Download Normal Distributions and the Empirical Rule

Given the following data
82, 94, 81, 93, 80, 100, 97, 102, 80, 80, 81
Find the mean, median, and the mode.
Sketch a box and whisker plot
Create a frequency table with width size of 5
starting at 80 -84. Then find the angles to
represent each width.
Normal Distributions
and the Empirical Rule
OBJECTIVE: Use the empirical rule (68-95-97 rule) to
analyze data
Page 11
Data that is normally distributed
 ACT or SAT Scores
 Height
 IQ scores
 Biological measures
Normal Distribution
Normal Distribution is a type of
frequency distribution graph.
The graph of a Normal Distribution is
called a statistic distribution curve or
more commonly referred to as a bell
curve. .
Properties of the Normal
Distribution





Mean, median, & mode are the same
The data is symmetric about the mean
Area under the curve equals 1 or 100%.
Curve never goes below the x-axs
Standard deviation σ controls the spread of the
curve.
Limits to the mean and standard
deviation
 The mean ranges between 1 and infinity
 The standard deviation must be positive
The Empirical rule
(68-95-99.7 rule)
In the normal dist. with mean μ and
standard deviation σ.
 50% of the observations fall below the
mean.
 50% of the observations fall above the
mean.
The Empirical rule
(68-95-99.7 rule)
In the normal dist. with mean μ and
standard deviation σ.
 68% of the observations fall within 1σ of
the mean.
 95% of the observations fall within 2σ of
the mean.
 99.7% of the observations fall within 3σ of
the mean.
Behold the normal curve
68%
34%
0.15%
2.35%
13.5%
95%
99.7%
34%
13.5%
2.35% 0.15%
Let’s Practice (p. 12)
Classwork & Homework
 Classwork – get with your project partner
and decide on a topic for your project and
a time to complete the survey.
 Homework – page 13 in your packet