1 Practice. Collecting and Working with Data

Transcription

1 1 Practice Collecting and Working with Data 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 ladybugs with the number of dots on the outer wings of each ladybug recorded. Record Sheet for Ladybug Dots (9, 13,, 13, 11, 9,, 13, 13, 7,, 13, 9, 7,, 13, 9, 1, 13, 13) Complete this frequency table for Ladybug Dots using the information from the record sheet. Dots Frequency. 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 Table of Loose Coins Pennies Nickels Dimes Quarters Half-dollars Frequency 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. Tally Sheet Sports Drama Sitcoms Movies Nature/Science Science Fiction Wrestling Other 6

2 1 Practice 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 6th grade boys 6th grade girls 7th grade boys 7th grade girls 8th grade boys 8th grade girls sprints relay long jump sit-ups pull-ups 1. Make a table to organize the data on the tally sheet.. Which of the six groups won the most medals? 3. Which of the three classes was probably the most athletic?. 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 Times ø 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? 1. Which numbers were rolled the most often? Why do you think this happened? Extension Roll two dice 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 1 members of your class. (Include yourself.) 7

3 1 Practice Organizing Data 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 1 Room 13 Room 1 Room 15 Room 16 Room 17 Room Create a table to organize this data both by day and by weekly totals.. What were the total absences for the week in the 7th grade? 3. Which homeroom had the fewest absences?. 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? 1. 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. 11. Create a table to organize this data. Snack Table Sales for Thursday 1. Which product was the best seller? apples juice 13. Which two products were the least colas popular? candy bars 1. Did the students mainly buy healthy snacks or sweets? chips 15. How many snacks were sold peanuts altogether? raisins 16. If every snack sold for $.5, how candy jellies much money was collected? 8

4 5 Practice Using Correlation,Extrapolation, and Interpolation A scattergram is made by plotting two sets of data as coordinate pairs on a graph. Students in 8th Grade 1. How long did the students with the best language arts grades (9 or above) read?. How long did the students with the lowest grades (3 or below) read? 3. Is there a correlation between hours read and grades in this class?. Is the correlation weak or strong? 5. Is the correlation positive or negative? Grade Percentage in Language Arts Trend Line Hours Spent Reading Weekly Number of Five-gallon Tubs of Ice Cream Consumed Ice Cream Sales at The Vanilla Express 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? 1. Using interpolation, make an estimate for the number of tubs consumed on the day the temperature was Using extrapolation, make an estimate for sales on the following days if the temperature pattern remains the same.

5 5 Practice Looking for Trends Directions: Use the scattergrams below and the information on page 1 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. Number of Shots Made Distance (meters) from the Basket 1. How many shots did the player make five feet from the basket?. How many shots did the player make 5 feet from the basket? 3. Is there a correlation between shots made and distance?. 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. Science Grade (%) Language Arts Grade (%) 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? 1. 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? 3

6 5 Practice Applying Data Analysis Directions: Use the scattergrams and the information from page 1 to complete the page. An 8th grader made a graph illustrating how many feet she ran in 15-second increments. 59 Sheila s Running Record 88 Distance Run (in meters) Time (in seconds) 1. Draw a trend line on the graph indicating the direction of the data.. How many meters did Sheila run in 3 seconds? 3. How many meters did Sheila run in 6 seconds?. Using interpolation, determine about how many meters Sheila had run in 5 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 1 seconds?

7 3 How to How to Interpret Pictographs, Histograms, and Special Graphs 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 pictograph uses 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 8th Grade Students fantasy science fiction humor romance true life mystery Key = 1 books Double-Bar Graph A double bar graph is 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 3-minute Programming Key = music KBIF KLAB KMAL KCLL KBBB = commercials Radio Station Number of Minutes 13 Multiple-line Graph A multiple-line graph compares 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 Number of Snacks Sun Mon. Week Two Week One Tues. Wed. Thurs. Fri. Sat. Histogram A histogram is 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. Per Square Mile Day of the Week U.S. Population Density ** *projected

8 3 Practice 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?. 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?. 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? 1. 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? 1 Number of States 6 Key = 5 years = 1 years Directions: This histogram illustrates the frequency of graduation rates in a recent year and the states where this frequency occurs. Public High School 7. How many states have between 81% and 9% of its students graduating? Graduation Rates 8. How many states have between 51% and 6% of its students graduating? 9. What percentage of students is graduating in 18 states? How many states are represented in all? About 65% of California s public high school 1 students graduate. In what frequency is California recorded on the graph? % 61-7% 71-8% 81-9% Percentage of Graduate Students

9 3 Practice Working with Double Bar Graphs A double-bar graph is 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. 6% 58% 56% 5% 5% 5% 8% 6% % % % Male/Female Attendance at Major Colleges UCLA Directions: Use the information on page 13 and this graph to answer these questions. NYU 1. What percentage of students at UCLA is male? What percentage is female?. 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?. 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. Points Scored Key = bulldogs = wildcats Key = male = female USC Michigan State Bulldogs/Wildcats Football Game 1 8. What was the Bulldogs best quarter? 6 9. What was the Wildcats best quarter? 1 1. How many total points did each team score in 1 the game? 11. Which team got better in the first three quarters? 1 1. How might a coach use this graph? 8 6 1st nd 3rd th 15 Yale Harvard UC Irvine Pepperdine

10 3 Practice Working with Multiple-line Graphs A multiple-line graph compares 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. Key Number of Pages Read Pages Read per Day for One Week = Alyssa = Greg Sun. Mon. Tues. Wed. Thurs. Fri. Sat. Day of the Week 1. How many pages did Greg read on Sunday?. How many pages did Alyssa read on Sunday? 3. How many pages did Greg read on Friday?. 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? 1. How many total pages did Alyssa read? 11. How many total pages did Greg read? 1. Which student was more consistent in doing the assigned reading? 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. Key Minutes of Piano Practice Each Week for Six Weeks Number of Pratice Minutes = Sarah = Catherine 1st nd 3rd th Week 5th 6th 13. How many minutes did Sarah practice the first week? 1. 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. 16

11 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. Graphing Terms The range is the difference between the least and the greatest values in a set of data. (,, 7, 8, 1, 1) 1 = 1 The range is 1. The scale is the set of values or numbers along the side of a graph. The interval is the regular difference between each unit on the scale. The interval is always the same between each unit of the scale. The axes are 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 graphs offer 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. How to Use and Interpret Bar, Circle, and Line Graphs Percentage of Land Use Land Use in the United States Farmland Meadows/ Pastures Forests/ Woodlands Permanent Crops Other Single Line Graphs Single line graphs are 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 1%. Labels, listing names and amounts, are written on the slices of the graph. Books Read by 6th Grade Students Number of Books Sept. Oct. Nov. Dec. Jan. Feb. Racial Distribution in U.S. Population 8% White 1% African American % Other 1% Native American 3% Asian 9

