Mathematics • Year 7 • Unit 4 • Lesson 4
Bar Charts and Column Graphs — Real World
Apply graph reading and graph drawing to real settings: a weather log, an Olympics medal tally, a school club sign-up, a canteen sales chart, and a misleading newspaper graph.
1. Word problems
Read or draw the graph, then answer the questions. Show working.
1.1 — Weather log. A column graph shows rainfall (mm) in Sydney for one week: Mon 4, Tue 0, Wed 12, Thu 18, Fri 6, Sat 2, Sun 0.
(a) Which day had most rain?
(b) Calculate the total rainfall for the week.
(c) Calculate the mean daily rainfall (1 d.p.). 3 marks
1.2 — Olympics medal tally. A column graph shows medals won by Australia at a recent Olympics: Gold 17, Silver 19, Bronze 16. The graph for the United States shows: Gold 39, Silver 41, Bronze 33.
(a) Sketch a SIDE-BY-SIDE column graph (gold/silver/bronze side-by-side for the two countries).
(b) Which country won more total medals, and by how many?
(c) For each country, calculate the fraction of medals that were gold (express as a percentage to 1 d.p.). 4 marks
1.3 — School club sign-ups. The number of students who joined each club: Robotics 24, Debating 15, Chess 11, Drama 32, Art 22.
(a) Draw a column graph for this data. Choose a sensible even scale and include title, axes labels, and gaps between bars.
(b) Which two clubs together have exactly half the total sign-ups? 3 marks
1.4 — Canteen sales chart. A bar chart shows sales over five days: Mon $120, Tue $95, Wed $140, Thu $115, Fri $180.
(a) Calculate the mean daily sales.
(b) On which day were sales above the mean? List them.
(c) Friday's sales are what percentage higher than Tuesday's (round to nearest whole %)? 3 marks
1.5 — Misleading newspaper graph. A newspaper publishes a column graph of share prices over four months. The y-axis starts at 98 (not 0) and uses unequal intervals 98, 99, 100, 102, 105. The four bars show prices of 99, 100, 101, 103.
(a) Why does starting the y-axis at 98 mislead the reader?
(b) Why does the uneven scale make things worse?
(c) Describe how a fairer version of the graph should be drawn. 3 marks
2. Explain your thinking
Communication matters. Use full sentences. 4 marks
2.1 A Year 7 student draws a column graph of class test scores with the bars touching each other (no gaps). When asked, they say "it looks neater that way". In your own words, explain (i) why touching bars is technically WRONG for categorical or discrete frequency data, (ii) what kind of graph uses touching bars and why, and (iii) what advice you would give the student so their graph still looks clean but is also correct.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Weather log
(a) Thursday (18 mm).
(b) Total = 4 + 0 + 12 + 18 + 6 + 2 + 0 = 42 mm.
(c) Mean = 42 ÷ 7 = 6.0 mm per day.
1.2 — Olympics medals
(a) Side-by-side graph: at each of Gold / Silver / Bronze on the x-axis, draw one bar for Australia and one for the USA side by side. Scale 0–45 in fives. Heights — Gold: AUS 17, USA 39; Silver: AUS 19, USA 41; Bronze: AUS 16, USA 33. Include a key showing which colour is which country.
(b) Total AUS = 17 + 19 + 16 = 52. Total USA = 39 + 41 + 33 = 113. USA wins by 113 − 52 = 61 more medals.
(c) Australia: 17/52 × 100 ≈ 32.7% gold. USA: 39/113 × 100 ≈ 34.5% gold.
1.3 — School clubs
(a) Column graph: scale 0–35 in fives; five bars with gaps; heights 24, 15, 11, 32, 22 in the order Robotics, Debating, Chess, Drama, Art. Title: "Year 7 club sign-ups (n = 104)". x-axis: "Club". y-axis: "Number of students".
(b) Total = 24 + 15 + 11 + 32 + 22 = 104. Half = 52. Drama + Robotics = 32 + 24 = 56 (too high). Drama + Debating = 32 + 15 = 47 (too low). Drama + Art = 32 + 22 = 54 (close). Drama + Chess = 32 + 11 = 43. Robotics + Art + Chess = 24 + 22 + 11 = 57. There is no pair that totals exactly 52, but Robotics + Art = 24 + 22 = 46 and Robotics + Drama − 4 = 52… the closest matching pair is Drama + Art (54) or Robotics + Drama − Debating (41). Accept any reasoning showing the student tried valid pair sums; the closest pair to half is Drama + Art = 54 (just over half).
1.4 — Canteen sales
(a) Total = 120 + 95 + 140 + 115 + 180 = 650. Mean = 650 ÷ 5 = $130.
(b) Days above $130: Wednesday ($140) and Friday ($180).
(c) Friday vs Tuesday: (180 − 95) ÷ 95 × 100 = 85 ÷ 95 × 100 ≈ 89% higher.
1.5 — Misleading share-price graph
(a) Starting the y-axis at 98 makes a tiny absolute change look HUGE — the bar at 103 looks five times taller than the bar at 99, even though the real difference is only about 4%.
(b) Uneven intervals (98, 99, 100, 102, 105) distort the visual heights even more — equal differences in price are no longer equal distances on the graph.
(c) A fair version starts the y-axis at 0 and uses equal intervals (e.g. 0, 20, 40, 60, 80, 100, 120). All four bars will then be almost the same height — which is the honest message because prices only varied by ~4%.
2.1 — Explain your thinking (sample response)
Touching bars are wrong for categorical or discrete frequency data because the gaps between bars are part of how the reader understands the graph: they show that categories like "Maths", "English" and "Science" are separate things, not points on a continuous scale. A graph with touching bars is called a histogram, and it is used for continuous data — like height in cm or time in seconds — where the categories really do flow into one another with no real gaps in possible values. My advice to the student would be: keep the bars looking neat and equal in width, but leave a small uniform gap between them (e.g. one bar-width of space) so the reader instantly sees that the chart is showing categorical data, not continuous data.
Marking: 1 for explaining the gaps-mean-separate-categories point; 1 for naming a histogram and continuous data; 1 for the visual-appearance fix; 1 for clear, full sentences linking back to the lesson.