1. The Normal Distribution (Gaussian Distribution)
Honors Analysis
Learning Target: I can analyze data using the normal distribution.

2. Carl Friedrich Gauss (1777-1855)
German mathematician
Influenced statistics, algebra,
number theory, geometry,
physics.
Child prodigy!
Constructed heptadecagon
Triangular numbers
Proved Fundamental
Theorem of Algebra
Influenced development
of statistics, including
Normal Distribution
(Gaussian Distribution)
Carl Friedrich Gauss ( )

3. Imagine you took a test in two different classes.
In the first class, you made a 93%. The class mean was a 96%, and the standard deviation was 3%.
In the second class, you made a 78%. The class mean was a 74%, and the standard deviation was 2%.
Which test performance was better?

4. Normal Distribution (Gaussian Distribution)
𝜎=𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝜇=𝑚𝑒𝑎𝑛
Normal Distribution (Gaussian Distribution)

5. 68-95-99.7 Rule (Approximately) 68% within 1 std dev. of mean
95% within 2 std. deviations of mean
99.7% fall within 3 standard deviations of mean
Rule

6. Labeling a Simple Normal Curve
Calculate the mean (central value on curve)
Each region increases or decreases by one standard deviation from the mean
Ex: Test score mean: 74% Std. dev: 2%
Labeling a Simple Normal Curve

7. So what happens if you want to calculate a percentage for a value that ISN’T on your normal curve?
Ex: PSAT math test with mean of 48 and a std. deviation of 3. What percent of scores are below 50?

8. Standard Normal Distribution
Normal distribution with a mean of 0 and a standard deviation of 1.
Total area under curve = 1
Area to left of a given value on the curve gives the percentile rank – percent of scores LOWER than a given score.
Standard Normal Distribution

9. You can convert values to standard normal distribution form by calculating a z-score:
𝑍= 𝑋−𝜇 𝜎
Z-Score percentages can be looked up in a table or on a calculator.
Z-Scores

10. Example

15. Solution

16. Example Part II

23. Types of Bias Unrepresentative Sample
Undercoverage (Convenience sample, voluntary sample)
Non-response Bias
Voluntary response Bias
Measurement Error
Response Bias (Leading questions, social desirability)
Types of Bias