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Histograms

Histograms. What is a histogram? A histogram is a type of bar graph whose bars represent the frequencies of NUMERIC DATA within intervals. Y-Axis has

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Histograms

What is a histogram?

• A histogram is a type of bar graph whose bars represent the frequencies of NUMERIC DATA within intervals.

Y-Axis has the frequency

X-Axis has the intervals

Intervals

• You need to look at your data and decide your intervals. This is similar to a stem-and-leaf plot because of the intervals.

• Example: Amy lists her quiz scores. This is her list: 88, 95, 75, 72, 95, 96, 85, 83, 84, 80, 70, 92

• What intervals would you chose?

Stem-and-Leaf Plot• Example: Amy lists her quiz scores. This is her

list: 88, 95, 75, 82, 95, 96, 85, 83, 84, 80, 70, 92• The intervals could be 70-79, 80-89, and 90-99.• The stem-and-leaf plot would look like this:

Stems Leaves

7

8

9

0 5

0 2 3 4 5 8

3 5 5 6

Frequency Tables• Once you have your

intervals decided, make a frequency table.

• Frequency – the amount of times it occurs

• Example: Amy lists her quiz scores. This is her list: 88, 95, 75, 82, 95, 96, 85, 83, 84, 80, 70, 92

Intervals Frequency

70-79

80-89

90-99

Creating a histogram!

Intervals Frequency

70-79 2

80-89 6

90-99 4

Title:

Freq

uenc

y

Label:Intervals:

What observations can you make about the distribution of the data?

Stem-and Leaf Plot vs. Histogram• How are they similar? How are they

different?

Stems Leaves

7

8

9

0 5

0 2 3 4 5 8

3 5 5 6

Title: Amy’s Quiz Scores

Freq

uenc

y

Label: Quiz GradesIntervals: 70-79 80-89 90-99

6

5

4

3

2

1

0

Things to remember:• You will use NUMERIC DATA.• You decide intervals based on the data. It

does not always have to be in tens.• Must be constructed from a frequency table.• All bars must touch and be the same width.

• X-Axis has intervals and a label.• Y-Axis has frequencies.• You need to have a title.

Your turn!• Students were surveyed and asked how many

hours they play outside each week. They said: 6, 9, 4, 5, 0, 7, 1, 5, 4, 8, 3, 2, 2, 3, 2, 4, 9, 4, 0,

Title:

Freq

uenc

y

Label:

Intervals Frequency

Intervals:

How did you do?• Students were surveyed and asked how many

hours they play outside each week. They said: 6, 9, 4, 5, 5, 7, 1, 5, 4, 8, 3, 2, 2, 3, 2, 4, 9, 4, 0, 8

Title: Playing Outside

Freq

uenc

y

Label: Hours Outside

Intervals Frequency

0-1 2

2-3 5

4-5 7

6-7 2

8-9 4 Intervals: 0-1 2-3 4-5 6-7 8-9

12

10

8

6

4

2

0

Histograms

• What observations can you make about the distribution of the data in your histogram?

• How can a histogram be helpful to you?

• What things do you need to watch out for when making a histogram?

Percent Bar Graph

What is a percent bar graph?• A percent bar graph is a type of bar graph where

you graph relative frequencies to help you visualize how the data is distributed for CATEGORICAL DATA.

Y-Axis has the RelativeFrequency (%)

X-Axis has the categories

Make a Table• Example: Sue asked her 25 classmates what

their favorite color was. 4 people said green, 6 people said purple, 5 people said pink, 7 people said blue, and 3 people said yellow.

Favorite Colors

Color Green Purple Pink Blue Yellow

Frequency

Relative Frequency Table• To make a percent bar graph, you need to

know the relative frequency of each category.• Relative Frequency – the ratio of the

frequency to the total as a fraction or percentFavorite Colors

Color Green Purple Pink Blue Yellow

Frequency 4 6 5 7 3

Relative Frequency

4 ---- = ----25 100

6 ---- = ----25 100

5 ---- = ----25 100

7 ---- = ----25 100

3 ---- = ----25 100

Creating a percent bar graph!Title: Favorite Colors

Rela

tive

Freq

uenc

y (%

)

Categories: Green Purple Pink Blue Yellow

What observations can you make about the data?

Color Green Purple Pink Blue Yellow

Frequency 4 6 5 7 3

% 16 24 20 28 12

30

25

20

15

10

5

0

Label: Color

Creating a percent bar graph!Title: Favorite Colors

Rela

tive

Freq

uenc

y (%

)

Categories: Green Purple Pink Blue Yellow

What observations can you make about the data?

Color Green Purple Pink Blue Yellow

Frequency 4 6 5 7 3

% 16 24 20 28 12

30

25

20

15

10

5

0

Label: Color

Things to remember:• You will use CATEGORICAL DATA.• You need to make a relative frequency table.• The percentage is the frequency out of the

whole. You need to get to 100%.• All bars must touch and be the same width.

• X-Axis has categories and a label.• Y-Axis has relative frequencies (percents).• You need to have a title.

Your turn!Title:

Rela

tive

Freq

uenc

y (%

)

Categories:

What observations can you make about the data?

Elective Art Band Orchestra Theatre

Frequency 10 18 14 8

%

0

Label:

When I went to lunch, I asked people what their elective was. Their answers are in the table.

How did you do?Title: Elective Classes

Rela

tive

Freq

uenc

y (%

)

Categories: Art Band Orchestra Theatre

What observations can you make about the data?

Elective Art Band Orchestra Theatre

Frequency 10 18 14 8

% 20 36 28 16

Label: Elective Class

When I went to lunch, I asked people what their elective was. Their answers are in the table.

40

30

20

10

0

Percent Bar Graph

• What observations can you make about the data in your percent bar graph?

• How can a percent bar graph be helpful to you?

• What things do you need to watch out for when making a percent bar graph?

Compare

• How are histograms and percent bar graphs similar?

• How are histograms and percent bar graphs different?

• How do you know which kind of graph to use?