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Chapter 3: Measures of Variability
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Observe that there will be more variability for the number of fatalities when
compared to the number of killer tornadoes.
Section Review
3-7
The Empirical Rule
Knowing the value of the mean and the value of the standard deviation for a
data set can provide a great deal of information about that data set. In
particular, if the data set has a generally “bell-shaped” distribution, then one
can state certain properties of the distribution, in terms of the mean and the
standard deviation, which will hold for any such shaped distributions. These
properties constitute what we refer to as the
Empirical Rule
. This rule
gives some general statements relating the mean to one standard deviation,
two standard deviations, and three standard deviations for any bell-shaped
distribution.
We will use data to illustrate the Empirical Rule.
Illustration:
The following data set summarizes the chest sizes of Scottish
militiamen in the early 19th century. Chest sizes are measured in inches,
and each observation reports the number of soldiers with that chest size.
Data Source:
http://lib.stat.cmu.edu/DASL/Datafiles/MilitiamenChests.html Click here for the Basic Statistics Workbook e-Self Review