Practice Mode in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The mode is the value or values that appear most frequently in a data set — it is the most common or most popular data value.

The mode is the "most popular" value — if you had to guess one number and wanted to be right as often as possible, pick the mode.

Showing a random 20 of 50 problems.

Example 1

easy

Find the mode of

4, 4, 4, 9, 9

Example 2

medium

The data set

\{3, 5, 5, 7, 8, x\}

has mean

5.5

and mode

5

. Find

x

Example 3

challenge

Explain why a perfectly uniform data set like

5,5,7,7,9,9

is ambiguous for the mode.

Example 4

medium

\{2, 5, 5, 7, 9, 9, 9, 12\}

, find the mode and the gap between mode and mean.

Example 5

easy

Find the mode of

\{4, 4, 7, 7, 7, 9, 11\}

Example 6

medium

The data

9, 11, 11, 13, 15

— find the mode and state whether it is unique.

Example 7

challenge

Construct a

10

-value data set where mode

=2

, median

=5

, and mean

=10

Example 8

medium

A frequency table lists: value

1

(count 4), value

2

(count 9), value

3

(count 9), value

4

(count 2). Find the mode.

Example 9

easy

Find the mode of

\{0, 0, 1, 2, 3\}

Example 10

easy

In the data

10, 10, 20, 30, 30, 30

, find the mode.

Example 11

medium

3, 5, 5, 7, 7, 7, 9, x

, the unique mode is

7

. What values of

x

are allowed?

Example 12

easy

Find the mode of

5, 6, 7, 8

Example 13

medium

Test scores:

80, 80, 85, 90, 90, 95, 100

. Compare mode, median, mean.

Example 14

medium

Find the mode of

\{2.1, 2.1, 2.1, 3.0, 4.5, 5.0\}

Example 15

easy

True or false: the mode must be a value that appears in the data set.

Example 16

easy

Shoe sizes sold:

6, 7, 7, 8, 8, 8, 9, 10

. Find the mode.

Example 17

medium

Find the mode of

2.5, 2.5, 3.1, 3.1, 3.1, 4.0

Example 18

hard

For data set

\{x_1, x_2, \ldots, x_n\}

with unique mode

m

, prove that any data set you get by adding values

\ne m

keeps the mode if you add fewer than

(\text{count of } m) - (\text{next highest count})

extra of any single value.

Example 19

medium

A data set

a, a, b, b, b, c

has mode

b

. After removing one

b

, what is the new mode?

Example 20

hard

A data set has values

\{5, 5, 5, 7, 9, 12\}

. If you append a value

v

so the new set is bimodal with modes

5

and

7

, what must

v

be?

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Related Concepts

Mean Median Frequency