Mathematics Year 7: Two sets of data in one graph
Mathematics, Year 7 (Portugal): Compare two sets of data with a line graph (time on one axis) or overlapping bars, on a fair scale, with title, source and legend, and justify the graph you choose.
Two sets, one graph, the same scale
To compare two sets of data, draw them in the same graph. If you have bivariate data and one variable is time, use a line graph: time goes on the horizontal axis and each set has its own line, on the same scale. If you have two sets of one characteristic, such as the shoe sizes of two classes, use overlapping bars: the two bars of each category sit in the same place. Either way, add a title, the source and a legend saying which line or bar is which.
Comparing shows what one set hides
A graph of one set tells half the story. With two lines in the same graph you see whether they rise together, whether one falls behind or whether they drift apart, and that suggests explanatory hypotheses: if the number of swimmers in a club rises a lot and the number of coaches barely moves, maybe each coach has more and more pupils. It is only a hypothesis, to be tested with more data. With overlapping bars you see at a glance where two classes look alike and where they differ.
Swimmers and coaches over six years
A club records, over six years, swimmers: 120, 135, 160, 170, 198, 216 and coaches: 8, 9, 10, 10, 11, 12. Step 1: years on the horizontal axis; vertical axis from 0 to 220, 1 cm for 20. Step 2: the swimmers climb from 6 cm to 10.8 cm, but the coaches stay between 0.4 and 0.6 cm: an almost flat line, although they rose by 4. The magnitudes are too different. Step 3: draw one graph per variable on the same time axis, or calculate swimmers per coach: 15, 15, 16, 17, 18, 18. Each coach looks after more and more swimmers.
The bar that hides behind another
Class A has 20 pupils, class B has 25; shoe sizes 36 to 40. Relative frequencies: A 15%, 25%, 30%, 20%, 10%; B 8%, 24%, 36%, 20%, 12% (use these, not the counts: the classes differ in size). Draw B behind and A in front, both solid: at size 36, A has 15% and B only 8%, so B's bar is completely hidden. Swapping the order does not fix it: at size 38, B is taller (36% against 30%) and hides A. Use transparent colours, or make the front bar narrower, and put both in the legend.
Choose the graph and say why
Before drawing, ask three questions: what kind of variable is it? What do I want to show? Who will read it? Categories: bars. Numbers in classes: histogram. Change over time: lines. Parts of a whole, with few parts: pie chart. Two sets of one characteristic: overlapping bars. Then write your reason in one sentence: “I used lines because time is a variable and I want to see the change.” You see these graphs in newspapers, club reports and weather bulletins.
Test what you learned
When does it make sense to use overlapping bars?
- a) To show how one single quantity changes over the years
- b) To compare two sets of one characteristic, such as the shoe sizes of two classes
- c) To show what share of a whole each category takes
- d) To compare two different variables with very different magnitudes, such as swimmers and coaches
Correct answer: b) To compare two sets of one characteristic, such as the shoe sizes of two classes — Right: for each category the two bars sit in the same place, so the differences are seen at a glance.
In year 4 a club had 170 swimmers and 10 coaches; in year 6 it had 216 swimmers and 12 coaches. How many swimmers per coach in each year?
- a) 1 700 / 2 592
- b) 160 / 204
- c) 17 / 18
- d) About 0.06 / 0.06
Correct answer: c) 17 / 18 — 170 ÷ 10 = 17 and 216 ÷ 12 = 18. Each coach looks after one more swimmer, a change that two graphs of very different magnitudes would hide.
In overlapping bars, at size 36 class A has 15% (solid, in front) and class B has 8% (behind). What happens to B's bar, and what fixes it?
- a) It shows fully, because it is the smaller bar
- b) It is hidden, but swapping the order fixes every size
- c) It is hidden, and using the counts instead of percentages fixes it
- d) It is hidden behind A's taller bar; use transparent colours or a narrower front bar
Correct answer: d) It is hidden behind A's taller bar; use transparent colours or a narrower front bar — Right: transparency, or a narrower bar in front, lets both bars be read at every size, and the legend says which is which.
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