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Math 6 NOTESNameTypes of Graphs: Different Ways to Represent DataLine Graphs Line graphs are used to display continuous data. Line graphs can be useful in predicting futureevents when they show trends over time.Bar Graphs Bar graphs are used to displaycategories of data. A bar graph is one method ofcomparing data by using solidbars to represent uniquequantities.Histograms A special kind of bar graph that uses bars torepresent the frequency of numerical datathat have been organized into intervals. Because the intervals are all equal, all of thebars have the same width Because the intervals are continuous(connected; ongoing), there is no space between the bars.

Frequency Table Frequency tables show thenumber of pieces of data that fallwithin given intervals.Line Plot Line plots are diagrams that show the frequency of data on anumber line. An “x” is placed above a number on a number lineeach time that data value occurs.Stem and Leaf Plot

In a stem-and-leaf plot, the data are organized from least togreatest. The digits of the least place value form the leaves, and thenext place value digits form the stems.Circle Graph Circle graphs are used toshow a relationship of theparts to a whole. Percentages are used to showhow much of the whole eachcategory occupies.Box and Whisker Plot A box-and-whisker plot is a diagram that summarizes data bydividing it into four parts (quartiles). Box and whiskers show us the spread (range) and median (middle) of thedata.

NAME DATE PERIODStudy Guide and InterventionFrequency TablesA frequency table uses tally marks to show how many times each piece of data appears. If the datais numerical, the table should have a scale which includes the least and the greatest numbers. Also,each table should have an interval which separates the scale into equal parts.ATHLETIC SHOES The table showsPrices of Athletic Shoes ( )prices of 20 types of athletic shoesat a recent sidewalk sale. Make afrequency table and then determinehow many types are available forless than lly552323Frequency57323Step 2 Draw a table with three columns and label thecolumns Price, Tally, and Frequency.Step 3 Complete the table.Step 4 Two categories include prices less than 80. 40– 59 5 types 60– 79 7 typesSo, 5 7 or 12 types of shoes cost less than 80.Price( )40–5960–7980–99100–119120–139For Exercises 1 and 2, use the table below.Hours Spent Studyingfor Math Exam31210871811121038601582159121. Make a frequency table of the data.HoursTally552512Frequency2. Use your frequency table to determine how many students studied10 hours or more. Glencoe/McGraw-Hill67Mathematics: Applications and Concepts, Course 2Lesson 2–1Step 1 Choose an appropriate interval and scale for thedata. The scale should include the least price, 43,and the greatest price, 135.

NAME DATE PERIODPractice: Word ProblemsFrequency TablesFAVORITE COLORS For Questions 1–3, useHOLIDAYS For Questions 4–6, use thetable below. It shows the number ofholidays in each month of 2003.the table below. It shows the favoritecolors of the students in Mr. Swatzky’sclass.BYGPFavorite Colors ofMr. Swatzky’s StudentsR R O B Y G G PB B Y R O B R BB O Y B Y G G GY R R G2003 Holidays355544102652BYGB blue, R red, G green, Y yellow,1. Make a frequency table of the data.Favorite ColorTallyFrequency3. If one student changed his or her vote fromred to purple, what would be the favoritecolor of the fewest students?5. Make a frequency table of the data.Holidays Glencoe/McGraw-HillTally2. If one student changed his or her votefrom blue to yellow, what would be thefavorite color of most students?4. What is wrong with using theintervals 1–2, 3–4, and 5–6 torepresent the data in a frequencytable?6. What is the interval and scale of yourfrequency table from Question 5?Frequency69Mathematics: Applications and Concepts, Course 2Lesson 2–1O orange, P purple

NAME DATE PERIODEnrichmentNumber PatternsThe dot diagram below illustrates a number pattern.You can discover what number in the pattern comes next by drawing the nextfigure in the dot pattern. You can also use thinking with numbers. Try to seehow two consecutive numbers in the pattern are related.13 26 310 415 5It looks like the next number in the pattern is obtained by adding 6 to 15. Thenext number in the pattern is 21. You can check this by drawing the nextfigure in the dot pattern.Write the next two numbers in the number pattern for each dotdiagram.1.2.3. A staircase is being built from cubes. How many cubes will it take tomake a staircase 25 cubes high? Glencoe/McGraw-Hill76Mathematics: Applications and Concepts, Course 2

NAME DATE PERIODStudy Guide and InterventionLine PlotsA line plot is a diagram that shows the frequency of data on a number line.SHOE SIZE The table shows the shoe size of studentsin Mr. Kowa’s classroom. Make a line plot of thedata.Step 1 Draw a number line. Because the smallest size is 4 and the largestsize is 14, you can use a scale of 4 to 14 and an interval of 2.Step 2 Put an “ ” above the number that represents the shoe size of eachstudent. 41068Shoe Sizes10 6 4 65 11 10 106 9 6 87 11 7 145 10 6 10 1214Use the line plot in Example 1. Identify any clusters, gaps, oroutliers and analyze the data by using these values. What is therange of data?Many of the data cluster around 6 and 10. You could say that most of the shoe sizes are 6 or10. There is a gap between 11 and 14, so there are no shoe sizes in this range. The number14 appears removed from the rest of the data, so it would be considered an outlier. Thismeans that the shoe size of 14 is very large and is not representative of the whole data set.PETS For Exercises 1–3 use the table at the right thatshows the number of pets owned by different families.1. Make a line plot of the data.Number213183of Pets2012142. Identify any clusters, gaps, or outliers.3. What is the range of the data? Glencoe/McGraw-Hill77Mathematics: Applications and Concepts, Course 2Lesson 2–3The greatest shoe size is 14, and the smallest is 4. The range is 14 – 4 or 10.

