636 Chapter 16 Business Statistics
Topics Key Ideas, Formulas, and Techniques Examples
Measures of
Variation, p. 626- Range highest value lowest value.
- Standard deviation is calculated by completing
the table as shown in this section.
Calculate the standard deviation of the
wind speeds of 2, 9, 16, 23, and 30 mph.
(Example 16.3.1)Interpreting
Standard
Deviation, p. 629- The higher the standard deviation, the greater
the variation. - The lower the standard deviation, the less the
variation.
Suppose that you are considering
investing in two different mutual funds.
Over the past 10 years, the annual returns
of the Hopewell American Growth Fund
have had a standard deviation of 11.25%.
The annual returns of the Hopewell
Adrenaline Aggressive Growth Fund have
had a standard deviation of 28.4%. Which
investment has seen the greatest variation
in its annual rates of return?
(Example 16.3.2)Chebyshev’s
Theorem, p. 629- At least ¾ of the data must fall within 2 standard
deviations of the mean. - At least 88.9% of the data must fall within
3 standard deviations of the mean.
If the mean is 78.2 and the standard
deviation is 8.3, use Chebyshev’s theorem
to interpret what this tells you about where
the class’s scores fell.
(Example 16.3.3)The Empirical
Rule, p. 630- Approximately 68% of the data falls within
1 standard deviation of the mean. - For 2 standard deviations the value is 95%, for
3, it’s 99%. - Can be used only if the data is normally
distributed (the bell curve).
Suppose that your teacher tells you that
the class’s test scores were normally
distributed. If the mean is 78.2 and the
standard deviation is 8.3, use the Empirical
Rule to interpret what this tells you about
where the class’s scores fell.
(Example 16.3.4)