Our learning goal is to able to collect and display data.

Learning Goal Assignments:

1.Make a Table

2.Range, Mean, Median, and Mode

3.Additional Data and Outliers

4.Bar Graphs

5.Frequency Tables and Histograms

6.Ordered Pairs

7.Line Graphs

8.Misleading Goals

9.Stem-and-Leaf Plots

Learning Goal Assignment

Learn to organize data in frequency tables and histograms.

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6-5 Frequency Tables and Histograms

6th Grade Math HOMEWORK

Page 292#5-8

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6-5 Frequency Tables and Histograms

6-5 Frequency Tables and Histograms

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpCreate a bar graph of the data.

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6-5 Frequency Tables and Histograms

Favorite rides at fair:Ferris wheel = 5, loop the loop = 4, merry-go-round = 3, bumper cars = 7, sit and spin = 9

Favorite Rides at Fair

0

2

4

6

8

10

Ferris Wheel Loop the loop Merry-go-round

Bumper cars Sit and spin

Problem of the Day

A set of 7 numbers has a mean of 36, a median of 37, a mode of 37, and a range of 6. What could the 7 numbers be?

Possible answer: 33, 33, 36, 37, 37, 37, 39

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6-5 Frequency Tables and Histograms

Learning Goal Assignment

Learn to organize data in frequency tables and histograms.

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6-5 Frequency Tables and Histograms

Vocabulary

frequency tablecumulative frequencyhistogram

Insert Lesson Title Here

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6-5 Frequency Tables and Histograms

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6-5 Frequency Tables and HistogramsAdditional Example 1: Making a Tally Table

Students in Mr. Ray’s class recorded their fingerprint patterns. Which type of pattern do most students in Mr. Ray’s class have?

whorl loop whorl loop

arch arch loop whorl

loop arch whorl arch

arch whorl arch loop

Make a tally table to organize the data.

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6-5 Frequency Tables and HistogramsAdditional Example 1 Continued

Students in Mr. Ray’s class recorded their fingerprint patterns. Which type of pattern do more students in Mr. Ray’s class have?

whorl loop whorl loop

arch arch loop whorl

loop arch whorl arch

arch whorl arch loop

Step 1: Make a column for each fingerprint pattern.

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6-5 Frequency Tables and HistogramsAdditional Example 1 Continued

Students in Mr. Ray’s class recorded their fingerprint patterns. Which type of pattern do more students in Mr. Ray’s class have?

whorl loop whorl loop

arch arch loop whorl

loop arch whorl arch

arch whorl arch loop

Step 1: Make a column for each fingerprint pattern.

Step 2: For each fingerprint, make a tally mark in the appropriate column.

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6-5 Frequency Tables and HistogramsAdditional Example 1 Continued

Students in Mr. Ray’s class recorded their fingerprint patterns. Which type of pattern do more students in Mr. Ray’s class have?

whorl loop whorl loop

arch arch loop whorl

loop arch whorl arch

arch whorl arch loop

Step 1: Make a column for each fingerprint pattern.

Step 2: For each fingerprint, make a tally mark in the appropriate column.

Number of Fingerprint Patterns

Whorl Arch Loop

l l l l l l l l l l l l l

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6-5 Frequency Tables and HistogramsAdditional Example 1 Continued

Students in Mr. Ray’s class recorded their fingerprint patterns. Which type of pattern do more students in Mr. Ray’s class have?

whorl loop whorl loop

arch arch loop whorl

loop arch whorl arch

arch whorl arch loop

Number of Fingerprint Patterns

Whorl Arch Loop

l l l l l l l l l l l l l

Most students in Mr. Ray’s class have an arch fingerprint.

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6-5 Frequency Tables and Histograms

A group of four tally marks with a line through it means five. llll = 5 llll llll = 10

Reading Math

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6-5 Frequency Tables and HistogramsTry This: Example 1

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 tally table to organize the data.

whorl loop whorl loop

arch whorl loop whorl

loop whorl whorl arch

arch whorl arch loop

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6-5 Frequency Tables and HistogramsTry This: Example 1 Continued

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.

whorl loop whorl loop

arch whorl loop whorl

loop whorl whorl arch

arch whorl arch loop

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6-5 Frequency Tables and HistogramsTry This: Example 1 Continued

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.

whorl loop whorl loop

arch whorl loop whorl

loop whorl whorl arch

arch whorl arch loop

Step 2: For each fingerprint, make a tally mark in the appropriate column.