NAME DATE PERIODPractice: Word ProblemsLine PlotsTELEVISION SETS For Exercises 1–6, use the table below. It shows thenumber of television sets owned by 30 different families.of TVs4 33 43 42 13 0020201. Make a line plot for the data.2. How many televisions do most familiesown?3. What is the greatest number oftelevisions owned by a family?4. What is the range of the data?5. Identify any clusters, gaps, or outliers,if any exist, and explain what theymean.6. Describe how the range of the datawould change if 5 were not part of thedata set. Glencoe/McGraw-Hill795Mathematics: Applications and Concepts, Course 2Lesson 2–322135Number1 23 22 21 33 4

NAME DATE PERIODStudy Guide and InterventionIn a stem-and-leaf plot, the data are organized from least to greatest. The digits of the least placevalue usually form the leaves, and the next place value digits form the stems.Make a stem-and-leaf plot of the data below. Thenfind the range, median, and mode of the data.42, 45, 37, 46, 35, 49, 47, 35, 45, 63, 45Order the data from least to greatest.Stem345635, 35, 37, 42, 45, 45, 45, 46, 47, 49, 63The least value is 35, and the greatest value is 63.So, the tens digits form the stems, and the onesdigits form the leaves.Leaf5 5 72 5 5 5 6 7 93range: greatest value least value 63 35 or 28median: middle value, or 45mode:most frequent value, or 456 3 63Make a stem-and-leaf plot for each set of data. Then find the range,median, and mode of the data.1. 15, 25, 16, 28, 1, 27, 16, 19, 282. 1, 2, 3, 2, 3, 1, 4, 2, 5, 7, 12, 11, 11, 3, 103. 3, 5, 1, 17, 11, 45, 174. 4, 7, 10, 5, 8, 12, 7, 6 Glencoe/McGraw-Hill87Mathematics: Applications and Concepts, Course 2Lesson X–52–5Stem-and-Leaf Plots

NAME DATE PERIODPractice: Word ProblemsStem-and-Leaf PlotsLesson 2–5ENDANGERED SPECIES For Exercises 1–6, use the table below. It showsthe number of endangered species in the U.S.Endangered Species in U.S.GroupNumber ofSpeciesGroupNumber hes1. Make a stem-and-leaf plot of the data.2. What group has the greatest number ofendangered species in the U.S.?3. What group has the least number ofendangered species in the U.S.?4. What is the range of the data?5. Use your stem-and-leaf plot todetermine the median and mode.6. How many groups have less than 30endangered species in the U.S.? Glencoe/McGraw-Hill8968Mathematics: Applications and Concepts, Course 2

NAME DATE PERIODStudy Guide and InterventionBar Graphs and Line GraphsA graph is a visual way to display data. A bar graph is used to compare data.A line graph is used to show how data changes over a period of time.Make a bar graph of the data. Comparethe number of students in jazz classwith the number in ballet class.Dance Class Attendance1210StudentsStep 1 Decide on the scale andinterval.Step 2 Label the horizontal andvertical axes.Step 3 Draw bars for each style.Step 4 Label the graph with atitle.About twice as many studentstake ballet as take jazz.Dance TapBalletJazz ModernStyleMake a line graph of the data. Thendescribe the change in Gwen’s allowancefrom 1998 to 2002.Gwen's AllowanceYear199719981999200020012002Amount ( )101515182025Decide on the scale and interval.0Label the horizontal and vertical axes.Draw and connect the points for each year.YearLabel the graph with a title.allowance did not change from 1998 to 1999 and then increased from 1999 to 2002.19919 7919 8920 9020 0200102Step 1Step 2Step 3Step 4Gwen’sAmount ( )Gwen’s Allowance262422201816141210Make the graph listed for each set of data.1. bar graph2. line graphRiding the BusStudentGetting Ready for SchoolTime (min)DayTime y3430372025PaulinaOmarUlariJacobAmita Glencoe/McGraw-Hill66Mathematics: Applications and Concepts, Course 1

NAME DATE PERIODPractice: SkillsBar Graphs and Line GraphsMake a bar graph for each set of data.1.Cars Made in 2000CountryCars le in America in 1630ColonyPeople (hundreds)MaineNew HampshireMassachusettsNew YorkVirginia459425Use the bar graph made in Exercise 1.3. Which country made the greatest number of cars?4. How does the number of cars made in Japan compare to the numbermade in Spain?For Exercises 5 and 6, make a line graph for each set of data.Yuba County, California6.Year Population rglades National ParkMonthRainfall (inches)JanuaryFebruaryMarchAprilMayJune22227107. POPULATION Refer to the graph made in Exercise 5. Describe the changein Yuba County’s population from 1990 to 2000.8. WEATHER Refer to the graph made in Exercise 6. Describe the change inthe amount of rainfall from January to June. Glencoe/McGraw-Hill67Mathematics: Applications and Concepts, Course 1Lesson 2–25.

