7-3 Histograms

Course 2

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

7-3 Histograms

Warm UpFind the mean, median, mode, and range for the data set.

35, 45, 48, 53, 53, 27, 66, 36, 24

43; 45; 53; 42

7-3 Histograms

Problem of the Day

Which number does not belong with the others? Why?81, 64, 36, 27, 49

Possible answer: 27; the others are perfect squares.

7-3 Histograms

Prep for MA.7.S.6.2 Construct and analyze histograms….

Sunshine State Standards

7-3 Histograms

Vocabulary

histogram

7-3 Histograms

A histogram is a bar graph that shows the frequency of data within equal intervals. There is no space between the bars in a histogram.

7-3 Histograms

The histogram shows the results of a survey asking people the number of hours they sleep per night. Use the histogram to answer each question.

Additional Example 1A: Analyzing Histograms

A. How many people sleep less than 9 hous per night?

Add the number of students in the 3-5 and 6-8 intervals.

23 + 58 = 7878 people sleep less than 9 hous per night.

7-3 Histograms

Additional Example 1B: Analyzing Histograms

B. What is the approximate median number of hours people sleep per night?

Since 100 people were surveyed, the median is the mean of the 50th and 51st persons’ hours.

The 50th and 51st persons’ hours are in the middle of the 6-8 interval. So, a good estimated is 7 hours.

Interval Frequency Rank (by weight)

3-5 25 1-25

6-8 53 26-78

9-11 17 79-95

12-14 5 96-100Determine the interval of the 50th and 51st people.

7-3 Histograms

The histogram shows the results of a local 10K race. Use the histogram to answer each question.

Check It Out: Example 1A

A. How many runners completed the race in less than 50 minutes?

Add the number of runners in the first four intervals.

4 + 6 + 10 + 13 = 3333 runners completed the race in less than 50 minutes.

7-3 Histograms

Check It Out: Example 1B

B. What is the approximate median time people ran the race?

The 25th and 26th times are in the middle of the 45:00-49:59 interval. So, a good estimated is 47:30.

Interval Frequency Rank (by weight)

33:00-34:59 4 1-4

35:00-39:59 6 5-10

40:00-44:59 10 11-20

45:00-49:59 13 21-33

50:00-54:59 12 34-45

55:00-59:59 5 46-50

Since there were 50 runners, the median is the mean of the 25th and 26th times.

Determine the interval of the 25th and 26th times.

7-3 Histograms

The table below shows the number of hours students watch TV in one week. Make a histogram of the data.

Additional Example 2: Making a Histogram

Step 1: Make a frequency table of the data. Be sure to use equal intervals. 6 ///

7 //// ////

8 ///

9 ////

1 //

2 ////

3 //// ////

4 //// /

5 //// ///

Number of Hours of TV

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

7-3 Histograms

Additional Example 2 ContinuedStep 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

20

16

12

8

4

0

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Additional Example 2 ContinuedStep 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

20

16

12

8

4

0

Because the intervals are equal, all of the bars should have the same width.

Caution!

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Additional Example 2 ContinuedStep 4: Label the axes and give the graph a title.

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

20

16

12

8

4

01–3 4–6 7–9

Hours of Television Watched

Frequ

ency

Hours

7-3 Histograms

The table below shows the number of hats a group of students own. Make a histogram of the data.

Check It Out: Example 2

Step 1: Make a frequency table of the data. Be sure to use equal intervals.

1–3

FrequencyNumber of Hats Owned

12

4–6 18

7–9 24

1 //

2 ////

3 //// /

4 //// /

5 //// ///

6 ////

7 //// /

8 //// ////

9 //// ////

Number of Hats Owned

Frequency

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Check It Out: Example 2 Continued

Step 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.

1–3

FrequencyNumber of Hats Owned

12

4–6 18

7–9 24

30

25

20

15

10

5

0

7-3 Histograms

Step 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.

1–3

FrequencyNumber of Hats Owned

12

4–6 18

7–9 24

30

25

20

15

10

5

0

Check It Out: Example 2 Continued

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Step 4: Label the axes and give the graph a title.

1–3

FrequencyNumber of Hats Owned

12

4–6 18

7–9 24

30

25

20

15

10

5

01–3 4–6 7–9

Number of Hats Owned

Frequ

ency

Number of Hats

Check It Out: Example 2 Continued

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Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

7-3 Histograms

Lesson Quiz: Part I

Use the histogram to answer each question.

1. How many entrees cost $10 or more?

2. Sarah wants to go to a restaurant where most entrees are less than $10. Should she go to the restaurant whose entrees are represented in the graph? Explain.

29

No; 11 entrees are less than $10, but 29 are more.

7-3 Histograms

Lesson Quiz: Part II

4. The list shows the number of laps students ran one day. Make a histogram of the data.

4, 7, 9, 12, 3, 6, 10, 15, 12, 5, 18, 2, 5, 10, 7, 12, 11, 15

Nu

mb

er

of

Stu

den

ts Number of Laps Run

10–1

4

0–4

5–9

8

6

4

2

0

15–1

9

Number of Laps

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Lesson Quiz for Student Response Systems

1. How many students scored below 80?

A. 6

B. 13

C. 19

D. 37

7-3 Histograms

Lesson Quiz for Student Response Systems

2. How many students took the final exam?

A. 20

B. 50

C. 60

D. 100