Mode Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Mode.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

The mode is the value that appears most often in a data set. A set can have no mode (all values appear equally), one mode (unimodal), or multiple modes (bimodal or multimodal). It is the only measure of center that works for categorical data.

The mode is the most popular value - the one that shows up the most. If 5 kids pick pizza, 3 pick tacos, and 2 pick burgers, pizza is the mode because it's the favorite.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Mode asks what single value best stands for the center of the data, then checks whether that value is fair for the situation.

Common stuck point: Students often know a procedure related to mode but skip the recognition step: Do I need one number that represents the center of the data, and have I checked whether extreme values change that choice? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Do I need one number that represents the center of the data, and have I checked whether extreme values change that choice?

Worked Examples

Example 1

medium

A survey of

50

kids' shoe sizes:

6

(5 kids),

7

(12),

8

(18),

9

(10),

10

(5). Find the mode and explain how a store would use it.

Answer

8

First step

Largest count

= 18

at size

8

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Example 2

hard

Why does a clothing retailer often care more about the mode than the mean of customer sizes?

Example 3

challenge

Construct a data set of seven positive integers whose mean is

6

, median is

5

, and mode is

4

Example 4

easy

Find the mode of the data set: 4, 7, 2, 7, 3, 7, 5, 2.

Example 5

medium

A shoe shop records sizes sold in one day: 6, 7, 8, 7, 9, 8, 7, 10, 8, 6. Is this data unimodal, bimodal, or multimodal?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Find the mode of

2, 3, 3, 5

Example 2

easy

Find the mode of

7, 7, 7, 4, 9

Example 3

easy

Find the mode of

1, 2, 2, 3, 3, 3

Dot plot of the data set {1, 2, 2, 3, 3, 3}

Example 4

easy

In responses pizza, pizza, taco, burger, what is the mode?

Example 5

easy

Find the mode of

5, 5, 8, 8, 8, 2

Example 6

easy

Find the mode of

10, 20, 30

Example 7

easy

Find the mode of

4, 4, 6, 6, 9

Dot plot of the data set {4, 4, 6, 6, 9}

Example 8

easy

Find the mode of

1, 1, 1, 1

Example 9

medium

A shoe store sold sizes

8,9,9,10,10,10,11

. Which size should they restock most?

Example 10

medium

3,5,5,7,7,9

, compare the mode count of

5

and

7

Dot plot of the data set {3, 5, 5, 7, 7, 9}

Example 11

medium

Data

2,4,4,4,6,6,8

has mean

a

and mode

b

. Find

b-a

Example 12

medium

A quiz score frequency table: score

3

(x2),

4

(x5),

5

(x3). Find the mode.

Example 13

medium

Add one value to

2,2,3,4

so the data becomes bimodal. What value?

Example 14

medium

Find the mode of

1.5, 2.5, 2.5, 2.5, 3.5

Example 15

medium

7,7,8,8,9,9

, how many modes are there?

Example 16

challenge

A set of five integers has mode

6

(appearing exactly twice), median

6

, and mean

5

. List a valid set.

Example 17

challenge

For data

x, x, y, z

with distinct

x,y,z

, prove the mode is always

x

Example 18

challenge

Data

a,a,a,b,b,c

has mode

a

. If one

a

is removed, when does it become bimodal?

Example 19

medium

Frequency table: red (x4), blue (x4), green (x2). Find the mode(s).

Example 20

medium

Data

5,5,6,7,8

gains one value to make

6

the mode. What value?

Example 21

easy

Find the mode of

4, 4, 5, 6, 6, 6, 7

Example 22

easy

Find the mode of

1, 2, 3, 4, 5

Example 23

easy

Find the mode of

9, 9, 9, 9, 9

Example 24

easy

Twenty students voted favorite color: red (5), blue (8), green (4), purple (3). What is the modal color?

Example 25

easy

Find the mode of

3, 3, 5, 5, 7

Dot plot of the data set {3, 3, 5, 5, 7}

Example 26

easy

Find the mode of

0, 1, 0, 2, 0

Example 27

easy

A frequency table shows letter grades: A (4), B (7), C (12), D (5), F (2). Find the modal grade.

Example 28

medium

Find the mode of

2, 3, 5, 7, 11, 13

Example 29

medium

A bakery sells

40

donuts:

15

glazed,

12

chocolate,

8

jelly,

5

maple. Which type is the mode, and what does it tell the baker?

Example 30

medium

Data:

\{1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5\}

. Find mean, median, and mode.

Example 31

medium

Why is the mode the only measure of center that works for categorical data like favorite ice cream flavor?

Example 32

medium

Data:

\{1, 1, 2, 2, 3, 3, 4, 4\}

. What is the mode?

Example 33

medium

The mode of

\{4, 7, 4, x, 8, 7, 9\}

7

. Which values of

x

make this true?

Example 34

medium

A histogram of test scores has its tallest bar at the

80

89

range. What value is the modal class?

Example 35

medium

Data:

\{12, 15, 12, 18, 12, 20, 15, 12\}

. Find the mode and its frequency.

Example 36

hard

A data set has mean

5

, median

5

, and mode

5

. What does this say about the shape?

Example 37

hard

Data:

\{3, 3, 5, 5, 5, 7, 7, 9, 9, 9, 11\}

. Find the modes.

Dot plot of the data set {3, 3, 5, 5, 5, 7, 7, 9, 9, 9, 11}

Example 38

hard

Data:

\{2, 5, 7, 7, 8\}

. Find mean, median, mode and decide which best describes a 'typical' value.

Example 39

hard

If every value in a unimodal data set is doubled, what happens to the mode?

Example 40

hard

Survey:

25

kids picked favorite subject. Math

= 8

, Science

= 8

, English

= 5

, Art

= 4

. What is the mode?

Example 41

easy

Find the mode of: Red, Blue, Green, Blue, Red, Blue, Green, Yellow.

Example 42

easy

Find the mode or modes of the data set: 2, 4, 4, 6, 6, 8, 9.

← Back to Mode Formula Explained Practice Mode

Related Concepts

Tally Chart Spread vs Center Mean as Fair Share Median

Background Knowledge

These ideas may be useful before you work through the harder examples.

tally chartspread vs center