The class measured the room temperature every hour, from 8 a.m. to 4 p.m. Which graph shows best how it changed, and why?

A line graph, with the hours on the horizontal axis, because the value changes over time. — Right: the question is about change over time, and the line graph shows what rises, falls and when.

A newspaper shows the 20 weights with classes of 0.5 kg, but the last bar has been wiped out. The other eight are 1, 2, 5, 2, 2, 5, 1 and 1. What is the last bar's value?

1 — Right: the bars add up to 20 students, 19 in the eight known ones, so the last has 20 − 19 = 1.

Two newspapers publish histograms of the same 20 weights: one has three bars (8, 10 and 2), the other nine bars. What do you conclude?

They can be the same data with different classes: I compare the class limits and check that the bars add up to 20. — Right: 8 + 10 + 2 = 20 and the nine bars also add up to 20. What changes is what each graph lets you see.

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Mathematics Year 6: Reading graphs critically and choosing the right graph

Mathematics, Year 6 (Portugal): The same data can give different pictures: learn to compare graphs from the media, to see what the choices hide and to justify the graph you choose.

A graph is made of choices

A graph is not the data: it is a way of showing them, and every choice changes what you notice. With graphs from the media, ask four questions. Does it have a title, a source and a legend? Does the scale have equal steps, and where does it start? If it is a histogram, do the classes have equal width and do you know the limits? Does the type of graph fit the question? A graph can have every number right and still give an idea that the data do not support.

Choose the graph by the question, and say why

Whoever makes the graph decides, and when it is you making it you must be able to justify it. The question rules: “How did it change over time?” calls for a line graph; “How are the measured values distributed?” calls for a histogram; “Which category is largest?” calls for bars, and “What part of the whole?” for a pie chart, as you saw in Year 5. And justify it in one sentence: “I used a histogram because the weights are measured and I want to see where they gather.”

The same 20 weights, three histograms

With classes of 2 kg, the histogram has three bars: [2, 4) 8, [4, 6) 10 and [6, 8) 2; it looks like one single group, around 4 to 6 kg. With classes of 0.5 kg there are nine bars: 1, 2, 5, 2, 2, 5, 1, 1, 1; two bars of 5, in [3.5, 4) and [5, 5.5), with a valley of 2 between them: it looks like two groups. The data are the same 20 values (8 + 10 + 2 = 20 and 1 + 2 + 5 + 2 + 2 + 5 + 1 + 1 + 1 = 20). With classes of 1 kg (1, 7, 4, 6, 2) the two groups show up with less noise.

Different graphs do not mean one is lying

Two newspapers publish histograms of the same 20 weights: one with three bars (8, 10 and 2), the other with nine. Common reaction: “one of them is wrong”. But neither has to be. Check: the bars of each add up to 20 (8 + 10 + 2 and 1 + 2 + 5 + 2 + 2 + 5 + 1 + 1 + 1) and the classes are different. What changes is what each graph lets you see. The question to ask is “which classes were used, and why?”, and be wary when the graph does not say what they are.

News, reports and your conclusions

In the news, in school reports and in phone apps you will find histograms and line graphs, often with no title or no source. When you have to draw a conclusion, write what the graph shows, what it does not show and what you would ask next. When you have to make a graph, choose the type by the question, try more than one choice of classes and say why. This is statistical literacy.

Test what you learned

The class measured the room temperature every hour, from 8 a.m. to 4 p.m. Which graph shows best how it changed, and why?
- a) A histogram, because temperature is a measurement.
- b) A pie chart, because they are parts of the day.
- c) A line graph, with the hours on the horizontal axis, because the value changes over time.
Correct answer: c) A line graph, with the hours on the horizontal axis, because the value changes over time. — Right: the question is about change over time, and the line graph shows what rises, falls and when.
A newspaper shows the 20 weights with classes of 0.5 kg, but the last bar has been wiped out. The other eight are 1, 2, 5, 2, 2, 5, 1 and 1. What is the last bar's value?
- a) 1
- b) 0
- c) 19
- d) 20
Correct answer: a) 1 — Right: the bars add up to 20 students, 19 in the eight known ones, so the last has 20 − 19 = 1.
Two newspapers publish histograms of the same 20 weights: one has three bars (8, 10 and 2), the other nine bars. What do you conclude?
- a) One of them is wrong, because the graphs are different.
- b) The three-bar one is always right, because it is simpler.
- c) The nine-bar one is always right, because it has more detail.
- d) They can be the same data with different classes: I compare the class limits and check that the bars add up to 20.
Correct answer: d) They can be the same data with different classes: I compare the class limits and check that the bars add up to 20. — Right: 8 + 10 + 2 = 20 and the nine bars also add up to 20. What changes is what each graph lets you see.

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