Download Distribution Shapes

DISTRIBUTIONS: THE NATURE OR SHAPE
OF THE DATA WITHIN ITS RANGE.
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
 Uniform - Each value occurs in approximately the same amount.
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)
Some Common Distribution Shapes