DENSITY CURVES AND THE NORMAL DISTRIBUTION

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Chapter 2

• DENSITY CURVES AND THE NORMAL DISTRIBUTION

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Density Curve

• A graph that represents the relative frequency
  distribution for a set of data
• It can be used to describe the overall pattern of
  a distribution.
• Often an idealized version Mathematical Model
• ALWAYS above or on the horizontal axis
• ALWAYS bounds AREA 1
• AREA bounded is used to tell the proportion of
  observations within a range of values.

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Examples
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FROM HISTOGRAM TO A DESITY CURVE
TOTAL AREA OF ALL BARS 1
A Mathematical Model an idealized
representation of reality
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ACTUAL OF SCORES LESS THAN 6 .. IS THE AREA OF
THE HISTOGRAM BARS
AREA 0.303
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AREA OF THE APPROXIMATED DENSITY CURVE IS NOT
EXACT!
AREA OF SHADED REGION 0.293 (i.e. 0.01
lower than the actual area)
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Total Area 1.00
Area .12
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Lets ROLL A DISTRIBUTION

• P.84 2.5
• Simulate the act of Rolling a single die
• 1, 2, 3, 4, 5, 6
• Clear L1
• MATH gtgtgt PRB 5RandInt(1, 6, 100)
• STO ? L1
• WINDOW X 1, 7 Y -5, 25 YScl 5
• STAT PLOT Histogram for L1
• Repeat Are we all the same?

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Mean and Median

• MEAN If the distribution were to be made out of
  solid material the MEAN would be the balancing
  point.
• MEDAIN The point where the area under the curve
  is divided into to equal halves.
• Same ideas from last chapter regarding the
  impact of skewing.
• Skewed Data

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The NORMAL Distribution

• Normal Distribution

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Points of Inflection . ONE Standard Deviation
from the MEAN
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