Resources For Teachers For Tutors For Students & Parents Pricing
Create Free Account
Year 4 Maths Data

Interpret data displays

20 practice questions 0 video lessons Theory + worked examples
Practice 20 questions
Practice questions

Every question with a fully worked solution.

Start practising
Create a free accountTrack your progress and save your work as you go.
Create free account

Theory

Interpreting data displays is a Year 4 statistics skill: reading tables, picture graphs, column graphs and dot plots to find the most and least, work out totals, differences and missing amounts, find the mode and range, and draw simple conclusions. This page shows how to read each display and use the scale or the key correctly. Curriculum: VC2M4ST02 / AC9M4ST02.

A data display shows information so you can compare groups quickly. The number in each group is called its frequency (how many). A table lists groups in rows and columns; you read across a row to find its amount.

A picture graph uses a picture to stand for a number, and a key tells you how many each picture is worth. A column graph uses columns; you read the top of a column across to the scale. A dot plot puts one dot above a number line for each result, so a stack of dots shows how many got that value.

The mode is the most common value, the one with the most dots or the biggest count. The range is the difference between the largest and smallest values. A conclusion is a true statement about what the data shows, such as which group is the most popular.

Column graph of favourite fruit in class 4B A column graph with a scale in 2s. Columns: Apple 8, Banana 5, Orange 3 and Grapes 6. Apple is the tallest, so apple is the most popular fruit. Favourite fruit in class 4B 0 2 4 6 8 Apple Banana Orange Grapes Fruit Number of students
Column graph: apple (\(8\)) is the most popular; orange (\(3\)) is the least.
Picture graph of books read each week A picture graph where each picture stands for 2 books. Week 1 has 3 pictures (6 books), Week 2 has 4 pictures (8 books) and Week 3 has 2 pictures (4 books). Books read each week Week 1 Week 2 Week 3 Key:= 2 books
Picture graph: each picture stands for \(2\) books, so Week 2 (\(4\) pictures) means \(8\) books read.
Dot plot of siblings, the tallest stack is above 2 A dot plot from 0 to 4 with one dot for each student: 2, 5, 7, 3 and 1 dots. The tallest stack, above 2, is shown in red. Siblings of students in 4K 0 1 2 3 4 Number of brothers and sisters
Dot plot: the tallest stack is above \(2\), so the mode is \(2\). The range is \(4 - 0 = 4\).
FruitAppleBananaOrangeGrapes
Students8536

The same fruit data shown as a table. A table and a column graph can show the same information.

Once you have read the amounts from a table, picture graph, column graph or dot plot, these facts answer most questions.

\[ \text{total} = \text{add every amount} \]
total=addeveryamount
\[ \text{how many more} = \text{bigger} - \text{smaller} \]
howmanymore=bigger−smaller
\[ \text{missing amount} = \text{total} - \text{the amounts you know} \]
missingamount=total−amountsyouknow
\[ \text{range} = \text{largest value} - \text{smallest value} \]
range=largestvalue−smallestvalue
The mode is the most common value. On a dot plot it is the number under the tallest stack, not the height of the stack. On a table or column graph, the most common category is the biggest amount or the tallest column. Use the key on a picture graph and the scale on a column graph before you read any amount.

How to read and interpret a data display

  1. Read the title and labels. Find out what the display is about and what each row, column, picture or dot shows.
  2. Find the amount. Read across a table row, read the top of a column on the scale, count the pictures and multiply by the key, or count the dots above a value. If a column stops halfway between two marks, read the number halfway between them.
  3. Answer the question. For the most or least, look for the biggest or smallest. For a total, add the amounts. For "A or B", add just those two amounts. For how many more, subtract. For a missing amount, take the known amounts from the total.
  4. Check your conclusion. Say what the data shows, using the numbers. A good conclusion is true for the data, such as "Most students have \(2\) siblings". A display only answers questions about what was recorded: a column graph shows how many are in each group, not who they are.
Example 1 — How many more
The column graph shows the favourite sport of students in class 4R. How many more students chose soccer than cricket?
Column graph of favourite sport in class 4R A column graph with a scale in 1s. Columns: Soccer 7, Netball 5, Cricket 4 and Swimming 6. Favourite sport in class 4R 0 1 2 3 4 5 6 7 8 Soccer Netball Cricket Swim Sport Number of students
Solution
\(\text{Soccer}\)\(=\)\(7\)
\(\text{Cricket}\)\(=\)\(4\)
\(7 - 4\)\(=\)\(3\)
7−4=3

\(3\) more students chose soccer than cricket.

