Unit 1_ Exploring One-Variable Data.pptx

AP Statistics Unit 1

1. Unit 1: Exploring One-Variable Data 1.1 The Normal Model and Distribution

2. Let’s get the concepts right… (review) Statistic = numerical summary of a sample Parameter = numerical summary of a population

3. Statistics They come from actual samples of data You can get: -Sample mean (x-bar) -Sample standard deviation (Big S) -Sample proportion (p-hat)

4. Parameters Parameters ARE THEORETICAL . You can get: -Population mean: (mu) -Population s tandard deviation: (sigma) -Population Proportion: (p) Since the values are theoretical, we cannot graph them as easily, so we use a curve model to represent what the population looks like

5. Normal Model

6. What does it mean for a dataset to be “Normal”? Normally distributed means the set data is MOUND SHAPED, UNIMODAL, AND SYMMETRIC Once we see the population can look this way, we use Mu and Sigma Why don't we use x-bar and S?

7. So, let's assume… Making a Normal graph with mu=340g and sigma=20g

8. So, let's assume… Making a Normal graph with mu=340g and sigma=20g 340 360 380 400 320 300 280

9. Empirical Rule:

10. What do we do with this? We can see where any data set falls with JUST THE STANDARD DEVIATION AND MEAN . ( Standardized score) Standardized score lets you see exactly where a value is positioned in the population .

11. Z-SCORE Standardized score that measures how many standard deviations a value is away from the mean Z-scores are like a universal measuring tool to compare and analyze anything

12. So in context… I got a score of an 86 on a standardized exam The average score was 81, while the standard deviation was 1

13. So in context… I got a score of an 86 on a standardized exam The average score was 81, while the standard deviation was 1 x=86, mu=81, sigma=1 z=(86-81)/1= 5 So how did I do?

14. With a z-score of 5… YOU DID INCREDIBLE!!! This graph doesn’t even go that f ar So you would get top 0.15%

15. Keep in mind if a population is normal… -A large percentage of data (68%) will have a z-score between -1 and 1 -Almost all data (95%) will have a z-score between -2 and 2 -Virtually all data (99.7%) will have a score between -1 and 3 So, a value of a z-score SMALLER than -3 or LARGER than 3 is very unusual, unlikely, and significant value

16. Exercise problem:

17. Exercise problem: