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Algebra 1
Notes
Questions/Main Ideas:
Name: ________________________
Period: _______Date: ____________
TOPIC: STANDARD DEVIATION
Recall: a statistic Describes a data set (tells something about a data set)
Standard Deviation is a statistic that measures the spread of the data AWAY FROM
THE MEAN (average).
Think of Deviation as “how far from the average”

The symbol for Standard Deviation is called “Sigma”
The buttons to push
to get L1 are:

Where have we seen the
before?
In the same place we find
X
After you put a data set into the L1 then press
STAT
ENTER
1

Where do you find the sigma? The 5th item down in the list
Use your calculator to find the Standard Deviation and the mean of the following data set.
X  ______
{ 2, 4, 5, 5, 7, 7, 8, 10 }
Standard Deviation is used to measure a
The sample mean x̄
is what you compute
from your random
sample in order to
ESTIMATE the
population mean μ.
The sample mean is
summed over the
sample size n. The
population mean is
summed over the
population size N or
even ∞, if you knew
the whole
population. Usually
you do not, which is
why you take a
sample in the first
place.
By estimating μ with
x̄ you have an error,
called the sampling
error. They are not
the same thing.
Many different
samples will
produce different x̄
's for the same
population. The
Distance above and below the mean value of the data set.
  _____
Map the data set on this number line
{ 2, 4, 5, 5, 7, 7, 8, 10 }
X or 
0
-3

3
-2

“Mean”
6
-1

9
+1

+2
12

+3

 the Count of the Standard
Deviations
usual

Which values in the data set are within one standard deviation of the mean?
Which values are between
+1  and +2  ?
Are any values beyond 2  away from the mean?
________
________
________
To do the following problem we need to know the mean and the standard
deviation.
X  ___ 66.3 ___
Given the following data set { 53, 63, 62, 64, 66, 68, 70, 72, 79 }
Determine:
Which values are unusual
  ___ 6.84 __
_______ (How do we know “unusual” ? )
What is the value 2 standard deviations below the mean _______
Which value is within the first deviation from the mean
_______
Which values are between -1  and -2  from the mean
_______
How many values are below the mean? _______
Uses of Standard Deviation
If the mean temperature over the past 100 years for the first day in June in the city of Eye
Brow Kentucky is 89.5° Find the temperature that is 2 standard deviations below the
mean if the Standard Deviation is 6.5° degrees.
If the Height of the average full grown Collie is 37 inches with a Standard Deviation of 2.5
inches. Find the Height of a dog that is three standards above the mean.
If the average weight of a bottle of Ketchup is 567 grams with a standard deviation of 5.5
grams, find the weight of a bottle that is 4 standard deviations below the mean.
If the average bottle of ketchup weighs 567 grams. How many standards above a normal
bottle is a bottle that weighs 600 grams. Use a standard Deviation of 5.5 g
Standard Deviation Facts
 is for data that is normally distributed
68%,
Normally distributed is Data the is not skewed
Data that is centered close to the mean
Data that generally follows the
68, 95, 99 rule
95%, 99%