Maths: Reading Graphs and Tables

In these questions, you're given a chart, a graph or a table, and a question about it.

Your job is to read the numbers you need off the picture, then use them to answer the question. There are five answers to choose from.

In GL's papers the question usually wants readings put together, such as a total or a difference, and the scale often has to be worked out first. The video above and the worked example below work through the same question, with the options in the same order. The pictogram and the pie chart after it are the video's next two questions.

The method

Four steps: read the graph first, work out the scale, read the values across, answer the question asked.

The same four steps work on a pictogram and on a pie chart. In a pictogram, the key is the scale. In a pie chart, the whole circle is the total.

Worked example

The line graph shows how many children went to breakfast club each day from Monday to Friday. How many more children went to breakfast club on Thursday than on Monday?

Breakfast club — a line graph. Across the bottom: the days, Mon, Tue, Wed, Thu and Fri. Up the side: Number of children, from 0 to 40, with a labelled line every 10 and five small squares between each pair of labelled lines. The points are joined by straight lines. Mon is 4 small squares above the 10 line · Tue is 1 small square above 30 · Wed is 4 small squares above 30 · Thu is 4 small squares above 20 · Fri is 2 small squares above 10.

A. 1 B. 8 C. 10 D. 18 E. 28

1. Read the graph first. Before you look for any numbers, check what it shows. The title is breakfast club. Across the bottom are the days of the week. Up the side is the number of children, so the units are children. Each point on the line shows how many children came that day.
2. Work out the scale. Find two labelled lines next to each other, and count the small squares between them. From 20 up to 30 is 10, and there are five small squares. 10 shared between 5 is 2. So each small square is worth 2.
3. Read the values across. Find the day along the bottom, go up to its point, then look straight across to the scale. Thursday's point is four small squares above 20: 22, 24, 26, 28. So Thursday is 28. Monday's point is four small squares above 10, so Monday is 18.
4. Answer the question asked. The question says how many more, so find the difference: take the smaller reading away from the bigger one. If it asked how many altogether, you would add. 28 − 18 = 10. D and E are each just one reading, so they stop part-way. Cross them off. B reads Monday as 20, the nearest labelled line, which gives 8. So B is out. And A just counts the labelled line between the points, but those lines go up in tens, so A is out too. So the answer is C.

Answer: C — 10 (Thursday 28 − Monday 18 = 10 more children)

A second worked example: a pictogram

The pictogram shows the number of stars given out each day. One symbol stands for 10 stars. How many more stars were given out on Wednesday than on Friday?

Stars given out — a pictogram with a row for each day. Monday: 6 symbols · Tuesday: 4 symbols · Wednesday: 8 and a half symbols · Thursday: 2 and a half symbols · Friday: 2 and a half symbols. Key: one star symbol = 10 stars.

A. 70 B. 6 C. 85 D. 110 E. 60

1. Read the graph first. A row for each day.
2. Work out the scale. In a pictogram, the key is the scale. One symbol is 10 stars, so half a symbol is 5.
3. Read the values across. Count the whole symbols, then add the half. Wednesday: 8 and a half symbols, 85. Friday: 2 and a half, 25.
4. Answer the question asked. How many more? Take the smaller away from the bigger: 85 − 25 = 60. 6 (B) counts symbols, and 85 (C) is only Wednesday, so cross them both off. 110 (D) adds the rows, and 70 (A) has a symbol too many, so they're out too. So this one is E, 60.

Answer: E — 60 (Wednesday 85 − Friday 25 = 60 more stars)

A third worked example: a pie chart

The pie chart shows the 40 books in a class library. How many science books are there?

Books in the class library — a pie chart with three slices: Poetry, Science and History. Poetry fills half the circle. Science and History fill a quarter each, so each has a square corner at the centre.

A. 30 B. 25 C. 20 D. 10 E. 5

1. Read the graph first. Poetry, science and history.
2. Work out the scale. The whole circle is the total: all 40 books. So half of it is 20.
3. Read the values across. Science is a quarter: see the square corner. A quarter of 40 is 10.
4. Answer the question asked. Here, the reading is the answer. 20 (C) takes science as a half, and 5 (E) as an eighth, so cross them both off. 25 (B) uses 100 as the total, and 30 (A) is all the other books, so they're out too. So this one is D, 10.

Answer: D — 10 (a quarter of 40 books = 10)

Things to watch out for

1. Work out the scale first. One square isn't always worth one. A bar chart of favourite colours asks how many more children chose blue than purple, and its scale goes up in fives. The blue bar is four squares taller than the purple bar, but that doesn't mean four more children. Each square is worth 5, so it's 20 more.
2. The right bar, row or point. In a table, find the right row, then the right column, and read the number where they meet. In a table of team points, Blue and Game 2 meet at 24. The four wrong answers are the numbers all around it.
3. A reading is rarely the answer. Finish the question. In the worked example, 18 and 28 were both answers you could choose. Each one is a real reading, but only half the job.
4. Read the values, not the heights. Check where the axis starts. In a bar chart of the books each class read, it starts at 30, so the bars look tiny. Read as heights from the bottom, Class 3 and Class 6 come to just 6. Read from the scale, they are 32 and 34, which make 66.

Related

• The complete 11+ question-type guide
• Maths: Fractions — find the whole, cut it into equal parts
• Maths: Coordinates and Transformations — read the axes, across first, then up
• Maths: Word Problems — plan, then finish every step

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