Transcript The Normal Curve

Module 7 Percent Area and the
Normal Curve
• What it is
• History
• Uses
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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
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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
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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!
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History of Normal Curve
• Fred Gauss (who cares about)
– Laplace and DeMoive?
• Always looking up
• Noticed that orbit
• -estimates of planets
– Were normally distributed
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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
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Use of the Normal Curve
• The normal curve always has the following
proportions
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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
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Remember these Percentages
…you will use them
• The normal curve always has the following
proportions
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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
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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 %
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Uses:
% of Normal Curve
• What % have IQ between 85 and 115?
- Between + and – 1 SD?
- 34.13 + 34.13 = 68.26%
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