# Shapes of Distribution

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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