Notes Unit 8: Dot Plots and Histograms

I. Dot PlotsA. Definition

• A data display in which each data item is shown as a dot above a number line

• In a dot plot a cluster shows where a group of data points fall.

• A gap is an interval where there are no data items.

• Notes Unit 8: Dot Plots and Histograms

B. Steps to Create a Dot Plot

1. Order numbers from least to greatest.

2. Draw a number line, labeling the number line with the minimum and the maximum and then all the numbers that fall between them.

3. Put a dot above each number on the number line for each data entry in your set. Don’t forget a title and labels!

C. ExamplesEx 1:

A. In an airline training program, the students are given a test in which they are given a set of tasks and the time it takes them to complete the tasks is measured. The following is a list of the time (in seconds) for a group of new trainees.

61, 61, 64, 67, 70, 71, 71, 71, 72, 73, 74, 74, 75, 77,79, 80, 81, 81, 83

Display the data in a dot plot.

Answer!

Airline Training Program TestNew Trainees

= 1 person

Time in Seconds

61 8362 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

Are there any clusters?

Airline Training Program TestNew Trainees

= 1 person

Time in Seconds

61 8362 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

Yes!

Are there any gaps?

Airline Training Program TestNew Trainees

= 1 person

Time in Seconds

61 8362 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

Yes!

What is the average time?

Airline Training Program TestNew Trainees

= 1 person

Time in Seconds

61 8362 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

About 73

seconds

What is the median time?

Airline Training Program TestNew Trainees

= 1 person

Time in Seconds

61 8362 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

73 seconds

What is the Range?

Airline Training Program TestNew Trainees

= 1 person

Time in Seconds

61 8362 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

22 seconds

Ex 2:

B. In a science class, the students weighed some samples of dirt to the nearest 1/8 pound. The weights of the samples are given below.

1/8 lb, 3/8 lb, ¾ lb, ¼ lb, 1/8 lb, ¼ lb, 7/8 lb, ¼ lb, 3/8 lb, ¼ lb, ½ lb, 3/8 lb

Make a dot plot for the data.

Answer!

Sample Weights

= 1 sample

Weight in pounds

0 1

8

2

8

3

8

4

8

5

8

6

8

7

8

1

Are there any clusters?

Sample Weights

= 1 sample

Weight in pounds

0 1

8

2

8

3

8

4

8

5

8

6

8

7

8

1

Yes!

Are there any Gaps?

Sample Weights

= 1 sample

Weight in pounds

0 1

8

2

8

3

8

4

8

5

8

6

8

7

8

1

Yes!

What is the average weight?

Sample Weights

= 1 sample

Weight in pounds

0 1

8

2

8

3

8

4

8

5

8

6

8

7

8

1

3/8 or 0.375 lb

What is the median?

Sample Weights

= 1 sample

Weight in pounds

0 1

8

2

8

3

8

4

8

5

8

6

8

7

8

1

5/16 or 0.3125 lb

What is the range?

Sample Weights

= 1 sample

Weight in pounds

0 1

8

2

8

3

8

4

8

5

8

6

8

7

8

1

6/8 or 0.75 lb

You try:

Mrs. Jones took a survey of ten 6th grade students. She asked each student how many items they recycle in a day. Below are her results.

0, 1, 1, 1, 2, 2, 2, 3, 3, 5

Make a dot plot to display this data.

A. Bar Graphs

• A bar graph can be used to display and compare data

• The scale should include all the data values and be easily divided into equal intervals.

II. Bar Graphs and Histograms

How to interpret a Bar Graph?

• How many of Mr. Snow’s students are band members?

• How many of Mr. Snow’s students are not band members?

The bar graph shows Mr.

Snow’s students by gender

and band membership.Snow’s Students by Gender &

Band Membership

B. Double Bar Graph

0

10

20

30

40

50

60

70

80

90

1stQtr

2ndQtr

3rdQtr

4thQtr

• Can be used to compare two related sets of data

How to make a Double-Bar Graph?

1. Choose a scale and interval for the vertical axis.

2. Draw a pair of bars for each variable. If possible, use different colors.

3. Label the axes and give the graph a title.

4. Make a key to show what each bar represents.

Ex 1: The table shows the highway speed limits on interstate roads within three

states.

RuralUrbanState

70 mi/h65mi/hFlorida

70 mi/h70 mi/hTexas

65 mi/h55mi/hVermont

Step 1• Choose a scale and interval for the vertical axis.

RuralUrbanState

70 mi/h65mi/hFlorida

70 mi/h70 mi/hTexas

65 mi/h55mi/hVermont

Step 2• Draw a pair of bars for each state’s

data. Use different colors to show urban and rural.

RuralUrbanState

70 mi/h65mi/hFlorida

70 mi/h70 mi/hTexas

65 mi/h55mi/hVermont

Step 3 and 4

• Label the axes and give the graph a title.

• Make a key to show what each bar represents

Speed L

imit (

mi/h)

Urban

Rural

Speed Limit on Interstate Roads

C. Histogram

• Histogram is a bar graph that shows the frequency of data within equal intervals.

• There is no space in between the bars.

Step 1• Make a frequency

table of the data. Be sure to use equal intervals

Number of hours of TV

III6II1

IIII - IIII7IIII2

III8IIII - IIII3

IIII9IIII - I4

IIII - III5

FrequencyNumber of

hours of TV

151-3

174-6

167-9

a. Creating a histogram?

Step 2

FrequencyNumber of

hours of TV

151-3

174-6

167-9

• 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.

Step 3• Draw a bar for each interval. The

height of the bar is the frequency for that interval. Bars must touch but not overlap.

• Label the axes and give the graph title

FrequencyNumber of

hours of TV

151-3

174-6

167-9

Can you now make a bar graph, double bar Graph and a

histogram?

You try: The list below shows the results of a typing test in words per minute. Make a histogram of the data.

62, 55, 68, 47, 50, 41, 62, 39, 54, 70, 56, 70, 56, 47, 71, 55, 60, 42