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BEYOND THE BASICS OF

MEASURES OF
VARIATION
(Class Lecture in Statistics)

Part 6

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Range Rule of Thumb

minimum “usual” value
= (mean) – 2  (standard deviation)

 x  2s

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Range Rule of Thumb
 Usual values fall between the
maximum and minimum usual
values:

x  2s  x  x  2s
 Otherwise the value is unusual

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Example: Standard Deviation
Data (kg):
11 3 0 -2 3 -2 -2 5 -2
7 2 4 1 8 1 0 -5 2
Range rule of thumb:

11  (5) 16
s
  4 kg
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Properties of the
Standard Deviation
•

For many data sets, a value is
unusual if it differs from the mean
by more than two standard
deviations

• Compare standard deviations of

two different data sets only if the
they use the same scale and units,
and they have means that are
approximately the same
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7) Rule
For data sets having a distribution that is
approximately bell shaped, the following
properties apply:

 About 68% of all values fall within 1
standard deviation of the mean
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 About 99
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The Empirical Rule

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Chebyshev’s Theorem
The proportion (or fraction) of any set of
data lying within K standard deviations of
the mean is always at least 1–1/K2, where K
is any positive number greater than 1
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 For K = 3, at least 8/9 (or 89%) of all
values lie within 3 standard deviations
of the mean
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Comparing Variation in
Different Samples
It’s a good practice to compare two sample
standard deviations with s only when the
sample means are approximately the
same
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Sample

CV =

s · 100%
x

Population

CV =

s
· 100%
m

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Rationale for using n – 1
versus n
There are only n – 1 independent
values
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It causes s2 to
target 2 whereas division by n
causes s2 to underestimate 2
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Thank you for viewing /

purchasing! I hope you
learned something!

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