Construct & interpret dot plots
Theory
A dot plot stacks one dot for each result above its value on a number line. The height of a stack shows how often a value occurs; the mode is under the tallest stack and the range is the largest value minus the smallest.
A dot plot shows data as dots stacked above a number line, with one dot for each result.
The number below a stack is the value; the height of the stack is how many results share that value.
The mode is the value under the tallest stack — the most common result.
The range is the largest value take away the smallest value; it measures how spread out the data is.
A dot plot makes two summaries easy to read.
| Value | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Dots | 1 | 2 | 3 | 1 | 1 |
The tallest stack (\(3\) dots) is above \(2\), so the mode is \(2\).
The values run from \(0\) to \(4\), so the range is \(4-0=4\).
How to read a dot plot
- Pick a value on the number line.
- Count the dots stacked above it — that is how many results had that value.
- Add all the stacks to find the total number of results.
- Find the mode (tallest stack) and the range (largest minus smallest).
Count the dots in the stack above \(2\).
| dots above \(2\) | \(=\) | \(3\) |
Add the heights of all the stacks.
| \(1+2+3+1+1\) | \(=\) | \(8\) |
The mode is the value under the tallest stack.
| mode | \(=\) | \(2\) |
Take the smallest value from the largest.
| \(4-0\) | \(=\) | \(4\) |
Common pitfalls
Frequently asked questions
What does one dot stand for?
One result. Each dot is a single data point, so the height of a stack is how many results had that value.
How do I find the mode from a dot plot?
Look for the tallest stack. The value written below it is the mode — the most common result.
How do I find the total number of results?
Add the heights of every stack. Because each dot is one result, counting all the dots counts all the results.
What is the range?
The range is the largest value take away the smallest value. It measures how spread out the data is, so it is a difference, not one of the values.
Is the mode the number of dots?
No. The mode is the value under the tallest stack, not the height of that stack. Those two numbers usually mean different things.