Distributions: The nature or shape of the
data within its range.
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Essentials: Distribution Shapes
(Lots of them , but we will focus on three main types.)
• Be able to explain what constitutes a distribution.
• Be able to identify Left, Right and Normal distributions
(and a Uniform distribution).
• Be able to determine if a distribution is normally distributed
or skewed through use of a formula or computer software
and, be able to interpret the results of this process.
Distributions can occur in a number of
shapes including:
• Symmetric – a distribution is symmetric if
the left half of the distribution is roughly a
mirror image of its right half.
• Skewed – a distribution is skewed if it is not
symmetric and if it extends more to one
side than the other
The Shape of Distributions
Symmetric Distribution
• A vertical line can be drawn through the middle of a
graph of the distribution and the resulting halves are
approximately mirror images.
Larson/Farber 4th ed.
4
The Shape of Distributions
Skewed Left Distribution
(negatively skewed)
• The “tail” of the graph
elongates more to the left.
• The mean is to the left of
the median.
Larson/Farber 4th ed.
Skewed Right Distribution
(positively skewed)
• The “tail” of the graph
elongates more to the right.
• The mean is to the right of
the median.
5
The Shape of Distributions
Uniform Distribution (rectangular)
• All entries or classes in the distribution have equal or
approximately equal frequencies.
• Symmetric.
Larson/Farber 4th ed.
6
Symmetry


Symmetry – a distribution is symmetric if the left half of the
distribution is roughly a mirror image of its right half.
Skewness – a distribution is skewed if it is not symmetric and if it
extends more to one side than the other
Mode
=
Mean
=
Median
SYMMETRIC
Mean
Median
Mode
SKEWED LEFT
(negatively)
Mode
Median
Mean
SKEWED RIGHT
(positively)