Example 2 — Total from a table
The table shows how many books were borrowed from the library each day. How many books were borrowed over the four days altogether?
DayMonTueWedThu
Books1411169
Solution
\(14 + 11\)\(=\)\(25\)
\(25 + 16 + 9\)\(=\)\(50\)
14+11+16+9=50

\(50\) books were borrowed altogether.

Example 3 — Using the key
The picture graph shows stickers earned by three children. Each picture stands for \(2\) stickers. How many stickers did they earn altogether?
Picture graph of stickers earned by three children A picture graph where each picture stands for 2 stickers. Mia has 3 pictures (6), Sam has 4 pictures (8) and Ana has 2 pictures (4). Stickers earned Mia Sam Ana Key:= 2 stickers
Solution
\(\text{Mia } 3\times 2\)\(=\)\(6\)
\(\text{Sam } 4\times 2\)\(=\)\(8\)
\(\text{Ana } 2\times 2\)\(=\)\(4\)
\(6 + 8 + 4\)\(=\)\(18\)
6+8+4=18

They earned \(18\) stickers altogether.

Example 4 — Most and difference
The table shows the points scored by three teams. Which team scored the most, and how many more did they score than the Green team?
TeamRedBlueGreen
Points182415
Solution
\(\text{Most}\)\(=\)\(\text{Blue } (24)\)
\(24 - 15\)\(=\)\(9\)
24−15=9

Blue scored the most, \(9\) more points than Green.

Example 5 — Read a dot plot
The dot plot shows how many brothers and sisters each student in 4K has. Each dot is one student.
(i) How many students have exactly \(2\) siblings?
(ii) How many students are in the class?
(iii) What is the mode?
(iv) How many students have \(3\) or more siblings?
Dot plot of the number of siblings of students in 4K A dot plot from 0 to 4 with one dot for each student. 0 has 2 dots, 1 has 5 dots, 2 has 7 dots, 3 has 3 dots and 4 has 1 dot. Siblings of students in 4K 0 1 2 3 4 Number of brothers and sisters
Solution
\(\text{dots above 2}\)\(=\)\(7\)
\(2 + 5 + 7 + 3 + 1\)\(=\)\(18\)
\(\text{tallest stack}\)\(=\)\(\text{above } 2\)
\(3 + 1\)\(=\)\(4\)
2+5+7+3+1=18

(i) \(7\) students.
(ii) \(18\) students (count every dot).
(iii) The mode is \(2\) siblings, the number under the tallest stack.
(iv) \(4\) students (the dots above \(3\) and \(4\)).

Example 6 — Mode and range
Seven students scored \(6,\ 8,\ 7,\ 8,\ 10,\ 8,\ 9\) on a spelling test. What is the mode, and what is the range?
Solution

Put the scores in order: \(6,\ 7,\ 8,\ 8,\ 8,\ 9,\ 10\).

\(\text{mode}\)\(=\)\(8\text{ (it appears 3 times)}\)
\(\text{range}\)\(=\)\(10 - 6 = 4\)
10−6=4

The mode is \(8\) and the range is \(4\).

Example 7 — Find a missing amount
\(29\) students in 4D said how they travel to school: walk \(8\), car \(12\), bike \(4\) and the rest by bus. How many travel by bus, and which way is most common?
Solution
\(8 + 12 + 4\)\(=\)\(24\)
\(29 - 24\)\(=\)\(5\)
\(\text{largest}\)\(=\)\(12 \to \text{car}\)
29−24=5

\(5\) students travel by bus, and car is the most common way. On a column graph you would draw the missing bus column \(5\) tall.

