Dot Plot Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of 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 dot plot is a statistical chart that displays the frequency of data values using dots stacked above a number line. Each dot represents one observation, making it easy to see clusters, gaps, and the overall shape of a distribution for small to medium datasets.

Like a line plot, but dots instead of X's. Each dot is one data point stacked above its value. The height of the stack shows frequency. Great for seeing clusters and gaps.

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: 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 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 dot plot of class ages: 12 (one), 13 (eight), 14 (two), 15 (one). Mean, median, and outlier?

Answer

mean≈13.25,median=13,outlier=15\text{mean}\approx 13.25, \text{median}=13, \text{outlier}=15

First step

1
Mean: (12+13⋅8+14⋅2+15)/12=(12+104+28+15)/12=159/12≈13.25(12 + 13\cdot 8 + 14\cdot 2 + 15)/12 = (12+104+28+15)/12 = 159/12 \approx 13.25.

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Example 2

hard
Two dot plots compare two classes' quiz scores. Class A is tightly clustered at 8; Class B spreads from 5 to 10. Which has smaller standard deviation?

Example 3

easy
The number of books students read last month: 0, 1, 2, 1, 3, 2, 1, 0, 2, 1, 4, 2. Create a dot plot and identify the mode.

Example 4

medium
Two dot plots show test scores for Class A (scores clustered tightly around 75) and Class B (scores spread from 50 to 100). Both have the same median of 75. Compare the two distributions.

Example 5

medium
Create a dot plot for the data: 3, 5, 5, 6, 6, 6, 7, 8. What is the mode?

Practice Problems

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

Example 1

easy
A dot plot stacks dots above values: 3 has two dots, 4 has five dots, 5 has one dot. How many observations are at value 4?

Example 2

easy
On a dot plot, the value 12 has more dots than any other. What is the mode?

Example 3

easy
A dot plot shows: 1 (three dots), 2 (two dots), 3 (two dots). How many data points total?

Example 4

easy
A dot plot of pushups: 10 (one dot), 15 (two dots), 20 (one dot). What is the range?

Example 5

easy
A dot plot has a tight cluster from 5 to 7 and one lone dot at 15. What is the lone dot called?

Example 6

easy
A dot plot shows scores 8 (two dots) and 9 (two dots), all others empty. How many modes does it have?

Example 7

easy
Is a dot plot better for 15 reaction times rounded to whole seconds, or for 50,000 city temperatures?

Example 8

easy
A dot plot of goals: 0 (four dots), 1 (three dots), 2 (one dot). How many players scored fewer than 2 goals?

Example 9

medium
A dot plot shows minutes: 5 (two dots), 6 (three dots), 7 (one dot), 8 (two dots). What is the mean?

Example 10

medium
A dot plot of family sizes: 2 (one dot), 3 (three dots), 4 (two dots), 5 (one dot). Find the median.

Example 11

medium
A dot plot of test scores: 70 (one), 80 (four), 90 (three), 100 (two). What fraction scored at least 90?

Example 12

medium
A dot plot is described as right-skewed with a long tail of high values. Which is larger, the mean or the median?

Example 13

medium
A dot plot shows 6 (two dots), 7 (one dot), 8 (two dots). A new observation of 8 is added. What is the new mode?

Example 14

medium
A dot plot of 8 values has min 2 and max 14. The middle dots cluster near 6. Estimate whether the range or the cluster spread is larger, and give the range.

Example 15

medium
A dot plot shows: 1 (two dots), 2 (two dots), 3 (two dots), 4 (two dots), 5 (two dots). What is the shape, and what is the median?

Example 16

medium
A dot plot of 9 quiz scores has median 7. The dots are: 5 (two), 7 (b), 9 (two). Find b.

Example 17

medium
A dot plot of commute times (min): 10 (one), 20 (three), 30 (one), 60 (one). Which better represents a typical commute, the mean or the median, and what is the median?

Example 18

challenge
A dot plot has values 4, 6, 8 with frequencies 3, k, 2. The mean equals 6. Find k.

Example 19

challenge
A dot plot of 7 values has the property that adding the mean as an 8th value leaves the mean unchanged. The seven values sum to 49. What was and remains the mean?

Example 20

challenge
A dot plot of 55 distinct integer values from 11 to 1010 has mean 66 and median 77. Two of the values are 77 and 1010. Find a possible set of all five values.

Example 21

easy
A dot plot shows: 2 (one dot), 3 (three dots), 4 (two dots). Find the total observations.

Example 22

easy
A dot plot shows test scores: 80 (one), 85 (three), 90 (two), 95 (one). What is the mode?

Example 23

easy
A dot plot of pet counts shows: 0 (two), 1 (four), 2 (three), 3 (one). How many families have at least 2 pets?

Example 24

easy
A dot plot ranges from 44 to 1111 with no gaps. What is the range?

Example 25

easy
A dot plot shows quiz scores 6 (two), 7 (three), 8 (four), 9 (one). How many students scored less than 8?

Example 26

easy
A dot plot shows: 2 (one), 4 (one), 6 (one). What is the median?

Example 27

medium
A dot plot: 3 (two dots), 4 (four dots), 5 (one dot), 6 (three dots). Find the mean.

Example 28

medium
A dot plot of homework times (minutes): 10 (two), 20 (five), 30 (two), 40 (one). Find the median.

Example 29

medium
A dot plot has 20 observations. The values 10 (3), 11 (5), 12 (8), 13 (3), 14 (1). What is Q1Q_1 (the 5th-6th value position)?

Example 30

medium
A dot plot of jumps (feet): 4 (two), 5 (four), 6 (three), 7 (one). What is the range?

Example 31

medium
A dot plot shows 5 (two), 6 (three), 7 (two), 8 (three). Is the distribution bimodal?

Example 32

hard
A dot plot: 1 (one), 2 (three), 3 (five), 4 (three), 5 (one). Find the mean and population standard deviation.

Example 33

hard
A dot plot: 10 (two), 12 (three), 14 (four), 16 (one). Compute the interquartile range (IQR).

Example 34

hard
A symmetric dot plot has mean 55 and SD 1.51.5. About what fraction of dots lie within one SD of the mean (assume bell-shaped)?

Example 35

hard
A dot plot of soda counts: 0 (five), 1 (eight), 2 (four), 3 (two), 5 (one). The value 5 is suspected as an outlier. Find Q3+1.5⋅IQRQ_3 + 1.5 \cdot IQR to check.

Example 36

hard
A dot plot has 30 observations, all integers from 1 to 7. The mean is 4. If 25 of the values are between 3 and 5, what shape word best describes the distribution?

Example 37

hard
A dot plot of test grades: 60 (one), 70 (three), 80 (six), 90 (three), 100 (one). What percent of students scored at least 80?

Example 38

challenge
A dot plot of 7 values has mean 6 and median 5. Adding one new dot at value 14 changes both. Compute the new mean and new median.

Example 39

medium
A dot plot shows ages of participants in a fun run: 20(3 dots), 25(5 dots), 30(8 dots), 35(6 dots), 40(4 dots), 45(2 dots), 50(1 dot). Describe the shape of the distribution and estimate the median age.

Example 40

hard
A dot plot shows the number of absences for 20 students: 0(6), 1(5), 2(4), 3(2), 4(1), 8(1), 10(1). Calculate the mean, identify any potential outliers, and explain how the outliers affect the mean compared to the median.
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Background Knowledge

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

line plotfrequency table