Lessons 6.4 and 6.5

1. Lessons 6.4 and 6.5 Bar Graphs Line Plots Frequency Tables Histograms

2. Learn to display and analyze data in bar graphs. Learn to organize data in line plots, frequency tables, and histograms.

3. Vocabulary bar graph double-bar graph frequency frequency table line plot histogram

4. A bar graph can be used to display and compare data. A bar graph displays data with vertical or horizontal bars.

5. Example 1: Reading a Bar Graph Use the bar graph to answer each question. Which biome in the graph has the least average summer temperature? Find the lowest bar. The coniferous forest has the least average summer temperature.

6. Example 1B: Reading a Bar Graph Use the bar graph to answer each question. Which biomes in the graph have an average summer temperature of 30C or greater? Find the bar or bars whose heights measure 30 or more than 30. The grassland and the rain forest have average summer temperatures of 30C or greater.

7. Tickets Sold Grade 6 Grade 7 Grade 8 310 215 285 White board practice: Use the data to make a bar graph.

8. Tickets Sold Grade 6 Grade 7 Grade 8 310 215 285 Tickets Sold Tickets Grade6 Grade 8 Grade 7 Grade White board practice: Solution Use the data to make a bar graph. Step 1:Find an appropriate scale and interval. The scale must include all of the data values. The interval separates the scale into equal parts. Step 2:Use the data to determine the lengths of the bars. Draw bars of equal width. The bars cannot touch. Step 3: Title the graph and label the axes.

9. A double-bar graph shows two sets of related data.

10. Club Memberships Club Art Music Science Boys 12 6 16 Girls 8 14 4 Example 2: Problem Solving Application Make a double-bar graph to compare the data in the table. Understand the Problem You are asked to use a graph to compare the data given in the table. You will need to use all of the information given.

11. Example 2 Continued Determine appropriate scales for both sets of data. Use the data to determine the lengths of the bars. Draw bars of equal width. Bars should be in pairs. Use a different color for boy memberships and girl memberships. Title the graph and label both axes. Include a key to show what each bar represents.

12. Club Memberships Club Band Chess Year Book Boys 9 14 16 Girls 11 7 15 White board practice: Make a double-bar graph to compare the data in the table. Understand the Problem You are asked to use a graph to compare the data given in the table. You will need to use all of the information given.

13. White board practice: Solution Determine appropriate scales for both sets of data. Use the data to determine the lengths of the bars. Draw bars of equal width. Bars should be in pairs. Use a different color for boy memberships and girl memberships. Title the graph and label both axes. Include a key to show what each bar represents. Club Memberships Memberships Club

14. The frequency of a data value is the number of times it occurs. A frequency table tells the number of times an event, category, or group occurs.

15. whorl loop whorl loop arch arch loop whorl loop arch whorl arch arch whorl arch loop Example 3: Using Tally Marks to Make a Frequency Table Students in Mr. Ray’s class recorded their fingerprint patterns. Which type of pattern do most students in Mr. Ray’s class have? Make a table to organize the data.

16. whorl loop whorl loop arch arch loop whorl loop arch whorl arch arch whorl arch loop Number of Fingerprint Patterns Whorl Arch Loop Students in Mr. Ray’s class recorded their fingerprint patterns. Which type of pattern do more students in Mr. Ray’s class have? Step 1: Make a column for each fingerprint pattern. Step 2: For each fingerprint, make a tally mark in the appropriate column. Most students in Mr. Ray’s class have an arch fingerprint. l l l l l l l l l l l l l

17. whorl loop whorl loop arch whorl loop whorl loop whorl whorl arch arch whorl arch loop White board practice: Students in Ms. Gracie’s class recorded their fingerprint patterns. Which type of pattern do more students in Ms. Gracie’s class have? Make a table to organize the data.

