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Section 2.2, Part 2Determining Normality
AP Statistics
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AP Statistics, Section 2.2, Part 2 2
What is “Normal”?
Because we should only apply z-score to distributions that are normal, we need a process to determine whether a distribution is a normal distribution.
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AP Statistics, Section 2.2, Part 2 3
Symmetric?
The distribution should be roughly symmetric.
You can use a Boxplot to determine symmetry.
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AP Statistics, Section 2.2, Part 2 4
Are Walter Johnson’s Wins Normal? 5, 14, 13, 25, 25, 33,
36, 28, 27, 25, 23, 23, 20, 8, 17, 15, 17, 23, 20, 15, 5 into list L1
Run “1-Var Stats” Is the data set
symmetric? Where do you look?
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AP Statistics, Section 2.2, Part 2 5
Are Walter Johnson’s Wins Normal? Look also at boxplot Is the data set
symmetric?
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AP Statistics, Section 2.2, Part 2 6
68-95-99.7 Rule?
You can use the 68-95-99.7 rule with a histogram to see if the distribution roughly fits the rule.
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AP Statistics, Section 2.2, Part 2 7
Are Walter Johnson’s Wins Normal? 5, 5, 8, 13, 14, 15, 15, 17,
17, 20, 20, 23, 23, 23, 25, 25, 25, 27, 28, 33, 36
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AP Statistics, Section 2.2, Part 2 8
Are Walter Johnson’s Wins Normal? Last step is the creation of the “normal
probability plots Let’s look at the book example:
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AP Statistics, Section 2.2, Part 2 9
Example 2.12
X Midpoint Y
1 1/8=.1250 -1.15
2 3/8=.3750 -.319
2 5/8=.6250 .319
3 7/8=.8750 1.15
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AP Statistics, Section 2.2, Part 2 10
Example 2.12
X Midpoint Y
1 1/8=.1250 -1.15
2 3/8=.3750 -.319
2 5/8=.6250 .319
3 7/8=.8750 1.15
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AP Statistics, Section 2.2, Part 2 11
Example 2.12
X Midpoint Y
1 1/8=.1250 -1.15
2 3/8=.3750 -.319
2 5/8=.6250 .319
3 7/8=.8750 1.15
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AP Statistics, Section 2.2, Part 2 12
Somewhat normal (somewhat linear)
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AP Statistics, Section 2.2, Part 2 13
Example 2.12
X Midpoint Y
1 1/10=.1 -1.282
2 3/10=.3 -0.524
2 5/10=.5 0.000
3 7/10=.7 0.524
10 9/10=.9 1.282
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AP Statistics, Section 2.2, Part 2 14
Example 2.12
X Midpoint Y
1 1/10=.1 -1.282
2 3/10=.3 -0.524
2 5/10=.5 0.000
3 7/10=.7 0.524
10 9/10=.9 1.282
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AP Statistics, Section 2.2, Part 2 15
Example 2.12
X Midpoint Y
1 1/10=.1 -1.282
2 3/10=.3 -0.524
2 5/10=.5 0.000
3 7/10=.7 0.524
10 9/10=.9 1.282
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AP Statistics, Section 2.2, Part 2 16
Not normal (not linear)
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AP Statistics, Section 2.2, Part 2 17
Walter Johnston Normal?
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AP Statistics, Section 2.2, Part 2 18
Assignment
Exercises 2.26 – 2.31, 2.33, 2.36 to finish Section 2.2
Exercises 2.39, 2.40, 2.42, 2.45, 2.47 to finish Chapter 2