1. and the 68-95-99.7 Rule THE NORMAL DISTRIBUTION

2. SKEWED DISTRIBUTIONS & OUTLIERS

3. NORMAL = TYPICAL This is valuable information when studying human behavior i.e., the average woman is 5’4” tall (64 inches) …this means that we expect to see women of this height. It is uncommon to see women who are 6 feet tall or 4 feet tall. i.e., the average intelligence score is 100…it is rare to score 130 or 70.

4. Standard Deviation Range Mean Median Mode DESCRIBING ‘NORMAL’ W/ STATS CENTRAL TENDENCY VARIATION

5. IN ORDER TO INTERPRET THE NORMAL CURVE BOTH PIECES OF INFORMATION ARE NECESSARY. WHY?

6. Did everyone get a 30? Did half of the students get a 20 and the other half get a 40? Was my score good or bad? I.E., THE AVERAGE SCORE ON THE QUIZ WAS 50 POINTS…

7. We know how spread out the grades are but not how they are centered How did the class do in general? Is my grade good or bad? I.E., THE SD ON THE QUIZ WAS 5

8. Allows us to make accurate assumptions and inferences about data on a normal curve 68-95-99.7 RULE

9. 68% OF ALL DATA WILL FALL WITHIN ONE STANDARD DEVIATION OF THE MEAN.

10. 95% OF ALL DATA WILL FALL WITHIN TWO STANDARD DEVIATIONS OF THE MEAN.

11. 99.7% OF ALL DATA WILL FALL WITHIN THREE STANDARD DEVIATIONS OF THE MEAN.

12. QUIZ EXAMPLE…M=50 AND SD=5 Now we know that 68% of students scored between 45 and 55 95% of students scored between 40 and 60 99.7% of students scored between 35 and 65

13. Height example…M=64, SD=3 So…68% of all women are within 3 inches of 64. 68% of all women are within 1 standard deviation of the mean.

14. 95% of all women are within 2 standard deviations of the mean. Here 95% of all women are within 6 inches of 64.

15. 99.7% of all women are within 3 standard deviations of the mean. Here 99.7% of all women are within 9 in. of 64.

16. PRACTICE PROBLEMS The average height at TCC is 66 inches with a standard deviation of 4.5 inches. Display this information on a normal curve.

17. How tall is someone 2 standard deviations above the mean? Answer: 66+4.5+4.5=75 inches What percentage of students are between 61.5 and 70.5 inches? Answer: 68%

18. What percentage of students are below 70.5? Answer: 84% 50%+34%=84% What percentage of students are below 75? Answer: 97.5 What percentage of students are above 79.5? Answer: 0.15%