18. whorl loop whorl loop arch whorl loop whorl loop whorl whorl arch arch whorl arch loop Number of Fingerprint Patterns Whorl Arch Loop White board practice: Solution Students in Ms. Gracie’s class recorded their fingerprint patterns. Which type of pattern do more students in Ms. Gracie’s class have? Step 1: Make a column for each fingerprint pattern. Step 2: For each fingerprint, make a tally mark in the appropriate column. Most students in Ms. Gracie’s class have a whorl fingerprint. l l l l l l l l l l l l l l

19. A line plot uses a number line and x’s or other symbols to show frequencies of values.

20. Tennis Balls Collected 10 14 11 16 11 10 14 10 15 15 10 11 5 6 7 8 9 10 11 12 13 14 15 16 Example 4: Making a Line Plot Students collected tennis balls for a project. The number of balls collected by the students is recorded in the table. Make a line plot of the data. Step 1: Draw a number line. x x x x x x x x x x x Step 2: For each tennis ball, use an x on the number line to represent how many were collected. x

21. Cans Collected 5 7 11 14 11 5 7 14 14 5 15 11 White board practice: Students collected aluminum cans for a project. The number of cans collected by the students is recorded in the table. Make a line plot of the data.

22. Cans Collected 5 7 11 14 11 5 7 14 14 5 15 11 5 6 7 8 9 10 11 12 13 14 15 16 Write board Practice: Solution Students collected aluminum cans for a project. The number of cans collected by the students is recorded in the table. Make a line plot of the data. Step 1: Draw a number line. x x x x x x x x x x x Step 2: For each aluminum can, use an x on the number line to represent how many were collected. x

23. Pages Read Last Weekend 12 15 40 19 7 5 22 34 37 18 Example 5: Making a Frequency Table w/ Intervals Use the data in the table to make a frequency table with intervals.

24. Pages Read Last Weekend Number 1–10 11–20 21–30 31–40 Frequency Example 5 Continued Use the data in the table to make a frequency table with intervals 2 4 1 3 Step 1: Choose equal intervals. Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” row. This table shows that 2 students read between 1 and 10 pages, 4 students read between 11 and 20 pages, 1 person read between 21 and 30 pages, and 3 people read between 31 and 40 pages last weekend.

25. Number of Miles Driven on Saturday 17 29 9 19 7 5 27 34 21 38 White board practice: Use the data in the table to make a frequency table with intervals.

26. Number of Miles Driven on Saturday Number 1–10 11–20 21–30 31–40 Frequency White board practice: Solution Use the data in the table to make a frequency table with intervals. 3 2 3 2 Step 1: Choose equal intervals. Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” row. This table shows that 3 people drove between 1 and 10 miles, 2 people drove between 11 and 20 miles, 3 people drove between 21 and 30 miles, and 2 people drove between 31 and 40 miles on Saturday.

27. A histogram is a bar graph that shows the number of data items that occur within each interval.

28. Pages Read Last Weekend Number 1–10 11–20 21–30 31–40 Frequency Example 6: Making a Histogram Use the frequency table in Example 5 to make a histogram. 2 4 1 3 Step 1: Choose an appropriate scale and interval. Step 2: Draw a bar for the number of students in each interval. The bars should touch but not overlap. Step 3: Title the graph and label the axes.

29. Number of Miles Driven on Saturday Number 1–10 11–20 21–30 31–40 Frequency White board practice: Use the frequency table from your last white board practice to make a histogram. 3 2 3 2

30. Number of Miles Driven on Saturday Number 1–10 11–20 21–30 31–40 Number Miles Driven on Saturday Frequency People Number of Miles White board practice: Solution Use the frequency table from your last white board practice to make a histogram. 3 2 3 2 Step 1: Choose an appropriate scale and interval. Step 2: Draw a bar for the number of students in each interval. The bars should touch but not overlap. Step 3: Title the graph and label the axes.

31. Lesson Quiz: 1. Students listed the number of days they spent on vacation in one year. Make a tally table with intervals of 5. 2, 18, 5, 15, 7, 10, 1, 10, 4, 16, 7, 11, 17, 3, 8, 14, 13, 10

32. Use the bar graph to answer each question. 2. Which animal was least popular among students? 3. Which pet was more popular to twice as many students as rabbits were? Student Pet Survey bird dog

33. 4. Use your tally table from problem 1 to make a frequency table.

34. 5. Richard listed the number of books lent by their school library each day. Create a tally table with intervals of 5. 3, 18, 6, 14, 8, 10, 1, 10, 4, 17, 8, 11, 17, 4, 8, 14, 14, 10

35. 2. Create a frequency table for the given data.