Transcript 5 Minute Check, 26 Sep

Q1 = 16
Q3 = 44
IQR = 26 * 1.5 = 42
Prob and Stats, Sep 16
Measures of Variation II – Understanding
Measures of Variation and Other
Relationships
Book Sections: 2.4
Essential Questions: How do I compute and use statistical values? How
are measures of variation used and how do relationships between
categories manifest themselves?
Standards: S.ID.1, .2, .3, .4
Back to the Future
• We start this lesson at the doorstep of the
basic data representation, the frequency
histogram.
Manifestation of a Distribution
• A distribution (which is a sample set of data depicted
graphically) will appear today as a frequency histogram
with a curve imposed to illustrate symmetry.
President’s Ages at First Inauguration
Distribution Shapes
There are four basic shapes that the frequency
histogram takes on:
• Symmetric
• Uniform
• Skewed Left
• Skewed Right
The Picture of Data
Examples
• Name the approximate distribution that each graph represents.
1)
2)
3)
4)
More Examples (on the edge)
• Name the approximate distribution that each graph represents.
5)
6)
7)
8)
What Causes a Distribution to Be Skewed
• If the mean of a distribution is right of the
median, the set will be skewed right (the
‘bump’ is on the left)
• If the mean of a distribution is left of the
median, the set will be skewed left (the ‘bump’
is on the right)
• In a perfectly symmetric data set, the mean
and median are equal
Threshold of Skewness
• A distribution does not have to be perfect to be called
symmetric (and thus for the Empirical Rule to apply).
We will use an eyeball amount of tolerance on a not
perfectly symmetrical data set.
Mean and Standard Deviation
• Mean and standard deviation are related statistics
 Remember that the mean was a component of the variance
formula
• Standard deviation is a measure of how close (on
average) that the data is to the mean
• If a data set is fairly symmetrical, there is a special
rule that predicts how much data is within a multiple of
s to the mean – It is called the Empirical Rule
Understanding Measures of Variation
What is the Relationship Between Mean & Standard Deviation
The Empirical Rule
Normally Distributed Data
When the Empirical Rule Applies
• Data that has a symmetric distribution
(generally) is one in which the empirical rule
applies.
Empirical
Rule
Words 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 two standard
deviations of the mean
Example 1
• A data set has a mean of 58 and a standard
deviation of 19. What is the range of 68%,
95%, and 99.7% of the data?
Example 2
Of a sample of 808 men measured,
the mean was 69.9 in and the
standard deviation was 3 in.
• Roughly, which two heights contain the middle 95% of this data?
Example 3
• A symmetric data set has a mean of 50 and a
standard deviation of 10. What percent of the
data is between 40 and 60?
Class work: Classwork Handout 1-9
Homework: None