Statistics 2.2.1 - Mr. Fadoir's Website
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Transcript Statistics 2.2.1 - Mr. Fadoir's Website
Section 2.2, Part 1
Standard Normal
Calculations
AP Statistics
Berkley High School/CASA
Comparing data sets
How do we compare results when they are
measured on two completely different
scales?
One solution might be to look at
percentiles
What might you say about a woman that is
in the 50th percentile and a man in the 15th
percentile?
AP Statistics, Section 2.2, Part 1
2
Another way of comparing
Another way of comparing: Look at
whether the data point is above or below
the mean, and by how much.
Example: A man is 64 inches tall. The
heights of men are normally distributed
with a mean of 69 inches and standard
deviation of 2.5 inches.
AP Statistics, Section 2.2, Part 1
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Another way of comparing
Example: A man is 64 inches tall. The
heights of men are normally distributed
with a mean of 69 inches and standard
deviation of 2.5 inches.
We can see that the man is below the
mean, but by how much?
AP Statistics, Section 2.2, Part 1
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Another way of comparing
Example: A man is 64
inches tall. The
heights of men are
normally distributed
with a mean of 69
inches and standard
deviation of 2.5
inches.
z
x
64 69
z
2.5
z 2
AP Statistics, Section 2.2, Part 1
5
z-scores
The z-score is a way
of looking at every
data set, because
each data set has a
mean and standard
deviation
We call the z-score
the “standardized”
score.
z
x
64 69
z
2.5
z 2
AP Statistics, Section 2.2, Part 1
6
z-scores
Positive z-scores mean
the data point is above
the mean.
Negative z-scores mean
the data point is below
the mean.
The larger the absolute
value of the z-score, the
more unusual it is.
z
x
64 69
z
2.5
z 2
AP Statistics, Section 2.2, Part 1
7
Using the z-table
We can use the ztable to find out the
percentile of the
observation.
A z-score of -2.0 is at
the 2.28 percentile.
z
x
64 69
z
2.5
z 2
AP Statistics, Section 2.2, Part 1
8
Cautions
The z-table only gives the amount of data
found below the z-score.
If you want to find the portion found above
the z-score, subtract the probability found
on the table from 1.
AP Statistics, Section 2.2, Part 1
9
Standardized Normal Distribution
We should only use the z-table when the
distributions are normal, and data has
been standardized
N(μ,σ) is a normal distribution
N(0,1) is the standard normal distribution
“Standardizing” is the process of doing a
linear translation from N(μ,σ) into N(0,1)
AP Statistics, Section 2.2, Part 1
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Example
Men’s heights are N(69,2.5).
What percent of men are taller than 68
inches?
AP Statistics, Section 2.2, Part 1
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Working with intervals
What proportion of men are between 68 and
70 inches tall?
AP Statistics, Section 2.2, Part 1
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Working backwards
How tall must a man be in order to be in
the 90th percentile?
AP Statistics, Section 2.2, Part 1
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Working backwards
How tall must a woman be in order to be in
the top 15% of all women?
AP Statistics, Section 2.2, Part 1
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Working backwards
What range of values make up the middle
50% of men’s heights?
AP Statistics, Section 2.2, Part 1
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Assignment
Exercises 2.19 – 2.25, The Practice of
Statistics.
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