Mathematics • Year 7 • Unit 4 • Lesson 4
Bar Charts and Column Graphs — Mixed Challenge
Bring together graph drawing, graph reading, scale choice, side-by-side comparison and spotting misleading graphs. Then spot a student's drawing error and design your own graph from scratch.
1. Mixed problems
Show working. 2 marks each
1.1 A column graph shows favourite winter sport: Hockey 8, Netball 14, Soccer 21, Basketball 17. (a) Which is most popular? (b) How many students were surveyed?
1.2 Choose a sensible scale for a column graph whose highest frequency is 87. Justify with one short sentence.
1.3 A bar chart shows favourite fruit. Bars: Apple 12, Banana 18, Orange 9. The "Total" row of the frequency table says 40. Is the chart consistent with the table? If not, what's missing?
1.4 Sketch a column graph for: Monday 5, Tuesday 8, Wednesday 12, Thursday 7, Friday 10. Label everything.
1.5 Why is it usually wrong to draw a column graph with the y-axis starting at any value other than 0? Use one sentence and one short example.
1.6 A column graph and a histogram both use rectangles. List two ways they differ that would let you tell them apart at a glance.
2. Find the mistake
Another Year 7 student has drawn a column graph for favourite season data: Summer 10, Autumn 5, Winter 7, Spring 3 (total = 25). Below is a description of their graph. Exactly one feature contains a clear mistake. Spot it, explain, then describe how to correct it. 3 marks
Description of the student's graph:
Line 1: Title: "Favourite season (n = 25)" ✓
Line 2: x-axis label: "Season" ✓ y-axis label: "Number of students" ✓
Line 3: y-axis scale: 0, 2, 4, 6, 8, 10, 12 in equal steps of 2 ✓
Line 4: Bars: Summer 10 (wide bar), Autumn 5 (narrower), Winter 7 (narrowest), Spring 3 (wide bar). All bars touching each other.
Line 5: The student says it "looks neat with no gaps".
(a) Identify the mistake(s) in Line 4.
(b) Explain in one or two sentences why these features are wrong for categorical data.
(c) Describe how Line 4 should be drawn correctly.
Stuck? Look at TWO things on Line 4 — bar widths and whether bars touch.3. Open-ended challenge — design and critique
This question has many correct answers. Show your work clearly. 4 marks
3.1 A Year 7 cohort of 60 students was surveyed about how they spend their break times. Results: Sport 18, Library 9, Chatting with friends 21, Eating 8, Phone/games 4.
(i) Draw a column graph with the five categories. Choose a sensible even scale, label both axes, and add a title that includes n = 60.
(ii) Now draw a DIFFERENT version of the graph that would be considered misleading (e.g. y-axis doesn't start at 0, uneven intervals, different bar widths, or no title). Use one paragraph to identify what is misleading about your version.
(iii) State which version a school newsletter SHOULD print and why.
Bonus: redraw the data as a HORIZONTAL bar chart and comment on whether it makes any of the comparisons easier.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Winter sport
(a) Soccer (21). (b) Total = 8 + 14 + 21 + 17 = 60 students.
1.2 — Scale for max value 87
Use 0 to 90 in steps of 10 (or 0 to 100 in tens). Reason: equal intervals that go just above the highest value (87) make heights easy to compare without wasting too much white space.
1.3 — Bar chart consistency check
Apple 12 + Banana 18 + Orange 9 = 39, not 40. So either one bar is missing (the chart is incomplete) or one frequency is wrong. To match the table total of 40, one extra fruit with frequency 1 is missing — most likely a fourth bar (e.g. "Other") of height 1.
1.4 — Weekday column graph
Scale 0–14 in twos. Five bars with gaps, heights 5, 8, 12, 7, 10 in the order Mon, Tue, Wed, Thu, Fri. Title: "Daily count". x-axis: "Day". y-axis: "Frequency".
1.5 — Why y-axis at 0?
Bar heights represent values, so a non-zero baseline visually exaggerates differences. Example: with a baseline of 90, the bars 95 and 100 look 50%/100% taller than baseline, even though 100 is only about 5% bigger than 95.
1.6 — Column graph vs histogram
Difference 1: Bars touch in a histogram; bar/column graphs have gaps.
Difference 2: A histogram's x-axis shows continuous numerical intervals (e.g. 150–159, 160–169 cm); a bar/column graph's x-axis shows categories or discrete values (e.g. Maths, English, Science).
2 — Find the mistake
(a) Two issues on Line 4: bars have different widths and bars are touching each other.
(b) Different widths make some categories look more important than they are (a wider bar can look "bigger" even with the same height). Touching bars suggest the data is continuous (like a histogram), which is wrong because season is a categorical variable.
(c) Line 4 corrected: draw four equal-width bars with equal small gaps between them, heights 10, 5, 7, 3 in the order Summer, Autumn, Winter, Spring.
3 — Designed graph (sample answers)
(i) Fair column graph: scale 0–25 in fives; five equal-width bars with gaps; heights 18, 9, 21, 8, 4 in the order Sport, Library, Chatting, Eating, Phone/games. Title: "How Year 7 spend break time (n = 60)". x-axis: "Activity". y-axis: "Number of students".
(ii) Misleading version (sample): y-axis starts at 4 (instead of 0) and uses uneven steps 4, 6, 10, 18, 24. This makes Phone/games (4) look like nothing and exaggerates the differences between the others.
(iii) The school newsletter should print the fair version. Real numbers should be shown honestly so families and teachers see the actual size of each activity — a misleading graph could waste time on the wrong policy decisions (e.g. banning phones when only 4 students choose them).
Bonus: a horizontal bar chart works equally well; with five long category labels, horizontal bars are sometimes easier to read because the labels (Sport, Library, …) sit on the y-axis with room for full words, instead of being squashed below vertical columns.
Marking: 1 for fair graph with all five essentials (title, both axes, even scale, equal bars, gaps); 1 for a clearly misleading second version; 1 for paragraph explaining what is misleading; 1 for clear newsletter recommendation. Bonus for any sensible horizontal-version comment.