NAME DATE PERIODStudy Guide and InterventionBar Graphs and HistogramsA bar graph is one method of comparing data by using solid bars to represent quantities. Ahistogram is a special kind of bar graph. It uses bars to represent the frequency of numericaldata that have been organized into intervals.StudentNumber ofSiblingsSueIsfuMargaritaAkira1632Number of SiblingsSIBLINGS Make a bar graph to display the data in the table below.76543210SiblingsSueIstu Margarita AkiraStep 1 Draw a horizontal and a vertical axis. Label the axes as shown. Add a title.Step 2 Draw a bar to represent each student. In this case, a bar is used to represent thenumber of siblings for each student.SIBLINGS The number of siblings of 17 students have beenorganized into a table. Make a histogram of the data.FrequencyNumber 0Siblings0–1 2–3 4–56–7Number of SiblingsStep 1 Draw and label horizontal and vertical axes. Add a title.Step 2 Draw a bar to represent the frequency of each interval.1. Make a bar graph for the data inthe table.Student2. Make a histogram for the data inthe table.Number ofFree ThrowsLuisLauraOpalGad Glencoe/McGraw-HillNumber ofFrequencyFree : Applications and Concepts, Course 2Lesson 2–7Student

NAME DATE PERIODPractice: Word ProblemsBar Graphs and HistogramsPUPPIES For Exercises 1 and 2, use theEARTH SCIENCE In Exercises 3–6, usetable below. It shows the results of asurvey in which students were askedwhat name they would most like togive a new pet puppy.the table below. It shows the highestwind speeds in 30 U.S. cities.Name VotesMax15Tiger5Lady13Shadow 10Molly9Buster21. Make a bar graph to display the data.(mph)60 81 5846 51 4951 54 512. Use your bar graph from Exercise 1.Compare the number of votes the nameShadow received to the number of votesthe name Tiger received.Favorite New Puppy Names3. Make a histogram of the data.4. What is the top wind speed of most ofthe cities?Highest Wind Speeds5. How many cities recorded wind speedsof 80 miles per hour or more? Glencoe/McGraw-HillSpeeds54 9146 7349 566. How many cities recorded their highestwind speeds at 60 miles per hour ormore?99Mathematics: Applications and Concepts, Course 2Lesson X–12–7Highest Wind52 75 60 80 5553 73 46 76 5357 58 56 47 65

NAME DATE PERIODStudy Guide and InterventionMisleading StatisticsGraphs can be misleading for many reasons: there is no title, the scale does not include 0; there areno labels on either axis; the intervals on a scale are not equal; or the size of the graphicsmisrepresents the data.WEEKLY CHORES The line graphs below show the total hours Salomonspent doing his chores one month. Which graph would be best touse to convince his parents he deserves a raise in his allowance?Explain.816714612Total (hours)Total (hours)Graph ASalomon's Weekly Chores543108624120123Graph BSalomon's Weekly Chores041Week234WeekHe should use graph A because it makes the total hours seem much larger.PROFITS For Exercises 1 and 2, use the graphs below. It shows acompany’s profits over a four-month period.Graph ACompany ProfitsGraph BCompany Profits 70,000ProfitsProfits 60,000 50,000 40,000 30,000 20,000 10,000 0Jan.Jan.Feb.Mar.Apr.Feb.Mar.Apr.MonthsMonths1. Which graph would be best to use to convince potential investors toinvest in this company?2. Why might the graph be misleading? Glencoe/McGraw-Hill102Mathematics: Applications and Concepts, Course 2

NAME DATE PERIODPractice: SkillsMisleading Statistics1. INCOME The bar graphs below show the total U.S. national income (nonfarm).Which graph could be misleading? 302015100'60'70Year'80'90'00YearGEOGRAPHY For Exercises 2–4, use theMiles of Shorelinetable that shows the miles of shorelinefor five states.StateLength ofShoreline (mi)Virginia3,315Maryland3,190Washington3,026North Carolina3,375Pennsylvania892. Find the mean, median, and mode of the data.3. Which measure of central tendency is misleading in describing the milesof shoreline for the states? Explain.4. Which measure of central tendency most accurately describes the data? Glencoe/McGraw-Hill103Mathematics: Applications and Concepts, Course 2Lesson X–22–8600Income in Billions ofCurrent DollarsIncome in Billions ofCurrent DollarsGraph BU.S. Nonfarm IncomeGraph AU.S. Nonfarm Income

Math 6 NOTES Name _ Types of Graphs: Different Ways to Represent Data Line Graphs Line graphs are used to display continuous data. Line graphs can be useful in predicting future events when they show trends over time. Bar Graphs Bar graphs are used to display categories of data.

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