Statistics & Science
Statistics and Science
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What are statistics?
Statistics is a collection, classification, and
analysis of numbers.
Statistics is commonly used to describe:
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•
•
•
Sports
Politics
Health
Weather
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Mean
The mean is an
average.
Found by: Summing
and then dividing
the sum by the
amount of numbers.
Example: Find the mean of:
5, 8, 2, 1
• Add up the numbers:
5 + 8 + 2 + 1 = 16
• Divide the sum by the
number of scores: 4
• The mean is 16 ÷ 4 = 4
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Mean (µ) and Standard Deviation (σ)
The standard deviation is a measure of the
spread relative to the mean.
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If all the data points are clustered around
the mean, the standard deviation is low.
If the data points are widely dispersed
around the mean, the standard deviation is high.
If all the data points have the same value,
the standard deviation is zero.
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The Normal Distribution
• Bell-shaped
• Large data sets
• Characterized by:
 mean µ
 standard deviation s
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Errors and the
Normal Distribution
Measurements have random errors.
They often characterized by the normal
distribution.
Normal distribution  Probability of a given
error can be calculated.
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Normal Probability Distribution
• 68% of the data within
one standard deviation
of the mean.
• 95% of the data within
two standard deviations
of the mean.
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How are statistics related
to science?
• Science is about decision!
• Statistics  standards
for decisions.
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