Transcript 5.1 Normal Distribution - Palisades School District

Statistical Reasoning
for everyday life
Intro to Probability and
Statistics
Mr. Spering – Room 113
5.1 Normal Distribution
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Distribution:
 Describe how the data might be skewed.
 The incomes of people sitting in luxury boxes at the World
Series.
 The salaries of NFL football players on any particular team.
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Right skewed, very wealthy (outlier?)
Right skewed, some unique players make much more than the
majority of their teammates
5.1 Normal Distribution
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Normal Distribution symmetric…
 Bell shaped distribution…
 Single peak…
 Its peak corresponds to the mean, median, and mode of
the distribution.
 Its variation can be characterized by the standard
deviation.
 Also called the Gaussian distribution, after the famous
mathematician Carl Friedrich Gauss
5.1 Normal Distribution
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Examples Normal
Distribution Any unimodal
symmetric
data…
 Chest
Circumference
 Height
 Weight
 SAT scores
 Statistics from
large
populations…?
5.1 Normal Distribution
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Thinking test….is the data normal?
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11th Grade Language Arts Test scores
Skewed left
Weights of Great Danes compared to all canines
Skewed right
Ages of individuals in Florida
Relatively normal possibly skewed left
Heart rates of high school students
Normal
Normal Distribution in
the Cartesian Coordinate Plane
y
e
1
 [  x    /  ]2
2
 2
5.1 Normal Distribution
What is the total relative frequency for
any data set?
 100% or 1
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How does relative frequencies relate to normal
distribution?
Because the total relative frequency must be 100% or
1, the total area under the normal distribution curve
must be 1.
Area Under Curve
100%
or 1 the normal
Therefore the area that= lies
under
distribution curve corresponding to a range of values on
the horizontal axis is the relative frequency of those
values.
5.1 Normal Distribution
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ESTIMATING AREAS:
In the normal distribution below estimate the
percentage under the curve highlighted in red.
≈ 85% to 90%
Hence, approximate the area highlighted in blue.
≈ 10% to 15%
5.1 Normal Distribution
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More with what makes a variable normally
distributed?
1.
2.
3.
4.
The variable is determined by many different
factors (i.e. physiological variables or performance
variables)
The frequencies of the variable cluster around a
single peak that is near the mean of the
distribution.
The frequencies of the variable are symmetric
about the peak.
Large deviations from the mean are increasingly
rare.
5.1 Normal Distribution
Let’s try some more…
WHAT ABOUT….
Scores on a very difficult exam..
Right Skew, outlier 100%
Heights of random women…
Normal
In remembrance of Apple Crunch
day…the number of apples in each of
100 full bushel baskets…
Normal
5.1 Normal Distribution
SOME FUN…(TECHNOLOGY IS AWESOME!)
BellCurves.nbp
AreaOfANormalDistribution.nbp
SampleVersusTheoreticalDistribution.nbp
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http://www.shodor.org/interactivate/activities/skewdistribution/?versi
on=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc.
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
5.1 Normal Distribution
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HOMEWORK:
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Pg 201 Exercises: # 1-20 all
WORK