Report

Module 7 Percent Area and the Normal Curve • What it is • History • Uses 1 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 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 Normal Curve • Theoretical distribution – If an infinite number of observations were collected • But smaller Ns distribute themselves normally – But only IF….the underlying population is normally distributed! • Ns of 30 to 40 are usually enough • N of a few hundred is plenty! 4 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 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 Use of the Normal Curve • The normal curve always has the following proportions 7 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 Remember these Percentages …you will use them • The normal curve always has the following proportions 9 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 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 Uses: % of Normal Curve • What % have IQ between 85 and 115? - Between + and – 1 SD? - 34.13 + 34.13 = 68.26% 12