12 Practice Working with Single Bar Graphs This single bar graph shows the number of electoral votes for each of the 1 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 5 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 7 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?. How many electoral votes does Texas have? State 3. What is the interval between numbers on the scale?. 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 1 most populated states? 8. How many electoral votes are distributed among the remaining states and the District of Columbia? 9. Why would a candidate spend more time campaigning in California than in North Carolina? 1. How many more votes than these 1 states would be needed to win a presidential election? 11. Which two pairs of states have the same number of electoral votes as California? 1. Why did the intervals start with 1 votes? 13. What could be misleading about this graph? Number of Electoral Votes California Florida Illinois Michigan New Jersey New York North Carolina Ohio Pennsylvania Texas 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. Number of Fast Food Visits in One Week Name Frequency Name Frequency John 3 Freddy 5 Sherry 6 Elaine 1 Jimmy 1 Ginette Alex Harry 3 Marianne Hector 7 1

13 Practice Working with Circle Graphs 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?. 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?. Where would carbon, hydrogen, and sodium be included? 5. Which element makes up almost half of the earth s crust? Elements as a Percentage of the Earth s Crust 7% Oxygen 8% Silicon 9% Other 3.5% Calcium.5% Iron 8% Aluminum 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? 1. What body compound would have much of the hydrogen and oxygen? 11. Why is this type of graph so easy to use? Major Elements as a Percentage of the Human Body 65% Oxygen 18% Carbon 1% Hydrogen % Other % Calcium 3% Nitrogen Extension Survey 1 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 3% of the total. If one student prefers cheese, that is 1% of the total.) Create a circle graph illustrating the results of your survey. 11

14 Practice 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 Number of Hours Carlos Number of Hours Janet Mon. Tues. Wed. Thurs. Fri. Sat. Sun. Mon. Tues. Wed. Thurs. Fri. Sat. Sun. Days of the Week 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?. How many hours did Janet spend doing homework on Tuesday? 3. On which day did neither student do any homework?. 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 1 hours. He spent the following amounts of time on his scooter for the next six days: 3 hours, 1 1 hours, 1 hour, hours, 5 1 hours, and 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 singleline graph from this table. 1

15 x z m Answer Key 1. Dots Frequency pennies; 9 nickels; 15 dimes; quarters half dollars Answers will vary. 1. 6th grade boys 6th grade girls 7th grade boys 7th grade girls 8th grade boys 8th grade girls. 7th grade boys 3. 7th grade; The boys and girls won the most medals.. pull-ups; The fewest medals were awarded ,, 11, and 7; These combinations are the most common rolls. Answers will vary. 1.. Room 1 Room 13 Room 1 Room 15 Room 16 Room 17 Room 18 sprints Mon. Tues. Wed. Thurs. Fri Room 1. Wednesday 5. Monday and Friday 6. Answers will vary Room Room 1 and Room 16; There was at least one absence per day. relay long jump sit-ups pull-ups apples juice 6 colas 31 candy bar 33 chips peanuts 7 raisins 3 candy jellies candy jellies 13. apples and raisins 1. sweets $ New York There are more votes in California Illinois and Texas; New York and Ohio 1. All states have at least 1 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. oxygen and silicon 7. 15% 3. calcium and iron 8. 93%. other 9. Other 5. oxygen 1. water 11. It is visual and easy to read. Answers will vary hrs hrs. 3. Friday 8..5 hrs.. Carlos 5. Janet; Her work is done more regularly. Answers will vary. 1. years. years years. cans and bottles; 85 years / years 6. It shows how long it takes garbage to disintegrate. Answers will vary states 8. 8 states % 1. 5 states % % 13. Answers will vary. 1. 7% male; 53% female. 51% male; 9% female 3. 1% male; 59% female. USC and Yale 5. NYU 6. 1%; Students must be either male or female. 7. more females 8. nd quarter 9. 3rd quarter 1. Bulldogs 3; Wildcats Wildcats 1. To see how his team played as the game progresses. (Answers will vary.) 1. 3 pages. 5 pages pages. 7 pages 5. Wednesday 6. Monday 7. Alyssa pages 9. Tuesday, Friday, and Saturday 1. 1 pages pages 1. Alyssa minutes 1. 5 minutes minutes minutes 17. Catherine 18. better; She practiced more regularly. 1. (9, 1, 1, 16, 16, 19,, 3, 8) 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.. (7, 9, 1, 1, 11, 1, 1, 15, 18,, 1, 31, 38) Mode: 1, 1 No, the number 1 is too close to the first numbers. 1 is more representative. Median: 1 No, there are many greater numbers after (19, 5, 8, 8, 3,, 8, 8, 51, 57, 6, 7) Mode: 8, 8 No, 8 is too near the first numbers;

16 x z m Answer Key 8 is more representative. Median: 6 Yes, it s about in the middle of the values.. (31, 37, 39,,, 7, 7, 7, 8, 9, 9, 9, 61, 7) Mode: 7 and 9 Yes, 7 is near the center. 9 is less representative because it is nearer to the end of the series. Median: 7 Yes, it is representative because it is in the center and the same as one mode. Page Total: 6,988 Divide by: 1 Mean: (699) Yes, it is representative because most of the numbers are 6s and 7s.. Total: 65 Divide by: 9 Mean: 7. (7) No, the number of moons is very variable. 3. Total: 77 Divide by: 1 Mean: 19.8 () Yes, many of the numbers are near.. Total: 1,113 Divide by: 1 Mean: 79.5 (8) Yes, it is relatively representative of the numbers; a good average. 5. Total:,595 Divide by: 1 Mean: 16.3 (16) Yes, many of the numbers are in or near the low s. 6. Total: 11 Divide by: 16 Mean: 7 Yes, it matches the mode and is near the center between and 1. Page 1. Mode: 13 Median: 13 Mean: 9.6 (1) Most representative: mode and median Reason: They reflect the values best and are midway between high and low values.. Mode: 3 Median: 3 Mean: 3.3 (3) Most representative: 3 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.. Mode: 6 Median: 9 Mean: 51.9 (5) Most representative: mean and median Reason: They are closer to the center of the numbers in terms of value. 5. Mode: 3 Median: 9.5 Mean: 3. (3) Most representative: median and mean Reason: The mode is too near the first values; The others are representative of the numbers. Page 1. 5 to 1 hrs.. 1 to 3 hrs. 3. yes. strong 5. positive 6. (trend line on graph) Page shots. shots 3. yes. strong 5. negative 6. (trend line on graph) 7. 7 or 8 shots 8. (trend line on graph) 9. weak correlation 1. strong 11. likely Page 1. 7 Page 6 1. skateboarding. 16.7% (17%). aerobics and 5. biking; cheerleading and walking 3. 6 Page It should have shown the entire scale, if possible. 3. There was not enough space.. no 5. no Extension: Answers will vary. Page 8 1. (, 1, 3,,, 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, 1, 1, 1, 1, 1). 7 students 3. 1 student. 1 student 5. (, 1, 1) 6. 7, (7.1) 9. Yes 1. Yes. All of the measures are similar and close in value. Extension: Answers will vary. Page 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.! = x 3 x x 1;. 5! = 5 x x 3 x x 1; ! = 6 x 5 x x 3 x x 1; ! = 7 x 6 x 5 x x 3 x x 1; 5, 7. 1! = 1 x 9 x 8 x 7 x 6 x 5 x x 3 x x 1; 3,68,8

