Line Plots Examples in Math

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

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

Concept Recap

A line plot (dot plot) displays data by placing marks (dots or Xs) above a number line to show the frequency of each value.

Like stacking coins above each number — taller stacks mean that value appeared more often in the data.

Read the full concept explanation →

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: A line plot piles dots or Xs above each value on a number line to show how often it appears.

Common stuck point: The procedure for line plots is the easy part; the trap is leaving out values with zero marks. Asking "Am I stacking a mark for each data point above its value on a number line to show frequency?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I stacking a mark for each data point above its value on a number line to show frequency?

Worked Examples

Example 1

medium

Plot:

4\to 2

5\to 4

6\to 3

7\to 1

. Find the median.

Answer

5

First step

Total dots

= 2+4+3+1 = 10

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Example 2

medium

A line plot shows lengths in

\tfrac{1}{4}

-inch units:

\tfrac{1}{4}\to 2

\tfrac{2}{4}\to 3

\tfrac{3}{4}\to 1

. Find the total length.

Example 3

medium

A line plot of book pages read by

5

kids shows the mean is

20

. Four of the values are

10, 15, 20, 25

. What is the fifth?

Example 4

hard

Plot: values

1, 2, 3, 4

with frequencies

3, 4, 2, 1

and one more dot at unknown value

v

. The total sum of the data is

24

. Find

v

Example 5

hard

A line plot of weekly hours studied:

2\to 1

3\to 2

4\to 4

5\to 2

6\to 1

. If each value increases by

2

hours, what is the new mean?

Example 6

hard

Plot of lengths (in.):

\tfrac{1}{2}\to 3

1\to 2

1\tfrac{1}{2}\to 4

2\to 1

. Find the total length.

Example 7

challenge

Two line plots have the same range

[0, 10]

, same total count

20

, and same median

5

. Plot A:

0\to 10

10\to 10

. Plot B: all

20

dots at

5

. Which has greater spread, and what does this tell you about median alone as a summary?

challenge

A line plot has values

1, 2, 3

with frequencies

1 \to 2

2 \to a

3 \to 2

, for a total of

9

data points. What is the mean?

Example 17

challenge

Two line plots have the same range and median but look different. What feature must differ?

Example 18

challenge

A plot of 10 values has mean 6. If every value increases by 2, what is the new mean?

Example 19

medium

A line plot shows daily rainfall (mm): 0→3, 1→2, 2→1. On how many days did it rain?

Example 20

medium

Plot: 10→1, 20→2, 30→1. Find the mean.

Example 21

easy

A line plot shows 6 Xs above

2

. How many data points equal

2

Example 22

easy

A plot has dots at

1

(once),

2

(twice),

3

(three times). How many dots total?

Example 23

easy

On a line plot of pencil lengths (in.), there are

0

dots above

5

but dots at

4

and

6

. Should you still show

5

on the number line?

Example 24

easy

A line plot shows ages:

7

appears

4

times. What is the frequency of age

7

Example 25

easy

Dots:

0\to 2

1\to 5

2\to 3

. What value has the tallest stack?

Example 26

easy

A line plot's values go from

1

8

. What is the range?

Example 27

easy

A line plot shows scores

90, 92, 95, 95, 98

. What is the mode?

Example 28

medium

Plot:

0\to 1

1\to 2

2\to 2

3\to 5

. Find the mean.

Example 29

medium

A line plot shows pet counts for

12

kids. If

4

have

0

pets and

3

have

1

pet, how many have

\ge 2

pets?

Example 30

medium

Plot of plant heights (cm):

10\to 2

11\to 3

12\to 4

13\to 1

. What is the range?

Example 31

medium

A class line plot shows test scores. Out of

20

students,

14

scored

\ge 80

. What percent is that?

Example 32

medium

Plot:

5\to 1

6\to 2

7\to 3

8\to 2

9\to 2

. Find the median.

Example 33

medium

Frequencies:

1\to 3

2\to 4

3\to 3

. Is the distribution symmetric?

Example 34

medium

A line plot of

8

values has range

6

and minimum

4

. What is the maximum?

Example 35

hard

A line plot has values

2,4,6,8

with frequencies

1,3,3,1

. What is the median?

Example 36

hard

A line plot of

7

data values has mode

4

and mean

5

. What is the sum of the data?

Example 37

hard

A line plot of

9

values has median

7

. If you add one more dot at

20

, what is the new median?

Example 38

hard

A line plot of test scores is skewed right (long tail to high values). Which is greater: mean or median?

Example 39

hard

A line plot of

10

values has mean

6

. If one

6

is replaced by

16

, what is the new mean?

Example 40

hard

On a line plot,

20

kids reported siblings. Counts:

0\to 5

1\to 8

2\to 4

3\to 3

. What fraction have at least

2

siblings?

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Related Concepts

Counting Number Line Histogram Scatter Plot

Background Knowledge

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

countingnumber line