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Statistics: Normal Distributions, 68-95-99.7 Rule
Contemporary Math
Josh Engwer
TTU
04 August 2015
Josh Engwer (TTU)
Statistics: Normal Distributions, 68-95-99.7 Rule
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Increasing the Sample Size of a Data Set
n = 25
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Increasing the Sample Size of a Data Set
n = 50
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Statistics: Normal Distributions, 68-95-99.7 Rule
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Increasing the Sample Size of a Data Set
n = 100
Josh Engwer (TTU)
Statistics: Normal Distributions, 68-95-99.7 Rule
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Increasing the Sample Size of a Data Set
n = 1000
Josh Engwer (TTU)
Statistics: Normal Distributions, 68-95-99.7 Rule
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Increasing the Sample Size of a Data Set
n = 5000
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Statistics: Normal Distributions, 68-95-99.7 Rule
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Normal Distributions
A normal distribution describes many real-life populations such as:
Heights of people
Lifespans of a certain model consumer electronic device
Standardized exam scores
NOTATION: µ ≡ Mean of Population
NOTATION: σ ≡ Std. Dev. of Population
Josh Engwer (TTU)
(Greek letter ”mu”)
(Greek letter ”sigma”)
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Normal Distributions (Properties)
Proposition
(Properties of a Normal Distribution)
Mean = Median = Mode = µ
Curve is bell-shaped & symmetric w.r.t its mean, µ
The total area under the curve is 1
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Statistics: Normal Distributions, 68-95-99.7 Rule
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Varying σ Changes the Shape of a Normal Distribution
µ = 10
σ=1
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Varying σ Changes the Shape of a Normal Distribution
µ = 10
σ=2
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Statistics: Normal Distributions, 68-95-99.7 Rule
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Varying σ Changes the Shape of a Normal Distribution
µ = 10
σ=3
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68-95-99.7 Rule
Given a normal distribution:
Roughly 68% of the data values are within 1 standard deviation from the
mean.
Josh Engwer (TTU)
Statistics: Normal Distributions, 68-95-99.7 Rule
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68-95-99.7 Rule
Given a normal distribution:
Roughly 95% of the data values are within 2 standard deviations from the
mean.
Josh Engwer (TTU)
Statistics: Normal Distributions, 68-95-99.7 Rule
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68-95-99.7 Rule
Given a normal distribution:
Roughly 99.7% of the data values are within 3 standard deviations from the
mean.
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68-95-99.7 Rule
Given a normal distribution:
Roughly 50% of the data values are less than the mean.
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68-95-99.7 Rule
Given a normal distribution:
Roughly 50% of the data values are greater than the mean.
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Fin
Fin.
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