17 1 Calories Burned Per Hour Word Problems 1, Bar Graph Solving Word Problems with Data and Graphs Running Cross-Country Skiing Swimming Bicycling Tennis Walking Handball Type of Exercise Directions: Use the bar graph to answer these questions. 1. How many calories would you burn playing handball for one hour?. Approximately how many calories would you burn bicycling? 3. How many more calories would you lose running rather than playing tennis?. How many calories would you burn on a 1 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? Number of States Histogram State Population (1995) under 1 million 1 5 million 5 1 million Population over 1 million Directions: Use the histogram to answer these questions. 1. How many states have a population under a million? 11. How many states have a population over 1 million? 1. How many states have a population of 5 to 1 million? 13. What range of population is most common for the states? 1. 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? 1

18 Temperature Word Problems Multiple-Line Graph Monday Tuesday Daily Temperatures (High and Low) Wednesday Thursday Circle Graph Percentage of Body Weight Solving Word Problems with Graphs and Statistics Friday Saturday Day of the Week Sunday Directions: Use the multiple-line graph to answer these questions. 1. Which day had the highest temperature of the week?. Which day had the lowest temperature that week? 3. What was the usual difference between high and low temperatures during this week? 15 to? 5 to 3? 3 to?. On which day were the high and low temperatures exactly 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 7? 8. What was the average high temperature for the week? 9. What was the average low temperature for the week? 1. How does this kind of graph help you analyze the temperature data? Directions: Use the circle graph to answer these questions. Protein 17% Water 6% Fat 15% Other 3% Nitrogen 3% 11. Which component makes up the highest percentage of body weight? 1. 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? 1. 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?

19 ??? Answer Key 6. n + 9n + n= 1 1n = 1 n = 1 Daniel has 1 stamps. Bryan has stamps. George has 18 stamps. Page n + (n + 5) + (n + 3) = 93 3n + 8 = 93 n = 15 Fred is 15 years old. Mom is 38 years old. Dad is years old.. 3n + = 31 n = 3 The skateboard is $3. The scooter is $9. The bike is $ n + 6 = 3(n + 6) n = Jimmy is years old. Brother is 18 years old.. n + (n 5) + (n + ) + (n + 8) = 53 n + 5 = 53 n = 1 Jesse is 1 years old. Maybelle is 7 years old. Ellen is 1 years old. Jeanne is years old. 5. n + (n + 15) + (n 1) + (n + 3) = 18 n + 8 = 18 n = Joseph had $.. Elsa had $35.. Julian had $1.. Martha had $ n + n + n = 15 7n =15 n = 15 Melissa had $15.. Christina had $3.. Charmain had $ n + 3n + (3n 1) = 7 7n 1 = 7 n = 1 Kristin had $1.. Matthew had $36.. Joshua had $ n + (n + 8) + 3n + (n 5) = 63 6n + 3 = 63 n = 1 Andrew is 1 years old. Kenneth is 18 years old. Billy is 3 years old. Cameron is 5 years old. Page /7 or :7 /11 or :11 7/ or 7: 7/11 or 7:11. 5/8 or 5:8 5/13 or 5:13 8/5 or 8:5 8/13 or 8: /7 or 6:7 6/13 or 6:13 7/6 or 7:6 7/13 or 7:13. 6/1 or 6: /1 or 55: /1 or 16:1 7. 1,/1 or 1,:1 8. /1 or :1 9. 6/1 or 6: /1 or 365: /1 or 8:1 8 Page :3 :: n:18 n = 1 blocks. 5:3 :: n:6 n = 1 pages 3. 5:7 :: n:63 n = 5 minutes. 1:3 :: n:9 n = gallons 5. 17: :: n: n = 1, gallons 6. :3 :: 1:n n = 15 hours 7. 15:3 :: n: n = 1,16 lb. Page 1. 55:1 :: n:7 n = 385 miles. 18:1 :: n: n = 36 miles 3. 6:1 :: n:5.5 n = 33 minutes. :1 :: n:13.5 n = 3 hours 5.,,:1 :: n:8 n = 96,, tons 6.,98:n :: :1 n = 7.5 hr. 7. 1:9 :: n:.5 n = 5 miles 8. 16:1 :: n:5 n = 7 oz. Challenge: 86, sec.; 8,76 hr. Page calories. 65 calories 3. calories.,5 calories 5. handball and bicycling 6. 1,65 calories 7. bicycling and walking 8. 3-hr. walk 9. Answers will vary states states 1. 1 states to 5 million 1. Answers will vary. 15. California has the most. Wyoming has the least. 16. Answers will vary. Page 1. Friday. Thursday to. Monday 5. Wednesday and Friday 6. Tuesday and Saturday 7. Monday, Saturday, and Sunday or or 7 1. Answers will vary. 11. water 1. nitrogen 13. 3% 1. other category 15. 7% 16. Answers will vary. Page = -1 You owe $ = -8 8 below = -1 1 below par. -$1 + $75 = $5 $5 owed = -15 He needed 15 points to get to = -3 F (+)136 = difference (+)13 = -1 1 difference

20 Single Bar and Double Bar Graphs 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. Number of Years Life Spans of Animals dog cat camel mouse rabbit red fox chipmunk lion polar bear leopard giraffe pig opossum black bear Animals 1. Which animal on the graph has the longest life span?. Which four animals live about 1 years? 3. How many more years does a polar bear live than a black bear?. 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? 1. How much longer does a person live than a rabbit?

