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. Teacher
Introductory Statistics
Lesson 2.4 C
Objective: SSBAT interpret standard deviation and use
the Empirical Rule.
Standards: S2.5B
Review
Review
Variation of Data
 Describes how spread out or scattered the data is
Deviation of an Entry in a population
Measures of Variation
 The Difference between an entry in the data set (x)
and the mean of the data set
Deviation of x = x – ࣆ
1. Range
2. Variance
3. Standard Deviation
Salary (thousands $)
x
Deviation
x – 41.5
41
-0.5
38
-3.5
39
-2.5
45
3.5
47
5.5
41
-0.5
44
2.5
41
-0.5
37
-4.5
42
0.5
Standard Deviation: ߪ = 2.97
 Deviation is the distance each entry is away from the
Mean. We could not average the deviations together
because the sum will always be zero.
 Therefore, we squared each deviation and then found
the mean of these values – This was referred to as
the Variance
 Then, we square rooted the variance to come up with
the Standard Deviation – This gave us the typical
amount an entry deviates from the mean.
1
. Teacher
Standard Deviation  ࣌ or s
Bell Shape Curve (Normal Distribution)
 A measure of the Typical amount an entry
deviates from the Mean
 The distribution is symmetrical
(The typical difference an entry is away from
the mean)
 The more the entries are spread out, the
greater the standard deviation.
 When all the data entries are the Same, the
standard deviation is 0
http://www.tangopadawan.com/2008/05
Empirical Rule
Empirical Rule
For data with a bell-shape (symmetrical) distribution, the
Standard Deviation has the following characteristics:
 About 68% of the data lie within ONE standard
deviation of the mean (1 on each side of mean)
 About 95% of the data lie within TWO standard
deviations of the mean (2 on each side of mean)
 About 99.7% of the data lie within THREE
standard deviations of the mean (3 on each side of
mean)
Examples Using Empirical Rule
1. The mean rate for satellite television from a
sample of households was $49.00 per month,
with a standard deviation of $2.50 per month.
Between what 2 values does 99.7% of the data
lie?
 99.7% of the data lies within 3 standard
deviations of the mean
 Therefore, Add 2.50 three times to the mean
and then Subtract it three times from the
mean to get the two endpoints
http://sites.stat.psu.edu/~ajw13/stat200_notes/01_turning/graphics/emp_rule.gif
1. Continued
The mean rate for satellite television from a sample of
households was $49.00 per month, with a standard
deviation of $2.50 per month. Between what 2
values does 99.7% of the data lie?

49 + 2.5 + 2.5 + 2.5 = 56.5

49 – 2.5 – 2.5 – 2.5 = 41.5
 Therefore 99.7% of the data lies between
$41.50 and $56.50.
2
. Teacher
2. SAT verbal scores in a particular year were
normally distributed (bell shaped) with a Mean
of 489 and Standard Deviation of 93. Between
what two values does 68% of the data lie?
 68% of the data lies within 1 standard
deviation of the mean
 Therefore, Add 93 one time to the mean
and then Subtract it one time from the mean
to get the two endpoints
2. Continued
SAT verbal scores in a particular year were
normally distributed (bell shaped) with a Mean
of 489 and Standard Deviation of 93. Between
what two values does 68% of the data lie?

489 + 93 = 582

489 – 93 = 396
 Therefore, 68% of the data lies between
396 and 582.
Homework: Worksheet 2.4 C
3
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