section 2.2, part 2 determining normality ap statistics

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