21 Single Bar and Double Bar Graphs Practice 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. 1 Popularity Survey: Soccer vs. Football Percentage of Students football soccer 3rd th 5th 6th 7th 8th Grade Level 1. What percentage of third grade boys preferred to play football?. 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?. 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? 3

22 Single Line and Double Line Graphs Practice 1 This single line graph illustrates the percentage of children in the general population from 195 until. Study the graph and use the information to answer the questions below. Population of Children in the U.S. 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. Average Heights of Children Percentage of Children Year 199 Height in Inches Boys Girls Age 1. In which year did children comprise 36% of the population?. In which years were only 6% of the population children? 3. What year saw the highest percentage of children?. 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 onefourth 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? 1. At which two ages are girls on average taller than boys? 11. At what age do boys average inches taller than girls? 1. 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? 1. At what age do boys catch up and pass girls?

23 Answer Key Page marbles. 16 marbles marbles. 55 marbles 5. 1,316 marbles marbles marbles 8. marbles 9. 5 marbles marbles marbles 1 marbles 1. marbles Page 5 1. addition 19,56 bases. subtraction 1,689 at bats 3. addition,19 home runs. division 177 hits 5. multiplication 3,98,5 tickets 6. subtraction 1,578 strike outs 7. division,8 groups 8. subtraction 39 walks 9. division 175 hits (17 R13) 1. division.6 or 6% Page 6 1. subtraction 37,36 people. subtraction 1,3 people 3. addition 13,118 fans. addition 35,9 fans 5. division 86 packages 6. division, packages 7. subtraction 8,538 fans 8. division 8,5 packages 9. multiplication 61,536 fans 1. multiplication 3,69,5 tickets Page /1 lb.. 1 5/1 lb. 3. 1/8 lb.. 1/1 lb lb. 6. 1/ feet /1 lb / feet 9. 6 cups /3 lb. Page ounces. 3/ ounces 3. 1/ ounces. 5 students 5. 1 students 6. 1/1 ounces /1 ounces /5 ounces /8 ounces / lb / ounces 1. 8 cups Page /8 inches. 3 3/ inches 3. 7/8 inches. 51 5/8 inches /8 inches / lb. 7. 1/ lb. 8. 1/6 inches /8 ounces 1. 3/8 inches Page inches. 5 1/5 inches 3. 1 prints. 8 prints inches inches /3 inches 8. 7 prints inches 1. 8 prints Page / feet. 9 5/6 feet / feet. 3 1/8 feet 5. 1/3 feet 6. 6 /5 times 7. 1 lengths /1 feet / feet /1 feet Page 1 1. $5.. $ $ $ $ $5. 7. $ $ $ $ $ $17.1 Page centimeters centimeters centimeters..89 centimeters 5..6 centimeters centimeters centimeters centimeters centimeters centimeters centimeters centimeters Page lb.. 1. ounces ounces. 1. candies lb ants ounces 8. $.3 9. $ lb. Page % 6. 8%. 7% 7. 6% 3. 75% 8. 67%. 6% 9. 7% 5. 75% 1. 8% Page $3.. $. 3. $1.3. $ $7. 6. $.8 7. $.8 8. $. 9. $18. $. 1. $5. $9.71 Page mi..,6.8 mi feet. 9.1 mi mi mi m.p.h. 8. 3,3.957 lb mi mi. Page m.p.h.. 5 m.p.h m.p.h.. 6 m.p.h m.p.h m.p.h m.p.h. 8. m.p.h. 9. m.p.h m.p.h. Page , feet. min. 3. 1, feet. 7,18 feet min. 6. 7,7 feet 7., feet min min. 1. 3, feet Page 1. $1. $1 3. $ $ $ $6 Page $1. -$ $ $ $ Page 1. polar bear. leopard/camel dog/cat 3. yr.. pig 5. 9 yr yr yr yr yr yr. Page %. 5th/8th 3. 6%. no 5. 5% 6. % Page the same 9. 1/ / /8/9 13. taller 1. 1 Page Frequency. 1 Cat 8 3. Dog 1. Snake 5. Bird Mouse Hamster 8. 1 Fish 6 9. Other 3 1. dog 11. snake Page m.p.h.. the scale starts at rather than 7

24 Interpreting Data 7.1 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 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 1/8 65/ Burlington, VT 5/8 81/ Chicago, IL 9/13 8/ Denver, CO 3/16 88/ Houston, TX 61/ 93/ Washington, D.C. /7 89/ 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?. 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.. 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? 13

25 Sunflower Competition 1. 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 people have entered the competition. (Hint: This year s qualifying height is 7 inches.) Name Inches P. Jones 1 R. Smith A. Junor 8 L. Solby 5 D. Malik - R. Blundell 6 P. S. Foster V. Lapwood - 3 J. Vickers - F. Clark - 8 T. Lindus - 5 S. P. Carroll K. Tanner - 1 J. S. Camp 3 R. T. Formoy - 6 L. Godfrey - 7 J. Penney - 1 M. Moore - 9 K. L. Lilley - 11 T. R. Foot 1 The chart on the left shows how much above or below the qualifying height each sunflower is. 1. Who has the shortest sunflower?. Who has the tallest sunflower? 3. Whose sunflower was exactly the qualifying height?. What is the range of heights of sunflowers? 5. Write the names of the competitors in ascending order by the heights of their sunflowers. 8

26 Answer Key Page 1 1. mode 9, median 7, range 8. mode, median 3, range 5 3. mode 1, median 5/5, range 5 5/6. mode (none), median $1.9, range $ mode 65, median 7, range 6 6. Answers will vary. Page 7 1. finding the most frequently occurring data.. finding the point that shows half the population above and half the population below. 3. finding the difference between the highest and lowest data.. finding the average of the data. 5. Christopher 18.8, Yolanda 16.7, Ryan 11.3, Sandy 18, Mark 17, Cody mode 3 kg, median.5 kg, range 3 kg, mean.6 kg Page a. 1/ b. 1/ c. 1/8 d. 1/3 e. 1/ a. 5 b. 5 c. 1 Student Pages Page 3 1. The pie chart tells how many students (3) watched cartoons, dramas, and comedies: cartoons 1/3 or 1, dramas 1/6 or 5, comedies 1/ or 15.. a. 1 b. 7 c movies 5 candy 5 saved 1 saved and spent 1 magazines Page %. 6.5% %. transportation $35, accommodations $87.5, meals $ a. $1,5 b. $,65 c. $55 6. $, 19

27 Answer Key Student Pages Page Answers will vary. 3. If Arthur takes a green marble, there will be only 5 green left, along with the red. If he takes a red marble, there will be only 3 red ones left, along with the 6 green. Page Anchorage. 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.. Answers will vary. 5. Denver 6. Houston 7. They have similar amounts of snow or rain in a similar amount of time. 8. Answers will vary. 11

