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T6-_Normal_Distribution_.pptx-Statistics Through Example Lexi René, MSPH
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T6-_Normal_Distribution_.pptx-Statistics Through Example Lexi René, MSPH
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T6-_Normal_Distribution_.pptx-Statistics Through Example Lexi René, MSPH
Page 1
Statistics
Through Example
Lexi René, MSPH


Page 2
Review


Page 3
Normal Distribution
A normal distribution is described by a normal density curve,
also called the “bell curve.”
The normal distribution is symmetric with a single peak.
Defined entirely by the mean (μ) and standard deviation (σ)
μ determines where the peak occurs
σ determines the shape of the curve
Notation for a normal distribution with mean (μ) and standard
deviation (σ):
N(μ,σ)


Page 4
Normal Distribution
Normal distributions with same mean (µ) but different standard
deviation (σ):


Page 5
Empirical Rule
The empirical rule gives precise guidelines for the
percentage of data that lie
within
1, 2, and 3 standard
deviations (SD) of the mean for any
normal distribution
.
What percentage of the data lies within… ?
1 SD: About 68% (more precisely, 68.3%)
2 SD: About 95% (more precisely, 95.4%)
3 SD: About 99.7%


Page 6
Empirical Rule
You can use the empirical rule
only
if
the distribution of the population is
normal
.


Page 7
Empirical Rule


Page 8
Empirical Rule
If we are given the
population data, we
will use the
population
parameters.
If we are given
sample data, we will
use the sample
statistics.
Either way, the
sample statistics and
the population
parameters follow
the same rule.


Page 9
Example


Page 10
Some Statistics
The CDC found that the combined total cases of gonorrhea,
chlamydia and syphilis in the United States reached an
unprecedented high in 2015 -- and people age 15 to 24
accounted for a large number of these new cases.
Center for Disease
Control


Page 11
Some Statistics
Center for Disease
Control


Page 12
Empirical Rule Example
Let’s say that we sample sexually active college students
around the country. Imagine that we found that the
average number of times a college student is tested for an
STD throughout a semester is 3, with a standard deviation
of 1.
(3,1)
Interpret this story using the Empirical Rule.


Page 13
Empirical Rule Example
Let’s say that we sample sexually active college students
around the country. Imagine that we found, that the
average number of times a college student is tested for an
STD throughout a semester is 3, with a standard deviation
of 1.
Calculations:
68%
95%
99.7%
M-o
3-1 =
2
M-2O
3-2=
1
M-3O
3-3=
0
M+o
3+1=
4
M+2O
3+2=
5
M+3O
3+3=
6


Page 14
Empirical Rule Example
About 68% of sexually active colleges students are tested
for
STDs
between
2
and
4
.
times a semester.
About 95% of sexually active colleges students are tested
for STDs between
1
.
and
5
.
times a semester.
About 99.7% of sexually active colleges students are tested
for STDs between
0
.
and
6
.
times a semester.


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