Shapes of Distribution

Topics: Mode, Median, Skewness Pages: 4 (455 words) Published: October 12, 2013
4.2 Shapes of Distributions
Learning Goal: To be able to
describe the general shape of a
distribution in terms of its number
of modes, skewness, and
variation.

Number of Modes
—  One way to describe the shape of a

distribution is by its number of peaks, or
modes.
—  Uniform distribution—has no mode because
all data values have the same frequency.

Any peak is considered a mode, even if all
peaks do not have the same height.
—  A distribution with a single peak is called a

single-peaked, or unimodal, distribution.

—  A distribution with two peaks, even though not

the same size, is a bimodal distribution.

—  What is the following distribution?

How many modes would you expect for each of the following
distributions? Why? Make a rough sketch with clearly
labeled axes?

—  The body temperature of 2000 randomly

selected college students
—  The attendance at Disney World during

a year
—  The last digit of your phone number

Symmetry or Skewness
—  A distribution is symmetric if its left half

is a mirror image of its right half.

—  A symmetric distribution with a single

peak and a bell shape is known as a
normal distribution.

Symmetry or Skewness
—  A distribution is left-skewed

(or negatively skewed) if the values
are more spread out on the left,
meaning that some low values are
likely to be outliers.
—  A distribution is right skewed
or positively skewed if the
values are more spread out
on the right. It has a tail
pulled toward the right.

What is the relationship between mean,
median and mode for a normal distribution?
—  Find the mean median and mode of:

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7
—  Mean is 4.
—  Median is 4.
—  Mode is 4.

What is the relationship between mean, median
and mode of a left-skewed distribution?
—  Find the mean, median and mode of:

0, 5, 10, 20, 40, 45, 45, 50, 50, 50, 60, 60, 60, 60, 60,
60, 70, 70, 70, 70,...
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