28 6 How to 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 1; 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 Multiple-line Graph Scattergram compares sets of related data compares how two or more related sets of data change over a period of time 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 line or line of best fit. Use interpolation to find an unknown value within or between known pieces of data. Use extrapolation to find data beyond the values listed in a set of data. Look for positive or negative correlation to 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. Use common sense to determine if sets of data are related or accidentally have the same pattern. 5

29 6 Practice Collecting and Recording Your Own Data Directions: This bar graph illustrates the results of one 6th grade class survey of favorite exercises. Use the information on page 5 and the graph to answer these questions. Favorite Exercises Number of Students Walking Running Aerobics Skateboarding Cheerleading Biking Other None Type of Excercise 1. Which exercise was the most favorite?. Which two exercises together were as popular as skateboarding? 3. How many students were surveyed altogether?. 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.. 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? 6 Number of Hours Television Viewing Time st nd 3rd th 5th 6th 7th Day

30 6 Practice Correctly Interpreting Your Own Data Both the bar graph and the scattergram are misleading and can lead to misunderstanding the data. Number of Home Runs National League Home Run Leader Totals Year Grade (%) th Period History Grades Height (in inches) Directions: Use the information on page 5 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?. 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?. 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 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? 7

31 5 How to Analyze and Interpret Data 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 trend indicates the direction of the data. A trend line is 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 Number of Scooters Scooters Trend Line Jan. Feb. Mar. Apr. May June July Aug. Month Correlation Correlation is 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 correlation indicates that an increase in one set of data leads to an increase in a second set of data. Negative correlation indicates 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 extrapolation to 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 interpolation to estimate a probable value for an unknown piece of data falling between two pieces of data. Use the trend line to make this estimate. 1 Number of Scooters Skateboards Trend Line Jan. Feb. Mar. Apr. May June July Aug. Month

32 x z m Answer Key 8 is more representative. Median: 6 Yes, it s about in the middle of the values.. (31, 37, 39,,, 7, 7, 7, 8, 9, 9, 9, 61, 7) Mode: 7 and 9 Yes, 7 is near the center. 9 is less representative because it is nearer to the end of the series. Median: 7 Yes, it is representative because it is in the center and the same as one mode. Page Total: 6,988 Divide by: 1 Mean: (699) Yes, it is representative because most of the numbers are 6s and 7s.. Total: 65 Divide by: 9 Mean: 7. (7) No, the number of moons is very variable. 3. Total: 77 Divide by: 1 Mean: 19.8 () Yes, many of the numbers are near.. Total: 1,113 Divide by: 1 Mean: 79.5 (8) Yes, it is relatively representative of the numbers; a good average. 5. Total:,595 Divide by: 1 Mean: 16.3 (16) Yes, many of the numbers are in or near the low s. 6. Total: 11 Divide by: 16 Mean: 7 Yes, it matches the mode and is near the center between and 1. Page 1. Mode: 13 Median: 13 Mean: 9.6 (1) Most representative: mode and median Reason: They reflect the values best and are midway between high and low values.. Mode: 3 Median: 3 Mean: 3.3 (3) Most representative: 3 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.. Mode: 6 Median: 9 Mean: 51.9 (5) Most representative: mean and median Reason: They are closer to the center of the numbers in terms of value. 5. Mode: 3 Median: 9.5 Mean: 3. (3) Most representative: median and mean Reason: The mode is too near the first values; The others are representative of the numbers. Page 1. 5 to 1 hrs.. 1 to 3 hrs. 3. yes. strong 5. positive 6. (trend line on graph) Page shots. shots 3. yes. strong 5. negative 6. (trend line on graph) 7. 7 or 8 shots 8. (trend line on graph) 9. weak correlation 1. strong 11. likely Page 1. 7 Page 6 1. skateboarding. 16.7% (17%). aerobics and 5. biking; cheerleading and walking 3. 6 Page It should have shown the entire scale, if possible. 3. There was not enough space.. no 5. no Extension: Answers will vary. Page 8 1. (, 1, 3,,, 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, 1, 1, 1, 1, 1). 7 students 3. 1 student. 1 student 5. (, 1, 1) 6. 7, (7.1) 9. Yes 1. Yes. All of the measures are similar and close in value. Extension: Answers will vary. Page 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.! = x 3 x x 1;. 5! = 5 x x 3 x x 1; ! = 6 x 5 x x 3 x x 1; ! = 7 x 6 x 5 x x 3 x x 1; 5, 7. 1! = 1 x 9 x 8 x 7 x 6 x 5 x x 3 x x 1; 3,68,8

33 Tables, Plots, and Pictographs Practice This line plot illustrates a survey of hours spent during one week on computer generated games by 3 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. Number of Students X X X X X X XX X X XXX X X XX X X X X X X X X X X X X Hours Spent Weekly Note: Each x represents one student. Survey of Pets Owned by Sixth Grade Students Pets Tally Frequency Cat //////// 8 Dog //////////// Snake // Bird /// Mouse /// 1. How many students did not spend any time playing computer games?. How many students spent 3 hours a week playing computer games? 3. How many students spent 5 hours playing computer games?. How many students spent hours a week playing computer games? 5. How many students spent 1 hours a week playing computer games? 6. How many students in the class spent 1 hours or more a week on games? 7. How many students in the class spent less than 1 hours a week on games? 8. How many students spent 13 hours a week on games? Hamster //// Fish ////// Other /// 9. How many more dogs are owned than cats? 1. What is the most frequently owned pet? 11. What is the least frequently owned pet? 1. How many more cats are owned than mice? 13. What is the total number of pets owned by these students? 1. How many four-legged animals are owned? 5

34 Problems Involving Distorted or Misleading Data Practice 3 This bar graph illustrates the speeds of several animals in miles per hour. Study the graph and answer the questions below. 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. Speed in Miles Per Hour elephant Animal Speeds human rabbit cheetah lion zebra Type of Animal cat Thousands of Dollars Average Income During a Seven Year Span Year How much faster is a lion than a cat?. 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 times as fast as an elephant?. 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 times as fast as a rabbit? 7. How could the scale of the graph be changed to make it less distorted? 8. In which year did the average reach its highest point? 9. In which year did the average reach its lowest point? 1. How much more did the average person earn in than in 1999? 11. Why does the graph make it appear that income tripled from 1999 to? 1. What is the difference between the highest yearly income and the lowest yearly income? 13. How is the graph distorted or misleading? 1. How could the distortion be corrected? 6

