Line Plot (Dot Plot) Examples: 46 Problems with Answers

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

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

Concept Recap

A line plot (also called a dot plot) is a diagram that displays data values as marks — usually X's or dots — stacked above their corresponding values on a number line. Each mark represents one data point, making it easy to see the frequency of each value.

Imagine a number line where every time someone picks a number, you stack an X above it. Taller stacks mean more people chose that number. You can quickly see which values are popular.

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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: Line Plot (Dot Plot) organizes data so the right pattern is visible without distorting the counts or scale.

Common stuck point: Students often know a procedure related to line plot (dot plot) but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?

Worked Examples

Example 1

medium

A line plot of family-size data:

2

(

3

X's),

3

(

4

4

(

2

5

(

1

). Walk through finding the mean family size.

Family sizes — find the mean family size.

Answer

3.1

First step

Compute weighted sum:

2 \cdot 3 + 3 \cdot 4 + 4 \cdot 2 + 5 \cdot 1 = 6 + 12 + 8 + 5 = 31

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Example 2

hard

A line plot of

9

ages:

10

(

2

11

(

3

12

(

3

13

(

1

). Walk through finding the median age.

Example 3

easy

Students measured the lengths of 10 leaves (in cm): 5, 6, 5, 7, 6, 5, 8, 6, 7, 5. Create a line plot (dot plot on a number line) for this data.

Example 4

medium

A line plot shows the number of hours students spent on homework: 1 hour (2 dots), 1.5 hours (4 dots), 2 hours (5 dots), 2.5 hours (3 dots), 3 hours (1 dot). Find the total number of students and the total hours spent by all students combined.

Practice Problems

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

Example 1

easy

A line plot of pet counts has X's stacked above values: 0 has two X's, 1 has three X's, 2 has one X. How many families have exactly 1 pet?

Pet counts per family — how many families have exactly 1 pet?

Example 2

easy

On a line plot, the value 4 has the tallest stack of X's. What is the mode of the data?

Example 3

easy

A line plot shows test scores: 7 has two X's, 8 has four X's, 9 has one X. How many students were tested in total?

Test scores — how many students were tested in total?

Example 4

easy

A line plot of siblings: 0 has one X, 1 has three X's, 2 has two X's. How many people have at least 1 sibling?

Siblings per person — how many people have at least 1 sibling?

Example 5

easy

A line plot has marks at 2 (one X), 3 (two X's), 5 (one X). What is the range of the data?

Find the range of the data.

Example 6

easy

A line plot shows hours of sleep: 6 (one X), 7 (two X's), 8 (two X's). Which value is NOT a mode?

Example 7

easy

Should you use a line plot for 10,000 customer ages or for 12 students' quiz scores from 0 to 10?

Example 8

easy

A line plot shows goals scored: 0 (three X's), 1 (two X's), 2 (one X). What value did the most players score?

Example 9

medium

A line plot of books read: 1 (two X's), 2 (three X's), 3 (one X), 5 (two X's). What is the total number of books read by everyone?

Books read — find the total books read by everyone.

Example 10

medium

A line plot shows ages: 10 (two X's), 11 (one X), 12 (two X's). What is the mean age?

Ages — what is the mean age?

Example 11

medium

A line plot shows shoe sizes: 6 (one X), 7 (three X's), 8 (two X's), 9 (two X's). What is the median shoe size?

Shoe sizes (8 data points) — what is the median shoe size?

Example 12

medium

A line plot of quiz scores has X's at: 5 (one), 6 (two), 7 (four), 8 (three). What fraction of students scored 7 or higher?

Quiz scores — what fraction of students scored 7 or higher?

Example 13

medium

A line plot shows: 2 (two X's), 4 (three X's), 6 (two X's), 10 (one X). Which is larger, the mean or the median?

Daily customers — which is larger, the mean or the median?

Example 14

medium

A line plot of daily customers shows clustering at 20 to 22 and one mark far out at 40. What is this far-out value called, and does it raise or lower the mean?

Daily customers — identify the far-out value and its effect on the mean.

Example 15

medium

A line plot shows: 1 (two X's), 2 (two X's), 3 (two X's), 4 (two X's). Describe the shape and give the mode(s).

Describe the shape and give the mode(s).

Example 16

medium

On a line plot, 5 has two X's and 6 has three X's; all other values are empty. A new data point of value 6 is added. Does the mode change?

Example 17

medium

A line plot of minutes late: 0 (four X's), 1 (two X's), 2 (one X), 5 (one X). What percent of people were on time (0 minutes late)?

Minutes late (8 total) — what percent of people were on time?

