Interpreting Graphs

Before you read a single column, look at the scale up the side. On this graph the labelled numbers go up in twos, so every gridline is worth two students, not one. Now the reading is easy. The walk column reaches the line marked eight, so eight students walk. The bus column reaches twelve. The car column is the interesting one, because it stops halfway between six and eight, and halfway between six and eight is seven. The bike column stops halfway between two and four, which is three. Never assume that one gridline means one person. Checking what the scale counts in takes two seconds, and getting it wrong is the single most common mistake in this whole topic.

Once you can read the columns, most questions come down to two words. Which way of travelling is most common? Find the tallest column, which is bus with twelve. Which is least common? The shortest, bike with three. How many more take the bus than ride a bike? The words how many more mean subtract, so twelve take away three gives nine. How many students altogether? Altogether means add every column, so eight plus twelve plus seven plus three is thirty. And how many do not come by car? Take that column away from the total, so thirty minus seven is twenty-three. Underline those key words in the question before you even look at the graph.

A line graph is read differently, because the shape of the line carries the message. This bean plant is two centimetres tall in week one and fourteen by week five, and the line rises the whole way, so the plant never stopped growing. Look at the steps between the points: plus three, then plus four, then plus three, then plus two. The steepest section is week two to week three, which is where it grew fastest, and the flattest is week four to week five, where growth slowed down. The total growth is fourteen take away two, which is twelve centimetres. Be careful with that flattening at the end — a line that levels off means slower growth, not shrinking.

A dot plot answers four questions, each in its own way. How many games were played? Count all the dots, which gives twelve. What was the most common score? Look for the tallest stack, which sits above two, so two goals. How spread out are the scores? Take the lowest value from the highest, so four minus nought is four. And how many goals were scored altogether? That one needs multiplying: each value times the number of dots above it, so nought plus three plus eight plus six plus four, which is twenty-one goals. Keep games and goals apart in your head. Counting dots tells you how many games there were, never how many goals were scored.

Here is why the rule about starting at nought matters. Both of these graphs show the same two numbers, eight and twelve. On the left the scale starts at nought, and the bus column is one and a half times the walk column, which is exactly right. On the right the scale starts at six instead, so the bottom of both columns has been chopped off, and now the bus column looks three times as tall as the walk column. Nothing about the data changed — only the drawing. Advertisements use this trick deliberately to make small differences look enormous. So whenever you meet a graph, find where the scale starts before you believe what the picture seems to say.