35 Answer Key Page marbles. 16 marbles marbles. 55 marbles 5. 1,316 marbles marbles marbles 8. marbles 9. 5 marbles marbles marbles 1 marbles 1. marbles Page 5 1. addition 19,56 bases. subtraction 1,689 at bats 3. addition,19 home runs. division 177 hits 5. multiplication 3,98,5 tickets 6. subtraction 1,578 strike outs 7. division,8 groups 8. subtraction 39 walks 9. division 175 hits (17 R13) 1. division.6 or 6% Page 6 1. subtraction 37,36 people. subtraction 1,3 people 3. addition 13,118 fans. addition 35,9 fans 5. division 86 packages 6. division, packages 7. subtraction 8,538 fans 8. division 8,5 packages 9. multiplication 61,536 fans 1. multiplication 3,69,5 tickets Page /1 lb.. 1 5/1 lb. 3. 1/8 lb.. 1/1 lb lb. 6. 1/ feet /1 lb / feet 9. 6 cups /3 lb. Page ounces. 3/ ounces 3. 1/ ounces. 5 students 5. 1 students 6. 1/1 ounces /1 ounces /5 ounces /8 ounces / lb / ounces 1. 8 cups Page /8 inches. 3 3/ inches 3. 7/8 inches. 51 5/8 inches /8 inches / lb. 7. 1/ lb. 8. 1/6 inches /8 ounces 1. 3/8 inches Page inches. 5 1/5 inches 3. 1 prints. 8 prints inches inches /3 inches 8. 7 prints inches 1. 8 prints Page / feet. 9 5/6 feet / feet. 3 1/8 feet 5. 1/3 feet 6. 6 /5 times 7. 1 lengths /1 feet / feet /1 feet Page 1 1. $5.. $ $ $ $ $5. 7. $ $ $ $ $ $17.1 Page centimeters centimeters centimeters..89 centimeters 5..6 centimeters centimeters centimeters centimeters centimeters centimeters centimeters centimeters Page lb.. 1. ounces ounces. 1. candies lb ants ounces 8. $.3 9. $ lb. Page % 6. 8%. 7% 7. 6% 3. 75% 8. 67%. 6% 9. 7% 5. 75% 1. 8% Page $3.. $. 3. $1.3. $ $7. 6. $.8 7. $.8 8. $. 9. $18. $. 1. $5. $9.71 Page mi..,6.8 mi feet. 9.1 mi mi mi m.p.h. 8. 3,3.957 lb mi mi. Page m.p.h.. 5 m.p.h m.p.h.. 6 m.p.h m.p.h m.p.h m.p.h. 8. m.p.h. 9. m.p.h m.p.h. Page , feet. min. 3. 1, feet. 7,18 feet min. 6. 7,7 feet 7., feet min min. 1. 3, feet Page 1. $1. $1 3. $ $ $ $6 Page $1. -$ $ $ $ Page 1. polar bear. leopard/camel dog/cat 3. yr.. pig 5. 9 yr yr yr yr yr yr. Page %. 5th/8th 3. 6%. no 5. 5% 6. % Page the same 9. 1/ / /8/9 13. taller 1. 1 Page Frequency. 1 Cat 8 3. Dog 1. Snake 5. Bird Mouse Hamster 8. 1 Fish 6 9. Other 3 1. dog 11. snake Page m.p.h.. the scale starts at rather than 7

36 Answer Key (cont.) 3. no. 5 m.p.h. 5. m.p.h. 6. the scale doesn t go to 7 7. start at /use a different scale thousand dollars 11. the scale is distorted, starts at 1. 5 thousand dollars 13. scale starts at thousand dollars 1. starts at and go to 7 Page feet 8, feet. 88 feet,7 feet feet 8,1 feet. 6 feet, feet 5. 3 yd. 6, yd feet,5 feet m 7,3 m yd. 7,15 yd. Page 8 1. feet. 5 feet. 3. 1,35 feet. feet 5.,171 feet 6. 1,155 feet feet feet feet 1. 8 feet Page 9 1. C = πd C = 3.1 x centimeters. C = πd C = 3.1 x 3 7. centimeters 3. C = πr C = x 3.1 x 1.56 centimeters. C = πd C = 3.1 x 6.8 centimeters 5. C = πd C = 3.1 x centimeters 6. C = πr C = x 3.1 x inches 7. C = πr C = x 3.1 x 1.56 inches 8. C = πr C = x 3.1 x centimeters Page 3 1. A = πr A = 3 x 3 x cm. A = πr A = 3.1 x 8 x 8.96 inches 3. A = πr A = 3.1 x 6 x cm. A = πr A = 3.1 x 7 x millimeters 5. A = πr A = 3.1 x 9 x millimeters 6. A = πr A = 3.1 x x 1.56 feet 7. A = πr A = 3.1 x x 5. feet 8. A = πr A = 3.1 x.5 x cm 9. A = πr A = 3.1 x 3.5 x cm 1. A = πr A = 3.1 x 1.15 x cm Page inches 3. 7 cm inches 3. 8 inches inches cubic puzzles cubic magnifying glasses 8. 1, cm 3 blocks 9. 1 games 1. 1,78 cubic puzzles Page library. town hall 3. gas station. (-11, 1) 5. (, -) 6. (-5, -9) 7. park 8. (-1, -7) 9. (-9, 5) 1. general store 11. drug store 1. III 13. I 1. II Page /1 6. 3/. /15 7. /3 3. 9/5 8. 8/5. 11/16 9. /5 5. 1/ 1. 1/7 Page n = 35 1 n = n = 1 n = n 9 = 61 n = n = 53 n = n = 3 n = 6. n/ = 1 n = 8 7. n x 1 = 96 n = 8 8. n/8 = 11 n = n x 19 = 19 n = 1 1. /n = 6 n = 7 Page : or 5/. :5 or /5 3. :5 or /5. 5: or 5/ 5. 3:5 or 3/5 6. 5:3 or 5/3 7. :3 or /3 8. 3: or 3/ 9. :3 or /3 1. 3: or 3/ 11. 7:5 or 7/5 1. 5:7 or 5/ :7 or 3/7 1. 7:3 or 7/ : or 1/ or 6:1 or 6/1 16. :1 or /1 or 1:6 or 1/ :7 or 3/ :3 or 7/3 Page : :: :n n = 8 feet. 1: :: 5:n n = 5 feet 3. 3:15 :: 9:n n = 5 m. :1 :: 1:n n = 5 stories 5. 3:1 :: 33:n n = 11 yd. 6. 3:1 :: 15:n n = 5 m 7. 5:3 :: n:3 n = 5 inches 8. 7: :: :n or :7 :: n: n = 1 inches Page (58.67) (8.8) 3. 1, (89.) (13.8) (5.5) (13.6) (6.8) Page (6, 7, 8, 9, 5, 5, 5, 5, 53, 5, 56) 5 5. (7, 9, 55, 56, 57, 58, 59, 59, 59, 6, 6, 61, 63) (57, 59, 59, 6, 61, 61, 63, 63, 65, 66) 59, 61, (7, 9, 9, 9, 51, 5, 53, 5, 55, 57, 59) (39,,,, 5, 8, 5, 55, 57, 57, 58, 6, 6, 61), 57, Page 1. C 6. C. D 7. B 3. B 8. D. A 9. B 5. A 1. D Page 1 1. B 6. A. D 7. C 3. C 8. A. A 9. B 5. D 1. C Page 1. A 6. B. B 7. D 3. C 8. C. B 9. A 5. D 1. D Page 3 1. C 6. B. C 7. A 3. B 8. D. D 9. B 5. D 1. C Page 1. C 6. A. C 7. C 3. A 8. B. B 9. D 5. D 1. C Page 5 1. C 6. C. A 7. A 3. B 8. B 8

