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Year 6 Maths Data

Side-by-side column graphs

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Theory

A side-by-side column graph shows two sets of data on one graph. For each category there is a pair of columns, one for each group, and the legend tells you which colour is which. This Year 6 maths page shows how to read these graphs, find differences and totals, and decide when to use one.

A side-by-side column graph (also called a grouped column graph) puts the two columns for each category next to each other.

The legend (key) shows which colour belongs to which group. Always check it first.

Read a column by going across from its top to the scale. If the top is between two numbered lines, use the halfway value.

Use a side-by-side graph to compare two groups across the same categories, for example two classes on each day.

Library books borrowed by 6A and 6B A side-by-side column graph of library books borrowed on four days. 6A, in blue: Monday 9, Tuesday 13, Wednesday 5, Thursday 11. 6B, in orange: Monday 11, Tuesday 6, Wednesday 10, Thursday 7. The scale goes from 0 to 14 in steps of 2. 6A 6B 02468101214 Books borrowed Mon Tue Wed Thu Day
Blue columns are 6A and orange columns are 6B (see the legend).
How students arrive and leave A side-by-side column graph of how students travel past the school gate, morning and afternoon. Morning, blue: cars 14, bikes 6, scooters 3, walkers 9. Afternoon, orange: cars 10, bikes 9, scooters 5, walkers 12. Morning Afternoon 02468101214 Number of students 14 10 Cars 6 9 Bikes 3 5 Scooters 9 12 Walkers
Each category has a morning column and an afternoon column, labelled with its value.

Reading a side-by-side graph:

\[ \text{difference} = \text{taller column} - \text{shorter column} \]
difference = taller column − shorter column
\[ \text{total for one group} = \text{sum of that colour} \]
total for one group = sum of that colour
Day6A6BDifference
Mon\(9\)\(11\)\(2\)
Tue\(13\)\(6\)\(7\)
Wed\(5\)\(10\)\(5\)
Thu\(11\)\(7\)\(4\)
Legend first. Before reading any column, check which colour is which group.
Biggest gap. The biggest difference is the pair of columns that are furthest apart in height, not the tallest column.

How to answer a question from the graph

  1. Find the category along the bottom.
  2. Choose the column for the group, using the legend.
  3. Read across to the scale.
  4. Calculate a difference (subtract) or a total (add) if asked.
Example 1 — Read a value
How many books did 6A borrow on Tuesday?
Solution

The blue Tuesday column reaches \(13\).

Example 2 — Difference on one day
On Wednesday, how many more books did 6B borrow than 6A?
Solution
\(10 - 5\)\(=\)\(5\)
10−5=5

\(5\) more.

Example 3 — Greatest difference
On which day is the difference between the classes the greatest?
Solution

Differences: Mon \(2\), Tue \(7\), Wed \(5\), Thu \(4\).

Tuesday (\(7\) books).

Example 4 — Total for one group
(i) How many books did 6A borrow over the four days?
(ii) Which class borrowed more, and by how many?
Solution
\(9 + 13 + 5 + 11\)\(=\)\(38\)
\(11 + 6 + 10 + 7\)\(=\)\(34\)
\(38 - 34\)\(=\)\(4\)
38−34=4

(i) \(38\)
(ii) 6A, by \(4\) books

Example 5 — Both groups together
How many books did the two classes borrow on Thursday?
Solution
\(11 + 7\)\(=\)\(18\)
11+7=18

\(18\) books.

Example 6 — Use the legend
Use the second graph.
(i) Which colour shows the afternoon?
(ii) How many scooters were counted altogether?
Solution
\(3 + 5\)\(=\)\(8\)
3+5=8

(i) Orange
(ii) \(8\)

Example 7 — Compare across categories
For which ways of travel were there more students in the afternoon than in the morning?
Solution

Bikes (\(9 > 6\)), scooters (\(5 > 3\)) and walkers (\(12 > 9\)). Cars were the only one higher in the morning.

Example 8 — Choose a display
Two classes each counted their votes for four camp activities. Which graph shows both sets of votes together best?
Solution

A side-by-side column graph: each activity gets one column for each class, so the classes are easy to compare.

Example 9 — Find the mistake
Raj says 6A borrowed \(11\) books on Monday. What went wrong?
Solution

\(11\) is the orange column, which is 6B. Checking the legend, 6A (blue) borrowed \(9\) on Monday.

Common pitfalls

Ignoring the legend. Reading the wrong colour gives the other group’s value.
Tallest column is not the biggest difference. Compare the gap inside each pair.
Misreading the scale. If the scale goes up in \(2\)s, a column halfway between \(8\) and \(10\) is \(9\).
Adding both colours for one group. For one group’s total, add only its colour.

Frequently asked questions

What is a side-by-side column graph?

A column graph with two columns for each category, one for each group being compared.

What does the legend do?

It shows which colour stands for which group.

How do I find the difference between two groups?

Read both columns in the pair and subtract the smaller from the larger.

When should I use a side-by-side graph?

When you want to compare two groups across the same categories.

How do I find one group’s total?

Add the values of all the columns of that group’s colour.

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