1. Module 7 Percent Area and the Normal Curve What it is History Uses 1

2. Normal Curve Characteristics Inflection points (at + and – 1 SD) – Where slopes changes from down to out. Axes – X –axis (abscissa) =Scores (as usual) – Y –axis (ordinate) = freq of scores or % Asymptotic – Tails never touch abscissa – Allows for extreme scores 2

3. The Normal Curve The normal curve is symmetric, bell shaped, and asymptotic The inflection points fall at one standard deviation above and below the mean 3

4. Normal Curve Theoretical distribution – If an infinite number of observations were collected But smaller Ns distribute themselves normally – But onl y IF….the underlying population is normally distributed! Ns of 30 to 40 are usually enough N of a few hundred is plenty! 4

5. History of Normal Curve Fred Gauss (who cares about) – Laplace and DeMoive? Always looking up Noticed that orbit -estimates of planets – Were normally distributed 5

6. Sir Francis Galton Noticed that IQ is normally distributed – In the population And so is practically everything else – Psychological – Physical (height, weight) – Behavioral (achievement, sexual behavior) – Gun shots at a target (or person!) – As long as the events are independent 6

7. Use of the Normal Curve The normal curve always has the following proportions 7

8. Uses But real work events don’t always play by the rules – Because many are not independent – Can you think of some examples (Think about things that are related) Nevertheless …the Normal Curve is still useful – For real world “lumpy” or skewed distributions – i.e. “robust” to minor violations of shape 8

9. Remember these Percentages …you will use them The normal curve always has the following proportions 9

10. Uses con’t Look at p 92 figure 7.4 What are the Ms an SDs for: – IQ score? M = 100; SD =15 – SAT score? M =500; SD = 100 – Height (US adult males) M = 69.5 in; SD = 2 inches 10

11. Uses con’t With the known M and SD – We can use the percentages(under the curve) To interpret INDIVIDUAL scores E.g. the relative number of those scoring in porportoins of the curve – What % of males are taller than 6’ 3 ½”? (75.5 in) 0.13% (just a very few)…less tha 1/10 percent Notice that includes everyone below that height – Taller than 99.47 % 11

12. Uses: % of Normal Curve What % have IQ between 85 and 115? -Between + and – 1 SD? -34.13 + 34.13 = 68.26% 12