37 Pie Chart Problems 7.3 Name Date 1. A group of 3 students was asked whether they like watching the dramas, cartoons, or comedies. This pie chart shows their responses. comedies dramas Explain how to read this pie chart. What information does it give? cartoons. Students in one class were asked what time they went to bed on a Friday night. Seven students said 11 o clock. a. How many students went to bed at 1 o clock? b. How many went at 9:3 P.M.? c. How many students are there in this class? 1 P.M. 11 P.M. 9:3 P.M. 3. Fifty students were asked how they spent their pocket money. Twenty students said they bought magazines, ten saved their money, five said they bought candy, five went to the movies, and ten said they saved some and spent some. Complete this pie chart to represent this information. 3

38 Answer Key Page 1 1. mode 9, median 7, range 8. mode, median 3, range 5 3. mode 1, median 5/5, range 5 5/6. mode (none), median $1.9, range $ mode 65, median 7, range 6 6. Answers will vary. Page 7 1. finding the most frequently occurring data.. finding the point that shows half the population above and half the population below. 3. finding the difference between the highest and lowest data.. finding the average of the data. 5. Christopher 18.8, Yolanda 16.7, Ryan 11.3, Sandy 18, Mark 17, Cody mode 3 kg, median.5 kg, range 3 kg, mean.6 kg Page a. 1/ b. 1/ c. 1/8 d. 1/3 e. 1/ a. 5 b. 5 c. 1 Student Pages Page 3 1. The pie chart tells how many students (3) watched cartoons, dramas, and comedies: cartoons 1/3 or 1, dramas 1/6 or 5, comedies 1/ or 15.. a. 1 b. 7 c movies 5 candy 5 saved 1 saved and spent 1 magazines Page %. 6.5% %. transportation $35, accommodations $87.5, meals $ a. $1,5 b. $,65 c. $55 6. $, 19

39 1 Real Life Recognizing and Working with Misleading Statistics Some graphs are designed to create a false impression about the differences between the data being illustrated. Other graphs can be misinterpreted. In both cases, it is often the scale of the graph, which creates the problem. Directions: Look at the graphs below. Then answer the questions and create new graphs to accurately reflect the data. Dollars $11 $1 $9 $8 $7 $6 Skateboard and Scooter Costs Speedo Electro The Blade Longboard Bigfoot Slick Wide Body Scoots Lazer Liner Type of Skateboard/Scooter 1. In looking at the graph, the Lazer Liner appears to be six times as expensive as Bigfoot. What is the actual difference in price?. Is Bigfoot twice as expensive as Scoots? What is the difference in price? 3. Why does the Electro look more than three times as expensive as The Blade? What is the actual difference in price?. What could be done to make the graph more accurately represent the differences between the prices of the boards and scooters? 5. Use a separate piece of graph paper to redesign this graph and make it reflect the real differences in prices. Height (in Feet) 1 ' 9' 8' 7' 6' 5' ' 3' ' Heights of Trees Black Cherry Pepper Tree Peach Plum Common Apple Crab Apple Sweetgum Magnolia Live Oak Pear Sweet Cherry Sycamore 6. Which three trees are 3 feet high? 7. Which three trees are feet high? 8. Why do the trees, which are feet high, seem twice as tall as the 3-foot trees? 9. Which four trees are 8 feet high? 1. Why do the 8-foot trees appear to be three times as tall as the -foot trees and six times as tall as the 3-foot trees? 11. Use a separate piece of graph paper to redesign this graph and make it reflect the real differences in heights. 5

40 6 Practice Applying the Measures of Central Tendency to Your Data A line plot has a scale along the horizontal reference line and each piece of data plotted above the appropriate number on the scale. A line plot will demonstrate the range of the data, the mode, and any outliners. Line Plot of Hours Spent Sleeping for 36 Eighth Graders 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 X X X X X X X Directions: Use the information on page 5 and the line plot to answer these questions. 1. Complete this list of per student hours slept using the line plot above: (, 1, 3,,, 5, 5, 5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,). How many students slept for nine hours? 3. How many students didn t sleep at all?. How many students slept three hours? 5. What are the three outliers in this set of data? (The pieces of data on the ends of the range of data.) 6. Which two hours are the modes of this data? 7. What is the median for all 36 students? 8. What is the mean for this data? 9. Are the mode, median, and mean close to each other? 1. Do you think these are valid statistics? Explain. Extension Survey each member of your class to determine how many hours they sleep on an average night to the nearest hour. Use a tally sheet to record your answers. Make a numerical list of the answers from least to greatest. Create a line plot like the one above to graph your results. List any outliers. Determine the mode. 8 Determine the median. Compute the mean. How close are the mode, median, and mean to each other? Do you think the statistics are valid and useful? Why or why not?