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6-5 Frequency Tables and HistogramsTry This: Example 1 Continued

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.

whorl loop whorl loop

arch whorl loop whorl

loop whorl whorl arch

arch whorl arch loop

Step 2: For each fingerprint, make a tally mark in the appropriate column.

Number of Fingerprint Patterns

Whorl Arch Loop

l l l l l l l l l l l l l l

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6-5 Frequency Tables and HistogramsTry This: Example 1 Continued

Students in Ms. Gracie’s class recorded their fingerprint patterns. Which type of pattern do more students in Ms. Gracie’s class have?

whorl loop whorl loop

arch whorl loop whorl

loop whorl whorl arch

arch whorl arch loop

Number of Fingerprint Patterns

Whorl Arch Loop

l l l l l l l l l l l l l l

Most students in Ms. Gracie’s class have a whorl fingerprint.

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6-5 Frequency Tables and Histograms

A frequency table tells the number of times an event, category, or group occurs. The cumulative frequency column shows a running total of all frequencies.

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6-5 Frequency Tables and Histograms

Additional Example 2: Making a Cumulative Frequency Table

Step 1: Make a row for each pattern.

Step 2: The frequency is how many times each pattern occurred.

Number of Fingerprint Patterns

Fingerprint Pattern Frequency Cumulative Frequency

Whorl

Arch

Loop

Step 3: Find the cumulative frequency for each row by adding all frequency values above or in that row.

6

5

11

16

5 5

Use the tally table in Additional Example 1 to make a cumulative frequency table.

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6-5 Frequency Tables and Histograms

Try This: Additional Example 2

Step 1: Make a row for each pattern.

Step 2: The frequency is how many times each pattern occurred.

Number of Fingerprint Patterns

Fingerprint Pattern Frequency Cumulative Frequency

Whorl

Arch

Loop

Step 3: Find the cumulative frequency for each row by adding all frequency values above or in that row.

4

5

11

16

7 7

Use the tally table in Try This: Example 1 to make a cumulative frequency table.

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6-5 Frequency Tables and Histograms

Additional Example 3: Making a Frequency Table with Intervals

Use the data in the table to make a frequency table with intervals.

Number of Pages Read per Student Last Weekend

12 15 40 19 7

5 22 34 37 18Step 1: Choose equal intervals.

Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” row.

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6-5 Frequency Tables and Histograms

Additional Example 3 Continued

Number of Pages Read per Student Last Weekend

Number 1–10 11–20 21–30 31–40Frequency

This table shows that 2 students read between 1 and 10 pages, 4 students read between 11 and 20 pages, and so on.

2 4 1 3

Number of Pages Read per Student Last Weekend

12 15 40 19 7

5 22 34 37 18

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6-5 Frequency Tables and Histograms

Try This: Example 3

Use the data in the table to make a frequency table with intervals.

Number of Pages Read per Student Last Weekend

17 29 9 19 7

5 27 34 21 38

Step 1: Choose equal intervals.

Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” row.

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6-5 Frequency Tables and Histograms

Try This: Example 3 Continued

Number of Pages Read per Student Last Weekend

Number 1–10 11–20 21–30 31–40Frequency

This table shows that 3 students read between 1 and 10 pages, 2 students read between 11 and 20 pages, and so on.

3 2 3 2

Number of Pages Read per Student Last Weekend

17 29 9 19 7

5 27 34 21 38

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6-5 Frequency Tables and Histograms

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

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6-5 Frequency Tables and Histograms

Additional Example 4: Making a Histogram

Use the frequency table in Additional Example 3 to make a histogram.

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.

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6-5 Frequency Tables and Histograms

Try This: Example 4

Use the frequency table in Try This: Example 3 to make a histogram.

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.

0

1

2

3

4

1- 10 11- 20 21- 30 31- 40

Number of Pages Read per Student Last Weekend

Number of Pages

Stu

den

ts

Lesson Quiz: Part 1

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

Insert Lesson Title Here

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6-5 Frequency Tables and Histograms

Number of Days Spent on Vacation

1–5 6–10 11–15 16–20

|||| |||| | |||| |||

Lesson Quiz

2. Use your tally table from problem 1 to make a frequency and cumulative frequency table.

Insert Lesson Title Here

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6-5 Frequency Tables and Histograms

Number of Days Spent on Vacation

Number of Days FrequencyCumulative Frequency

1–5 5 5

6–10 6 11

11–15 4 15

16–20 3 18