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Year 5 Maths Data

Construct & interpret dot plots

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Theory

A dot plot shows numerical data as stacks of dots above a number line, one dot for each value. This Year 5 maths page shows how to draw a dot plot and read it: how many, the most common value, the range, and values that sit away from the rest.

A dot plot has a number line with one dot for each piece of data, stacked above its value.

The total is the number of dots. The most common value is the number under the tallest stack.

The range is the largest value minus the smallest value. It tells you how spread out the data are.

A cluster is a group of values close together. A gap is a value with no dots. An outlier is a value well away from all the others.

Dot plot of swims last month A dot plot above a number line from 0 to 8 showing how many times each of 11 students went swimming last month: one dot at 1, two at 2, four at 3, two at 4, one at 5 and one at 8. 012345678 Swims last month
\(11\) dots. Most common value \(3\). The \(8\) sits away from the rest: an outlier.
Dot plot drawn from a list A dot plot above a number line from 1 to 7 drawn from the list 2, 3, 3, 4, 4, 4, 4, 5, 6, 6: one dot at 2, two at 3, four at 4, one at 5, two at 6 and none at 1 or 7. 1234567 Books read in the holidays
From the list \(2, 3, 3, 4, 4, 4, 4, 5, 6, 6\): four dots above \(4\).

Reading a dot plot:

\[ \text{total} = \text{number of dots} \]
total = number of dots
\[ \text{range} = \text{largest} - \text{smallest} \]
range = largest − smallest
Value, not height. The most common value is the number on the line, not how many dots are in the stack.
Use the data, not the axis. The range uses the smallest and largest dots, not the ends of the number line.

Drawing a dot plot

  1. Draw a number line covering the smallest to largest value, evenly spaced.
  2. Put one dot above the value for each item in the list, stacking repeats.
  3. Check the number of dots equals the number of items, and add a label.

Answering questions

  1. Count the dots in the stacks asked about.
  2. For "more than", count only stacks to the right of the value (not the value itself).
Example 1 — Count at a value
Use the first diagram. How many students swam exactly \(4\) times?
Solution

\(2\) students.

Example 2 — Total and most common
Use the first diagram.
(i) How many students are shown?
(ii) What is the most common number of swims?
Solution

(i) \(11\)
(ii) \(3\) (four students)

Example 3 — Range and outlier
Use the first diagram.
(i) What is the range?
(ii) Which value is an outlier?
(iii) What is the range without it?
Solution
\(8 - 1\)\(=\)\(7\)
\(5 - 1\)\(=\)\(4\)
8−1=7,5−1=4

(i) \(7\)
(ii) \(8\)
(iii) \(4\)

Example 4 — More than
Use the first diagram. How many students swam more than \(3\) times?
Solution
\(2 + 1 + 1\)\(=\)\(4\)
2+1+1=4

\(4\) students (the stacks at \(4\), \(5\) and \(8\)).

Example 5 — Draw from a list
Draw a dot plot of \(2, 3, 3, 4, 4, 4, 4, 5, 6, 6\).
(i) How many dots go above \(4\)?
(ii) How many dots altogether?
Solution

(i) \(4\)
(ii) \(10\). See the second diagram.

Example 6 — Gaps and clusters
Use the second diagram. Describe the data.
Solution

The values cluster from \(3\) to \(4\); there are no dots at \(1\) or \(7\).

Example 7 — How many more?
Use the first diagram. How many more students swam \(3\) times than \(4\) times?
Solution
\(4 - 2\)\(=\)\(2\)
4−2=2

\(2\) more.

Example 8 — Find the mistake
Raj says the range is \(8\) because the number line goes from \(0\) to \(8\). What is wrong?
Solution
\(8 - 1\)\(=\)\(7\)
8−1=7

The range uses the smallest and largest dots, not the ends of the line: \(8 - 1 = 7\).

Common pitfalls

Height instead of value. Read the number under the tallest stack.
Including the value in "more than". "More than \(3\)" does not include \(3\).
Range from the axis. Use the smallest and largest dots.
Uneven number line. Space every value equally, even values with no dots.

Frequently asked questions

What is a dot plot?

A number line with one dot for each piece of data, stacked above its value.

How do I find the total?

Count all the dots.

What is the range?

The largest value minus the smallest: \(8 - 1 = 7\).

What is an outlier?

A value that sits well away from the rest of the data.

What does an empty space mean?

No one had that value.

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