notes unit 8: dot plots and histograms
TRANSCRIPT
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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
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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!
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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.
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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
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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!
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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!
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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
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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
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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
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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.
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Answer!
Sample Weights
= 1 sample
Weight in pounds
0 1
8
2
8
3
8
4
8
5
8
6
8
7
8
1
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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!
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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!
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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
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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
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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
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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.
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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
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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
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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.
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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
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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
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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
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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
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C. Histogram
• Histogram is a bar graph that shows the frequency of data within equal intervals.
• There is no space in between the bars.
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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?
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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.
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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
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Can you now make a bar graph, double bar Graph and a
histogram?
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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