Statistics
Part 10
Representing Data
• We can use many different ways to represent data. Some of
these ways include, but are not limited to:
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Tables
Charts
Pie graphs
Histograms
Bar graphs
Frequency Tables
• Frequency tables frequently bin data into small groups.
• We use a table to show this with columns for the data
category, frequency, relative frequency, and cumulative
frequency.
• Frequency is how often values in that bin occurred.
• Relative frequency is how often out of the total values in that bin
occur. (Related to probability.)
• Cumulative frequency is the total number of values thus far in the
table.
Example 1: Exam Grades
• On a certain exam, students scored exam grades
of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67,
67, 67, and 62. Use 5-point bins to make a
frequency table for the exam scores.
Exam Scores
Number of Students
Relative Frequency
Cumulative Frequency
95 - 100
3
3/15 = 0.2 = 20%
3
90 - 94
1
1/15 = 0.067 = 6.7%
85 - 89
3
3/15 = 0.2 = 20%
80 - 84
1
1/15 = 0.067 = 6.7%
3+1+3+1=8
75 - 79
1
1/15 = 0.067 = 6.7%
8+1=9
70 - 74
2
2/15 = 0.133 = 13.3%
9 + 2 = 11
65 - 69
3
3/15 = 0.2 = 20%
11 + 3 = 14
60 - 64
1
1/15 = 0.067 = 6.7%
14 + 1 = 15
Totals
15
15/15 = 100%
3+1=4
3+1+3 = 7
15
Example 2: Exam Grades
(Again)
• On a certain exam, students scored exam grades
of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67,
67, 67, and 62. This time, use 10-point bins to
make a frequency table for the exam scores.
Exam Scores
Number of Students
Relative Frequency
Cumulative Frequency
90 - 100
4
4/15 = 0.267 = 26.7%
4
80 - 89
4
4/15 = 0.267 = 26.7%
4+4=8
70 - 79
3
3/15 = 0.2 = 20%
4 + 4 + 3 = 11
60 - 69
4
4/15 = 0.267 = 26.7%
4 + 4 + 3 + 4 = 15
Totals
15
15/15 = 100%
15
Histograms
• A histogram is a bar chart for quantitative data.
• The bars have a natural order and the bar widths have specific
meaning.
• Review each example and construct the histograms to match.
Example 1: Exam Grades
• On a certain exam, students scored exam grades
of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67,
67, 67, and 62. Use 5-point bins to make a
frequency table for the exam scores.
Exam Scores
Number of Students
Relative Frequency
Cumulative Frequency
95 - 100
3
3/15 = 0.2 = 20%
3
90 - 94
1
1/15 = 0.067 = 6.7%
85 - 89
3
3/15 = 0.2 = 20%
80 - 84
1
1/15 = 0.067 = 6.7%
3+1+3+1=8
75 - 79
1
1/15 = 0.067 = 6.7%
8+1=9
70 - 74
2
2/15 = 0.133 = 13.3%
9 + 2 = 11
65 - 69
3
3/15 = 0.2 = 20%
11 + 3 = 14
60 - 64
1
1/15 = 0.067 = 6.7%
14 + 1 = 15
Totals
15
15/15 = 100%
3+1=4
3+1+3 = 7
15
Example 2: Exam Grades
(Again)
• On a certain exam, students scored exam grades
of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67,
67, 67, and 62. This time, use 10-point bins to
make a frequency table for the exam scores.
Exam Scores
Number of Students
Relative Frequency
Cumulative Frequency
90 - 100
4
4/15 = 0.267 = 26.7%
4
80 - 89
4
4/15 = 0.267 = 26.7%
4+4=8
70 - 79
3
3/15 = 0.2 = 20%
4 + 4 + 3 = 11
60 - 69
4
4/15 = 0.267 = 26.7%
4 + 4 + 3 + 4 = 15
Totals
15
15/15 = 100%
15
Bar Charts
• Bar charts look a lot like histograms but the bars are not
touching.
• The width of each bar has no real meaning.
• We use these for comparisons of data.
Example 3: Local Weather
• The weekend forecast for Las Cruces, NM indicates the
following:
• Friday 80/58
• Saturday 78/55
• Sunday 80/57
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The weekend forecast for Coeur d’Alene, ID indicates the
following:
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Friday 74/46
Saturday 73/49
Sunday 64/44
Construct a bar chart comparing the high temperatures for
the weekend in these two cities.
Believing Statistical Studies
1.
2.
3.
4.
5.
6.
Identify the goal, population, and type of study.
Consider the source.
Consider potential bias.
Look for problems in defining or measuring the variables of
interest.
Look for other variables that may confound (confuse) the
data.
Consider the setting and wording in the survey.