Mathematics • Year 7 • Unit 4 • Lesson 4
Bar Charts and Column Graphs
Build fluency with the five essentials of a clean graph: title, labelled axes, an even scale, equal-width bars with gaps, and accurate heights. A good column graph turns a frequency table into a picture you can read in seconds.
1. I do — fully worked example
Read every line. Each step is one ingredient of a correct graph.
Problem. Draw a column graph for the favourite colour data: Red 7, Blue 12, Green 5, Yellow 9, Purple 3.
Step 1 — Choose a scale (the vertical axis).
Highest frequency is 12. Use a scale of 0 to 14 going up in twos: 0, 2, 4, 6, 8, 10, 12, 14.
Reason: equal intervals (every step = 2) make heights easy to read. Always go ABOVE the max value.
Step 2 — Label axes and add a title.
x-axis: "Colour". y-axis: "Frequency". Title: "Favourite colour of 36 Year 7 students".
Reason: without a title, the reader doesn't know what the graph is about.
Step 3 — Draw 5 bars of equal width with GAPS between them.
Each bar represents one category. Gaps show categories are separate (not continuous).
Reason: a histogram has touching bars because data is continuous. Categorical data must have gaps.
Step 4 — Set each height precisely.
Red → 7 Blue → 12 Green → 5 Yellow → 9 Purple → 3
Reason: Blue is tallest because 12 is the highest count. Always check sum: 7+12+5+9+3 = 36 ✓.
Answer: a column graph with 5 equal-width bars at heights 7, 12, 5, 9, 3, even scale 0–14 in twos, both axes labelled, and a title.
2. We do — fill in the missing decisions
You will draw a column graph for: Cats 14, Dogs 20, Fish 8, Birds 6, Rabbits 12. Fill in each decision before drawing. 4 marks
Decision 1 — Total students: 14 + 20 + 8 + 6 + 12 = _____
Decision 2 — Highest frequency: _____ Lowest: _____
Decision 3 — Choose a scale that goes ABOVE the highest value:
Scale: 0 to _____ , in equal steps of _____ (suggestion: 0–22 in twos, or 0–25 in fives).
Decision 4 — Write a title and axis labels:
Title: ______________________________________________________
x-axis label: _________________________ y-axis label: _________________________
Decision 5 — Draw the graph in the box below. 5 equal-width bars with gaps between them, heights matching the frequencies, sitting on the x-axis.
3. You do — independent practice
For each, draw the graph in the dashed box (sketches are fine if the heights are correct and the scale is even).
Foundation — read a graph
3.1 A column graph shows pet ownership: Cats 14, Dogs 20, Fish 8, Birds 6, Rabbits 12. (a) Which is most popular? (b) How many more chose Dogs than Fish? (c) What fraction of the 60 students chose Cats? 3 marks
3.2 A bar chart shows weekday rainfall: Mon 2 mm, Tue 5 mm, Wed 1 mm, Thu 8 mm, Fri 4 mm. Which day had MOST rain, and which had LEAST? 1 mark
3.3 What is the difference between a bar chart and a column graph in one sentence? 1 mark
3.4 Why must bar charts and column graphs have GAPS between the bars (and a histogram does not)? 1 mark
Standard — draw a graph
3.5 Draw a column graph for favourite hot drink: Tea 9, Coffee 14, Hot chocolate 11, Milo 6. Choose a sensible scale and label everything. 2 marks
3.6 Draw a HORIZONTAL bar chart for transport choice: Walk 18, Bike 6, Bus 22, Car 14. Choose a sensible scale, label axes and add a title. 2 marks
Extension — push your thinking
3.7 A column graph for canteen sales has scale 0, 5, 10, 20, 40. List two problems with this scale, and write a sensible replacement. 2 marks
3.8 A column graph has these issues — describe how to fix each: (i) no title, (ii) y-axis goes 0, 10, 100, 1000 (uneven jumps), (iii) one bar is twice as wide as the others. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Pet column graph plan
Decision 1: total = 60. Decision 2: highest = 20 (Dogs); lowest = 6 (Birds). Decision 3: scale 0 to 22 in twos (or 0 to 25 in fives). Decision 4: Title: "Pet ownership of 60 Year 7 students". x-axis: "Pet type". y-axis: "Frequency". Decision 5: 5 bars with gaps, heights 14, 20, 8, 6, 12 in the order Cats, Dogs, Fish, Birds, Rabbits.
3.1 — Pet graph reading
(a) Dogs (height 20).
(b) 20 − 8 = 12 more.
(c) Total students = 60; Cats = 14; fraction = 14/60 = 7/30.
3.2 — Rainfall
Most: Thursday (8 mm). Least: Wednesday (1 mm).
3.3 — Bar chart vs column graph
A bar chart has horizontal bars; a column graph has vertical bars (columns). Both show categorical or discrete frequency data the same way.
3.4 — Why gaps?
Bar charts and column graphs show categorical (or discrete) data — the categories are separate, so gaps between bars show that "Maths" and "English" are different things. A histogram has touching bars because it shows continuous data with no gaps between possible values.
3.5 — Hot drink column graph
Scale 0–14 in twos; four bars with gaps; heights 9, 14, 11, 6 in the order Tea, Coffee, Hot chocolate, Milo. Title: "Favourite hot drink of 40 students". x-axis: "Drink". y-axis: "Frequency".
3.6 — Horizontal bar chart for transport
Scale 0–24 (or 0–25) in twos or fives along the x-axis; four horizontal bars (Walk, Bike, Bus, Car) with gaps; lengths 18, 6, 22, 14. Title: "How students travel to school (n = 60)". y-axis: "Transport". x-axis: "Frequency".
3.7 — Bad scale 0, 5, 10, 20, 40
Problem 1: uneven jumps (0→5 = 5, 5→10 = 5, 10→20 = 10, 20→40 = 20). Heights become impossible to read accurately.
Problem 2: it makes large values look artificially close to smaller ones — misleading.
Replacement: 0, 10, 20, 30, 40 (equal steps of 10), or any scale with equal intervals that covers 0 to just above the highest value.
3.8 — Three issues to fix
(i) Add a clear title that explains what the data is about (e.g. "Favourite season of 30 students").
(ii) Replace the scale with equal intervals (e.g. 0, 200, 400, 600, 800, 1000) so the heights are comparable.
(iii) Make every bar the same width — different widths make some categories look more important than they are.