Example 8 — Draw a conclusion
The canteen sold these numbers of pies: Monday \(22\), Tuesday \(18\), Wednesday \(30\), Thursday \(18\), Friday \(25\).
(i) How many pies were sold in the week?
(ii) Which two days sold the same number?
(iii) Write one conclusion.
Solution
\(22 + 18 + 30 + 18 + 25\)\(=\)\(113\)
22+18+30+18+25=113

(i) \(113\) pies.
(ii) Tuesday and Thursday (\(18\) each).
(iii) Wednesday was the busiest day for pies, and Tuesday and Thursday were the quietest. A conclusion must match the data.

Example 9 — A scale in 4s
The column graph shows the favourite sport of students in class 4S. The scale goes up in \(4\)s.
(i) How many students chose hockey?
(ii) How many more students chose hockey than tennis?
Column graph of favourite sport in class 4S, scale in 4s A column graph with a scale in 4s from 0 to 20. Hockey stops halfway between 16 and 20, so it shows 18. Tennis reaches 8. Golf reaches 12. Favourite sport in class 4S 0 4 8 12 16 20 Hockey Tennis Golf Sport Number of students
Solution

The marks are \(0, 4, 8, 12, 16, 20\). The hockey column stops halfway between \(16\) and \(20\). Halfway is \(2\) more than \(16\).

\(\text{hockey}\)\(=\)\(16 + 2 = 18\)
\(\text{tennis}\)\(=\)\(8\)
\(18 - 8\)\(=\)\(10\)
18−8=10

(i) \(18\) students.
(ii) \(10\) more students chose hockey than tennis.

Example 10 — What can the graph tell you?
Use the class 4S sport graph in Example 9.
(i) Can the graph tell you how many students chose golf?
(ii) Can the graph tell you which students chose tennis?
Solution

A column graph records one number for each group: how many chose it. It does not record any names.

(i) Yes. The golf column reaches \(12\), so \(12\) students chose golf.
(ii) No. The graph shows that \(8\) students chose tennis, but not who they are. You would need the list of answers from the survey.

Common pitfalls

Read the scale, not the columns. Watch out for a scale that counts by \(2\)s or \(5\)s. Read the number the top of the column reaches, not just how many marks tall it is.
Use the key on a picture graph. Each picture may stand for more than one. If the key is \(2\), then \(4\) pictures mean \(8\), so multiply by the key instead of just counting pictures.
The mode is a value, not a height. On a dot plot, the mode is the number under the tallest stack. If the tallest stack has \(7\) dots above the \(2\), the mode is \(2\), not \(7\).
"How many more" means subtract. Find both amounts and take the difference. Adding them answers "how many altogether" instead.

Frequently asked questions

How do you read a column graph?

Find the column you want, then look at the top of it. Follow the top across to the scale on the side and read the number. That number is how many the column stands for.

What is a picture graph key?

A key tells you how many each picture stands for. If the key says one picture equals \(2\), then \(3\) pictures mean \(6\). Count the pictures and multiply by the key.

What does how many more mean in a graph question?

How many more means find the difference. Read both amounts and subtract the smaller from the larger. If soccer is \(7\) and cricket is \(4\), then \(7 - 4 = 3\) more.

How do you find a missing amount when you know the total?

Add the amounts you know, then subtract that from the total. If \(29\) students were asked and the known amounts add to \(24\), the missing amount is \(5\).

What is the mode on a dot plot?

The mode is the value with the most dots. Look for the tallest stack of dots and read the number below it. That number is the most common result.

What is the range of a set of data?

The range is the largest value take away the smallest value. For scores of \(6\) to \(10\), the range is \(10 - 6 = 4\).

More in Data
Construct & interpret picture graphs (many-to-one)
20 questions
Plan & conduct a statistical investigation
20 questions