41 x z m Answer Key 8 is more representative. Median: 6 Yes, it s about in the middle of the values.. (31, 37, 39,,, 7, 7, 7, 8, 9, 9, 9, 61, 7) Mode: 7 and 9 Yes, 7 is near the center. 9 is less representative because it is nearer to the end of the series. Median: 7 Yes, it is representative because it is in the center and the same as one mode. Page Total: 6,988 Divide by: 1 Mean: (699) Yes, it is representative because most of the numbers are 6s and 7s.. Total: 65 Divide by: 9 Mean: 7. (7) No, the number of moons is very variable. 3. Total: 77 Divide by: 1 Mean: 19.8 () Yes, many of the numbers are near.. Total: 1,113 Divide by: 1 Mean: 79.5 (8) Yes, it is relatively representative of the numbers; a good average. 5. Total:,595 Divide by: 1 Mean: 16.3 (16) Yes, many of the numbers are in or near the low s. 6. Total: 11 Divide by: 16 Mean: 7 Yes, it matches the mode and is near the center between and 1. Page 1. Mode: 13 Median: 13 Mean: 9.6 (1) Most representative: mode and median Reason: They reflect the values best and are midway between high and low values.. Mode: 3 Median: 3 Mean: 3.3 (3) Most representative: 3 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.. Mode: 6 Median: 9 Mean: 51.9 (5) Most representative: mean and median Reason: They are closer to the center of the numbers in terms of value. 5. Mode: 3 Median: 9.5 Mean: 3. (3) Most representative: median and mean Reason: The mode is too near the first values; The others are representative of the numbers. Page 1. 5 to 1 hrs.. 1 to 3 hrs. 3. yes. strong 5. positive 6. (trend line on graph) Page shots. shots 3. yes. strong 5. negative 6. (trend line on graph) 7. 7 or 8 shots 8. (trend line on graph) 9. weak correlation 1. strong 11. likely Page 1. 7 Page 6 1. skateboarding. 16.7% (17%). aerobics and 5. biking; cheerleading and walking 3. 6 Page It should have shown the entire scale, if possible. 3. There was not enough space.. no 5. no Extension: Answers will vary. Page 8 1. (, 1, 3,,, 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, 1, 1, 1, 1, 1). 7 students 3. 1 student. 1 student 5. (, 1, 1) 6. 7, (7.1) 9. Yes 1. Yes. All of the measures are similar and close in value. Extension: Answers will vary. Page 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.! = x 3 x x 1;. 5! = 5 x x 3 x x 1; ! = 6 x 5 x x 3 x x 1; ! = 7 x 6 x 5 x x 3 x x 1; 5, 7. 1! = 1 x 9 x 8 x 7 x 6 x 5 x x 3 x x 1; 3,68,8

42 x z m Answer Key Page combinations. 1 combinations 3. outfits. 56 combinations 5. 1 possible combinations vanilla + chocolate; vanilla + strawberry; vanilla + peppermint; vanilla + peach; chocolate + strawberry; chocolate + peppermint; chocolate + peach; strawberry + peppermint; strawberry + peach; peppermint + peach 6. 1 possible combinations vanilla + chocolate + strawberry; vanilla + chocolate + peppermint; vanilla + chocolate + peach; vanilla + strawberry + peppermint; vanilla + strawberry + peach; vanilla + peppermint + peach; chocolate + strawberry + peppermint; chocolate + strawberry + peach; chocolate + peppermint + peach; strawberry + peppermint + peach possible combinations whistle + horn; whistle + ring; whistle + balloon; whistle + gun; whistle + car; horn + ring; horn + balloon; horn + gun; horn + car; ring + balloon; ring + gun; ring + car; balloon + gun; balloon + car; gun + car Page 3 1. H - T; 1/ ; 1/ ; 1/ ; /6 = 1/3 5. Red - Green - Blue - Black; 1/ 6. Red - Green - Blue - Black; / = 1/ 7. Red - Green - Blue - Black; 8. Red - Green - Blue - Black; 3/ 9. HH - TT - HT - TH; / = 1/ Pages 3 and 35 Answers will vary. Page Possible Rolls 6 - L1 D5 - L5 D1 - L D - L D - L3 D3 7 - L1 D6 - L6 D1 - L D5 - L5 D - L D3 - L3 D 8 - L D6 - L6 D - L5 D3 - L3 D5 - L D 9 - L3 D6 - L6 D3 - L5 D - L - D5 1 - L6 D - L D6 - L5 D L5 D6 - L6 D5 1 - L6 D6 Total /36 or.8%. /36 = 1/18 or 5.6% 5. /36 = 1/9 or 11.1% 6. 6/36 = 1/6 or 16.7% 7. /36 = 1/9 or 11.1% 8. 1/36 or.8% Page /5 x 1/3 = /15 or 13.3%. 17/ x /5 = 17/5 or 68% 3. /7 x 5/6 = 1/1 or 7.6%. 9/1 x 1/ = 9/ or 5% 5. 7/1 x /5 = 1/5 or 56% 6. 9/1 x /5 x /3 = 1/5 or 8% 7. /3 x 3/ x 9/1 = 9/ or 5% 8. 9/1 x 1/ x 1/3 = 3/ or 7.5% 9. 3/ x /3 x 1/ = 1/ or 5% Page A. 1/ B. 1/3 C. 1/ x 1/3 = 1/1 or 8.3%. A. /5 B. 1/ C. /5 x 1/ = 1/1 or 1% 3. A. /1 B. 1/9 C. /1 x 1/9 = 1/5 or.%. A. / B. 1/19 C. / x 1/19 = 1/19 or.5% 5. A. 1/8 B. /7 C. 1/8 x /7 = 1/8 or 3.6% Page 1. 13/6 or.% 1/6 or 1.7% 3/6 or 3.8%. /6 or.3% 17/6 or.8% 19/6 or 3.% 3. 1/6 or 16.7% /6 or 1 3 or 33.3% 3/6 or 1 or 5% /6 or 3 or 66.6%. 1/1 or 8.3% 1/1 or 1/6 or 16.7% 3/1or 1/ or 5% 5 1 or 1.7% 8 5. /5 or 1/13 or 7.7% 8/5 or /13 or 15.% 1/5 or 3/13 or 3.1% 16/5 or /13 or 3.8% 8/5 or /13 or 15.% 3/5 or 8/13 or 61.5% Page /1 = 7/. 1/1 = 3/5 3. 6/1 = 3/5. 5/1 = 9/ ,5 8. (trend line on graph) 9. weak 1. negative 11../3 min.; 1./5 min.;./15 min.; 3./1656 min. 1. no (in this survey) Page 1. 1/8 or 1.5%. 1/ or 5% 3. /8 or 1/ or 5%. /8 or 1/ or 5% 5. 1% 6. 1% 7. 1/ or 5% 8. 1/ or 5% Page 3 Answers will vary. 9. / or 1/ or 5% 1. / or 1/ or 5% 11. 3/ or 75% 1. 1/ or 5% 13. 1/ or 5% 1. / or 1/ or 5% 15. /8 or 1/ or 5% 16. 1/ or 5% Page 1. 1: or 1 in 7. 1:6 or 1 in 6. 3:1 or 3 to :1 or 5 to : or 1 in 9. 1:3 or 1 in 3. 1:1 or :1 or to :1 or 3 to :5 or 1 in :3 or 1 in :1 or 99 to :1,, or 3 in 1,, ,997:3 or 999,997 to 3 Page 5 1. $5. No; $5 3. The scale starts at $; $5. Start the scale at. 5. (student graph) 6. Peach, Plum, Crab Apple 7. Pepper Tree, Common Apple, Pear 8. The scale starts at ' instead of. 9. Black Cherry, Magnolia, Live Oak, Sycamore 1. The scale is truncated (starts at '). 11. (Graph by students.)