Reading column graphs carefully
Check the scale before you read any bar. Most mistakes in data questions come from assuming each gridline is worth one.
Check the scale before anything else
The two graphs below have bars of exactly the same height. One of them is worth 4 and the other is worth 20.
Nothing about the bar tells you which. Only the numbers up the side do. So read the axis before you read a single column — it takes two seconds and it is where most marks are lost.
When a bar stops between the lines
Bars often stop between two gridlines. Work out what one gap is worth first, then judge the fraction of it.
If the lines go up in fives and the bar stops halfway between 10 and 15, that half-gap is worth about 2 or 3 — so the bar is about 12 or 13. It is certainly not 11, which is what counting gridlines as ones would give you.
Answer the question that was asked
Questions rarely just ask you to read one bar. They ask for a difference, a total, or how many more one thing is than another.
Read the last sentence of the question again before you pick an option. The tallest bar is the answer to "which is most" — and the wrong answer to almost everything else.
The same picture can mean very different numbers
Two graphs can look identical and say completely different things, because the numbers up the side are not the same.
A bar reaching the second gridline means four on one graph and twenty on the other. Nothing about the shape tells you which — only the scale does.
So the first thing you do with any graph is read the axis, work out what one gridline is worth, and only then look at the bars.
Questions about the difference, not the height
Most marks in this topic are not for reading one bar. They are for comparing two, or for working out how many more, or for finding a total.
Read both bars, write both numbers down, then do the arithmetic the question asks for. Doing it in your head off the picture is where the slips happen.
Watch for questions that ask about something not drawn at all — "how many more would be needed to reach fifty" — where the graph gives you the starting number and you supply the rest.
Worked examples
A graph has gridlines labelled 0, 5, 10, 15, 20. A bar reaches the fourth line up. What is it worth?
The lines are 0, 5, 10, 15, 20, so the fourth line up from zero is 15. Counting lines instead of reading them would have given 4.
Answer: 15
On the same graph, red is 20 and blue is 15. The question asks how many more red than blue. What is the answer?
The question wants the difference, not either value: 20 − 15 = 5. Answering 20 would be reading the graph correctly and answering the wrong question.
Answer: 5
A bar stops exactly halfway between the 20 and 30 gridlines. What is it worth?
One gap is 30 − 20 = 10, so half a gap is 5. The bar is worth 20 + 5 = 25.
Answer: 25
A graph has gridlines labelled 0, 4, 8, 12, 16. A bar reaches the third gridline. What is its value?
Each gridline is worth 4. The third gridline above zero is 12.
Answer: 12
On a graph scaled in fives, cats reach 25 and dogs reach 15. How many more cats than dogs?
Read both values off the scale first, then subtract: 25 − 15. The question asks for the difference, not for either total.
Answer: 10 more cats
Four bars show 20, 15, 25 and 10. How many altogether?
The question asks for a total, so every bar counts. Add them in pairs to keep it simple: 20 + 10 = 30, and 15 + 25 = 40.
Answer: 70
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