1. Distributions: The nature or shape of the data within its range.

2. 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.

3. 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.

4. 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.

5. 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.
Skewed Right Distribution (positively skewed)
The “tail” of the graph elongates more to the right.
The mean is to the right of the median.
Larson/Farber 4th ed.

6. 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.

7. Symmetry SKEWED LEFT SKEWED RIGHT SYMMETRIC
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
SKEWED LEFT
(negatively)
SKEWED RIGHT
(positively)
Mode = Mean = Median
SYMMETRIC
Mean
Mode
Median 7

8. Some Common Distribution Shapes8