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The Normal distribution

The Normal distribution. and the 68-95-99.7 Rule. skewed distributions & outliers. Normal = typical. This is valuable information when studying human behavior

chandler-wiley
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The Normal distribution

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  1. The Normal distribution and the 68-95-99.7 Rule

  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. Describing ‘normal’ w/ stats CENTRAL TENDENCY VARIATION • Standard Deviation • Range • Mean • Median • Mode

  5. In order to interpret the Normal curve both pieces of information are necessary. Why?

  6. i.e., the average score on the quiz was 50 points… • 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?

  7. I.E., the SD on the quiz was 5 • 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?

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

  9. 68% of all data will fall within onestandard 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%

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