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Statistics 528  Lecture 3
Prof. Kate Calder
1
Section 1.1/1.2
Graphical and Numerical Summaries of Data
•
Shape of a Distribution
–
Modes
–
Symmetric vs. Skewed
–
Outliers
•
Measures of the Center
–
mean
–
median
•
Measures of Spread
–
IQR
–
standard deviation
•
Choosing Summaries of Distributions
•
Changing the Units of Measurement
Statistics 528  Lecture 3
Prof. Kate Calder
2
Modes
•
Question: Does the distribution have one or several major peaks?
Look at histograms and stemplots.
•
A distribution with one major peak is called
unimodal
. A
distribution with two major peaks is called
bimodal
.
•
Example of a bimodal distribution: scores on an exam
Statistics 528  Lecture 3
Prof. Kate Calder
3
Symmetric vs. Skewed
•
A distribution is
symmetric
if the values larger or smaller than the
midpoint are mirror images of each other.
•
A distribution is
skewed to the right
if the right tail (larger values) is
much longer than the left tail (smaller values).
•
A distribution is
skewed to the left
if the left tail (smaller values) is
much longer than the right tail (larger values).
Statistics 528  Lecture 3
Prof. Kate Calder
4
Left Skewed Symmetric Right Skewed
Statistics 528  Lecture 3
Prof. Kate Calder
5
Statistics 528  Lecture 3
Prof. Kate Calder
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Outliers
Outliers
– values that fall outside the overall pattern and are far from
the bulk of the data
•
Can be a result of natural variation.
•
Or, can be evidence of a mistake (equipment failure, incorrect
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 Winter '09
 Calder
 Statistics, Standard Deviation, Prof. Kate Calder

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