direction of the data. A trend line is sometimes called a line of best fit. It will plot the general direction of a set of data.

• The trend lines in the graphs below indicate that sales of scooters increased and sales of skateboards declined in this store during an eight-month period.

Sales of Scooters and Skateboards at the A-to-Z Sports Emporium

Correlation

• Correlationis an assessment of two pieces of data to determine how closely they are related or if

they are related. A correlation between two sets of data may be weak or strong, depending on the data.

• Positive correlationindicates that an increase in one set of data leads to an increase in a second

set of data.

• Negative correlationindicates that an increase in one set of data leads to decrease in another set of

data.

The graphs above indicate a strong negative correlation between the sales of scooters and skateboards in this store.

Extrapolation

• Use extrapolationto estimate or predict additional unknown data based on the trend of data you already know. Use the trend line on a graph to predict which data would probably come next. On the scooter graph, you can extrapolate that September’s sales will probably continue to rise.

Interpolation

• Use interpolationto estimate a probable value for an unknown piece of data falling between two pieces of data. Use the trend line to make this estimate.

Scooters Skateboards Month Month 20 18 16 14 12 10 8 6 4 2 0 Ja n . Fe b. Mar . Apr .

May _June July Aug. Tren dLi ne 20 18 16 14 12 10 8 6 4 2 0 Ja n . Fe b. Mar . Apr .

May _June July Aug.

Tren d Line Numb er of S c o ot ers Numb er of S c o ot ers

• • • • • • • • • • • • • • • • • • • • • • Answer Key

–

4

x

2

m

48 is more representative. Median: 46

Yes, it’s about in the middle of the values.

4. (31, 37, 39, 40, 40, 47, 47, 47, 48, 49, 49, 49, 61, 70)

Mode: 47 and 49

Yes, 47 is near the center. 49 is less representative because it is nearer to the end of the series. Median: 47

Yes, it is representative because it is in the center and the same as one mode.

Page 19

1. Total: 6,988 Divide by: 10 Mean: 698.8 (699)

Yes, it is representative because most of the numbers are 600s and 700s.

2. Total: 65 Divide by: 9 Mean: 7.2 (7)

No, the number of moons is very variable.

3. Total: 277 Divide by: 14 Mean: 19.8 (20)

Yes, many of the numbers are near 20.

4. Total: 1,113 Divide by: 14 Mean: 79.5 (80)

Yes, it is relatively representative of the numbers; a good average. 5. Total: 2,595

Divide by: 12 Mean: 216.3 (216)

Yes, many of the numbers are in or near the low 200s.

6. Total: 112 Divide by: 16 Mean: 7

Yes, it matches the mode and is near the center between 2 and 12. Page 20

1. Mode: 13 Median: 13 Mean: 9.6 (10)

Most representative: mode and median

Reason: They reflect the values best and are midway between high and low values.

2. Mode: 23 Median: 23 Mean: 23.3 (23) Most representative: 23 Reason: They are all the same. 3. Mode: 8 Median: 8

Mean: 8.3 (8)

Most representative: all Reason: They all are the same value.

4. Mode: 46 Median: 49 Mean: 51.9 (52)

Most representative: mean and median

Reason: They are closer to the center of the numbers in terms of value.

5. Mode: 23 Median: 29.5 Mean: 32.2 (32)

Most representative: median and mean

Reason: The mode is too near the first values; The others are representative of the numbers. Page 22 1. 5 to 10 hrs. 2. 1 to 3 hrs. 3. yes 4. strong 5. positive 6. (trend line on graph) Page 23 1. 7 shots 2. 2 shots 3. yes 4. strong 5. negative

6. (trend line on graph) 7. 7 or 8 shots

8. (trend line on graph) 9. weak correlation 10. strong 11. likely Page 24 1. Page 26 1. skateboarding 4. 16.7% (17%) 2. aerobics and 5. biking; cheerleading and walking 3. 60 Page 27 1. 8

2. It should have shown the entire scale, if possible.

3. There was not enough space. 4. no

5. no

Extension: Answers will vary.

Page 28 1. (0, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 12) 2. 7 students 3. 1 student 4. 1 student 5. (0, 1, 12) 6. 7, 9 7. 7.5 8. 7 (7.1) 9. Yes

10. Yes. All of the measures are similar and close in value.

Extension: Answers will vary.

Page 30 1. 6

2. ABCD BACD CABD DABC ABDC BADC CADB DACB ACBD BCAD CBAD DBCA ACDB BCDA CBDA DBAC ADCB BDAC CDBA DCAB ADBC BDCA CDAB DCBA 3. 4! = 4 x 3 x 2 x 1; 24 4. 5! = 5 x 4 x 3 x 2 x 1; 120 5. 6! = 6 x 5 x 4 x 3 x 2 x 1; 720 6. 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1; 5,040 7. 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1; 3,628,800

Practice 22

Tables, Plots, and Pictographs

Pets Tally Frequency

Cat //////// 8 Dog //////////// Snake // Bird /// Mouse /// Hamster //// Fish ////// Other /// This line plot illustrates a survey of hours spent

during one week on computer generated games by 30 sixth grade students in one classroom. Study the plot and answer the questions below.

This frequency table illustrates a survey of pets owned by sixth grade students in one classroom. Study the table, complete the frequency totals, and answer the questions below.

1. How many students did not spend any time playing computer games? ____________ 2. How many students spent 3 hours a week

playing computer games? ____________ 3. How many students spent 5 hours playing

computer games? ____________

4. How many students spent 20 hours a week playing computer games? ____________ 5. How many students spent 10 hours a week

playing computer games? ____________ 6. How many students in the class spent 10

hours or more a week on games? ____________

7. How many students in the class spent less than 10 hours a week on games?

____________

8. How many students spent 13 hours a week on games? ____________

9. How many more dogs are owned than cats? ____________

10. What is the most frequently owned pet? ____________

11. What is the least frequently owned pet? ____________

12. How many more cats are owned than mice? ____________

13. What is the total number of pets owned by these students? ____________

14. How many four-legged animals are owned? ____________ 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 X X X 0 5 10 15

Hours Spent Weekly

Note: Each x represents one student.

Survey of Pets Owned by Sixth Grade Students

N u m b e r o f S tu d e n ts

26

Practice 23

This bar graph illustrates the speeds of several animals in miles per hour. Study the graph and answer the questions below.

1. How much faster is a lion than a cat? ___________________________________ 2. The bar graph makes it look as if the lion is

3 times faster than the cat. Why does it look like that? _______________________ 3. Is a cat 2 times as fast as an elephant?

___________________________________ 4. How much faster is a cat than an elephant?

___________________________________ 5. How much faster than a rabbit is a cheetah? ___________________________________ 6. How does the graph distort the data and

make it look as if the cheetah was 2 times as fast as a rabbit? ____________________ 7. How could the scale of the graph be

changed to make it less distorted?

___________________________________ Animal Speeds S p e e d i n M il e s P e r H o u r

Type of Animal Year

e le p h a n t h u m a n ra b b it c h e e ta h lio n z e b ra c a t 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 1 9 9 9 2 0 0 0 70 65 60 55 50 45 40 35 30 25 20

This line graph illustrates average income for a group of people over 7 years. Study the graph. Decide how the graph could be misinterpreted. Answers the questions below.

8. In which year did the average reach its highest point? ____________

9. In which year did the average reach its lowest point? ____________

10. How much more did the average person earn in 2000 than in 1999? ____________ 11. Why does the graph make it appear that

income tripled from 1999 to 2000? ____________

12. What is the difference between the highest yearly income and the lowest yearly income? _____