Dot plots
Theory
Dot plots show data: each result is drawn as one dot above its number on a number line, so the dots make stacks. This Year 3 maths page shows how to read a stack, count all the dots, find the most and least common values, answer "more than" and "how many more" questions, draw a dot plot from a list or tally table, compare two dot plots and find a missing dot. The Year 3 Australian Curriculum and Victorian Curriculum do not have a dot plot content description, so there is no code from them. Curriculum: taught in Year 3 in Western Australia.
A dot plot shows data with dots above a number line. Each dot stands for one result, such as one student's answer. Dots for the same number are stacked one above another.
To read a dot plot, count the dots in a stack: \(3\) dots above the \(4\) means \(3\) people had the value \(4\). An empty space above a number means nobody had that value. Counting every dot gives the total number of results.
The most common value is the number under the tallest stack, and the least common is the number under the shortest stack. Dot plots make it easy to compare groups: a taller stack means more people gave that answer.
A dot plot is read by counting dots. These facts answer most questions.
How to read a dot plot
- Read the title and the number line. Find out what is being counted and what each number means.
- Count the stack. For "how many had exactly \(4\)?", count the dots above the \(4\).
- Answer the question. Count every dot for the total. Find the tallest stack for the most common value. Add stacks for "more than" or "less than". Subtract stacks for "how many more".
How to draw a dot plot
- Draw a number line. Go from the smallest value to the largest, with equal spaces, and label it.
- Draw one dot for each value. Cross off each value in the list or tally as you draw its dot.
- Stack neatly and check. Keep the dots the same size and evenly stacked, then check that the number of dots matches the number of results.
| \(\text{dots above 4}\) | \(=\) | \(3\) |
\(3\) students drank exactly \(4\) glasses.
| \(3 + 4 + 6 + 3 + 1\) | \(=\) | \(17\) |
\(17\) students are shown, because there is one dot for each student. Only \(1\) student drank \(5\) glasses. If a number had no dots above it, no student gave that answer.
Find the tallest stack, then read the number underneath it.
| \(\text{tallest stack}\) | \(=\) | \(6\text{ dots above } 3\) |
| \(\text{shortest stack}\) | \(=\) | \(1\text{ dot above } 5\) |
The most common number of glasses is \(3\) (not \(6\): \(6\) is how many students). The least common is \(5\).
(i) How many students drank more than \(3\) glasses?
(ii) How many more students drank \(2\) glasses than \(1\) glass?
"More than \(3\)" means the stacks to the right of \(3\): the \(4\) and the \(5\). The stack above \(3\) itself is not included.
| \(3 + 1\) | \(=\) | \(4\) |
| \(4 - 3\) | \(=\) | \(1\) |
(i) \(4\) students.
(ii) \(1\) more student.
Draw a number line from the smallest value (\(0\)) to the largest (\(3\)). Cross off each value in the list as you draw its dot, stacking dots neatly.
| \(\text{number of 2s}\) | \(=\) | \(4\) |
| \(2 + 2 + 4 + 1\) | \(=\) | \(9\) |
\(4\) dots go above the \(2\). Check: there are \(9\) dots for \(9\) friends.
Each tally mark becomes one dot. Count the tally for \(2\) books: one group of five and \(2\) more.
| \(5 + 2\) | \(=\) | \(7\) |
\(7\) dots go above the \(2\). The dot plot has \(4 + 7 + 2 = 13\) dots in all.
(i) Which class had more students who ate \(3\) pieces?
(ii) What is the most common number of pieces in each class?
| \(\text{3A above 3}\) | \(=\) | \(3\) |
| \(\text{3B above 3}\) | \(=\) | \(1\) |
| \(\text{3A tallest}\) | \(\text{above } 2\) | |
| \(\text{3B tallest}\) | \(\text{above } 1\) |
(i) Class 3A (\(3\) students, compared with \(1\)).
(ii) \(2\) pieces for 3A and \(1\) piece for 3B. Students in 3A ate a little more fruit.
| \(3 + 5 + 4 + 3\) | \(=\) | \(15\) |
| \(\text{dots above 3}\) | \(=\) | \(3 \text{ (table says 4)}\) |
Check each stack against the table. The stack above \(3\) has \(3\) dots but should have \(4\), so the missing dot goes above the \(3\).
Common pitfalls
Frequently asked questions
What is a dot plot?
A dot plot shows data as dots above a number line. Each dot stands for one result, and dots for the same number are stacked on top of each other.
How do you read a dot plot?
Find the number on the number line, then count the dots above it. That is how many people or things had that value.
How do you find the most common value on a dot plot?
Look for the tallest stack of dots and read the number underneath it. That number is the most common value.
How do you find the total on a dot plot?
Count every dot. Each dot is one result, so the total number of dots is the number of results.
What does an empty space on a dot plot mean?
An empty space above a number means nobody had that value. For example, no dots above \(4\) means no one gave the answer \(4\).
How do you draw a dot plot from a list?
Draw a number line from the smallest to the largest value, then draw one dot above the right number for each value in the list, crossing them off as you go.