Download Lesson 28 Sep IV

Math Tech IIII, Sep 28
The Empirical Rule 3
Book Sections: 2.4
Essential Questions: How do I compute and use statistical values? What
is the Empirical Rule? How can I use the Empirical Rule?
Standards: PS.SPID.1, .2, .3
The Empirical Rule
• A symmetric data set (mean and median about equal) has a
consistent distribution that relates the mean, standard
deviation, and a percent of data interval for all such
distributions.
• The Empirical Rule only applies to symmetric
distributions.
TheWords
Empirical
Rule
and Graph Together
• 68% of the data lies within
one standard deviation of the
mean
• 95% of the data lies between
two standard deviations of the
mean
• 99.7% of the data lies
between three standard
deviations of the mean
Standard Deviation Thresholds
• 68% - 1 x Standard deviation
• Range ( x - s, x + s)
•95% - 2 x Standard deviations
• Range ( x - 2s, x + 2s)
•99.7% - 3 x Standard deviations
• Range ( x - 3s, x + 3s)
Empirical Rule Problems
• Based on deviations (1, 2, or 3), you are trying to list a
range containing a percent.
x  sd  upper _ bound
• Given a range, determine a deviation (1, 2, or 3) that
corresponds to a percent. Solve this equation for d to
determine the deviation:
If d = 1, ans = 68%; d = 2, ans = 95%; d = 3, ans = 99.7%.
Example 1
• In a symmetrically distributed data set with a mean of 17
and a standard deviation of 4, what percent of that data lies
between 13 and 21?
Example 2
• Per the Empirical Rule, what is the range of 99.7% of the data in a
symmetrically distributed data set with a mean of 37 and a standard
deviation of 12?
Example 3
• In a symmetrically distributed data set with a mean of 100
and a standard deviation of 15, what percent of that data lies
between 85 and 115?
Example 4
• In a symmetrically distributed data set with a mean of 62
and a standard deviation of 8, what is the range of the
middle 68% of the data?
Example 5
• In a symmetrically distributed data set with a mean of 211
and a standard deviation of 12, what is the range of the
middle 95% of the data?
Example 6
• In a symmetrically distributed data set with a mean of 16
and a standard deviation of 3, what percent of the data lies
between 7 and 25?
Class work: CW 9/28/16, 1-10
Homework: None