Reading a graph to answer questions

From graph to answer

Reading a graph is only the first half of the job. The second half is answering the question the graph was drawn for. Almost every graph question asks you to compare, to add or to subtract, and each one follows the same three steps.

Step 1: read the values the question names. Step 2: decide what the question wants, a comparison, a total or a difference. Step 3: work out the arithmetic and check it against the graph. The wording gives the clue, so read it twice before you pick up a pencil.

Compare, total or difference

Words like "most" and "least" ask for a comparison. Find the tallest or shortest bar and name its category. Words like "altogether" and "in total" ask you to add. Words like "how many more" and "how many fewer" ask you to subtract the smaller value from the larger one.

Here is a bar graph of books read by five classes. Keep the three question words in mind as you read it.

The tallest bar answers "which class read the most": class 3C, with 15 books. The shortest bar answers "which class read the fewest": class 3D, with 6 books. To compare the two in a number, subtract: 15 − 6 = 9, so class 3C read 9 more books than 3D.

Adding values from a graph

For a total, read every value you need and add them. Class 3A read 12 books and class 3E read 9 books, so those two classes read 12 + 9 = 21 books. All five classes together read 12 + 8 + 15 + 6 + 9 = 50 books.

When the question names only two categories, add only those two. Adding every bar when the question asks about two of them is the most common mistake with graph questions.

The same method on a line plot

A line plot answers the same kinds of questions, because each stack works like a bar. This plot shows the goals scored in each match of a short season.

The tallest stack is above 2, so 2 is the most common number of goals. Three matches had 2 goals. To find the total number of goals, multiply each value by its stack height and add: 0 × 1 + 1 × 2 + 2 × 3 + 3 × 2 + 4 × 1 = 0 + 2 + 6 + 6 + 4 = 18 goals. The number of marks counts the matches: 1 + 2 + 3 + 2 + 1 = 9 matches.

Checking your answer

A good answer can always be checked against the graph. For a difference, add the smaller value back: if 3C read 9 more than 3D, then 6 + 9 should give 3C's 15 books. For a total, add the values in a different order and see if the answer stays the same. For a comparison, look at the graph again: the category you named must really have the tallest or shortest bar.