Example 18

challenge

A line plot has values 3, 4, 5, 6 with frequencies 1, x, 2, 1. The mean is exactly 4.5. Find x.

Example 19

challenge

A line plot shows 9 data points with median 6. Frequencies: 4 (two X's), 6 (a X's), 8 (rest). If the value 8 has three X's, how many X's are at 6?

Example 20

challenge

A line plot of 6 values reads: 2 (one), 3 (two), 5 (two), 8 (one). A 7th point is added so that the mean becomes a whole number. What is the smallest non-negative integer value that can be added?

Existing 6 data points — add a 7th so the mean becomes a whole number.

Example 21

easy

A line plot has X's stacked above values:

1

has

2

X's,

2

has

4

X's,

3

has

1

X. How many data points in total?

How many data points in total?

Example 22

easy

A line plot of test scores:

7

(

1

X),

8

(

2

X's),

9

(

2

X's). How many students scored at least

8

Example 23

easy

A line plot shows values

5, 6, 7

with

1

3

2

X's respectively. What is the range?

Find the range of the data.

Example 24

easy

A line plot shows pencil counts:

2

(

1

3

(

1

4

(

1

). What is the mean?

Pencil counts — what is the mean?

Example 25

easy

A line plot shows ages:

10

(

3

X's),

11

(

2

X's),

12

(

1

X). Which age is the median?

Example 26

easy

A line plot has X's at

1

(

2

2

(

1

3

(

3

). What is the mode?

What is the mode?

Example 27

medium

A line plot of hours studied:

1

(

2

X's),

2

(

1

3

(

4

4

(

3

). What is the mean (to one decimal)?

Hours studied — what is the mean (to one decimal)?

Example 28

medium

A line plot shows pencil lengths:

7

(

2

8

(

3

9

(

1

). What fraction of pencils are

8

cm long?

What fraction of pencils are 8 cm long?

Example 29

medium

A line plot shows:

0

(

1

1

(

2

2

(

3

3

(

2

4

(

1

). What is the median?

Example 30

medium

A line plot of pets owned:

0

(

5

1

(

3

2

(

1

3

(

1

). What percent of families own at least

1

pet?

Pets owned — what percent of families own at least 1 pet?

Example 31

medium

A line plot has stacks at

1

(

3

2

(

3

3

(

3

). How many modes?

How many modes does this data set have?

Example 32

medium

A line plot of shoe sizes:

6

(

1

7

(

4

8

(

4

9

(

1

). What is the median?

Shoe sizes (10 data points) — what is the median?

Example 33

medium

A line plot of dice rolls:

1

(

2

2

(

3

3

(

3

4

(

2

5

(

1

6

(

1

). What is the relative frequency of rolling a

2

Dice rolls — what is the relative frequency of rolling a 2?

Example 34

medium

A line plot of survey results:

1

(

1

2

(

2

3

(

4

4

(

2

5

(

1

). What is the total of all the data values?

Survey results — what is the total of all the data values?

Example 35

hard

A line plot has

20

data points. Removing the single largest value,

9

, lowers the mean from

5

4.8

. What is the new mean? (Hint: compute carefully.)

Example 36

hard

A line plot of

8

scores has mean

7

. After replacing one score

5

with

9

, what is the new mean?

Example 37

hard

A line plot shows X's at

1

(

a

2

(

3

3

(

a

4

(

1

), with total

11

data points. Find

a

Example 38

hard

A line plot shows scores:

80

(

2

85

(

3

90

(

4

95

(

1

). What is the weighted mean (to one decimal)?

Test scores — find the weighted mean.

Example 39

hard

A line plot has data

\{2, 2, 4, 5, 5, 7, 9\}

. What are the mean, median, and mode?

Data set {2,2,4,5,5,7,9} — find the mean, median, and mode.

Example 40

challenge

A line plot of jelly bean counts in

5

jars has mode

7

, median

7

, and mean

8

. Two of the values are

7

and

7

. What are the other three values?

Example 41

medium

A line plot shows the weights of 12 apples in fractions of a pound:

\frac{1}{4}

(3 dots),

\frac{1}{2}

(5 dots),

\frac{3}{4}

(3 dots),

1

(1 dot). What is the mean weight of the apples?

Example 42

hard

Two classes made line plots of their test scores. Class A: 70 (1), 75 (3), 80 (6), 85 (4), 90 (1). Class B: 60 (2), 70 (3), 80 (5), 90 (3), 100 (2). Compare the centres and spreads of the two distributions.

← Back to Line Plot (Dot Plot) Practice Mode

Related Concepts

Tally Chart Histogram Frequency Table

Background Knowledge

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

tally chart