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Section 2.2, Part 2Determining Normality
AP Statistics
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.
AP Statistics, Section 2.2, Part 2 3
Symmetric?
The distribution should be roughly symmetric.
You can use a Boxplot to determine symmetry.
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?
AP Statistics, Section 2.2, Part 2 5
Are Walter Johnson’s Wins Normal? Look also at boxplot Is the data set
symmetric?
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.
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
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:
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
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
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
AP Statistics, Section 2.2, Part 2 12
Somewhat normal (somewhat linear)
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
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
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
AP Statistics, Section 2.2, Part 2 16
Not normal (not linear)
AP Statistics, Section 2.2, Part 2 17
Walter Johnston Normal?
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
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