The bar graph shows the number of pens, pencils, rulers, and erasers sold by a store in one week, but the labels are missing. The store sold more pens than any other item, erasers were least popular, and more pencils were sold than rulers. How many rulers did they sell?
Let’s spend some time looking at this bar graph to understand it. If we look at the 𝑦-axis, we can see a scale that goes up in tens. And it’s labelled number of items sold. This is because the bar graph shows us the number of different items sold by a store in one week. There are four items, pens, pencils, rulers, and erasers. And these four items are represented by the four bars in our bar graph.
But unfortunately, if we look at our 𝑥-axis, we can’t see any labels. We can just see the general heading, items. Now, the question asked us, how many rulers did the store sell? But how can we work this out? How can we read the graph if we don’t know which of the bars represents rulers? Well, in the next part of the problem, we’re given some clues to help us. Let’s read through it carefully and try to work out which of the four bars represents rulers.
The first clue we’re given is that the store sold more pens than any other item. Another way of saying this is that pens were the most popular item; they had the most sales. We know that the higher up the scale we go on the side of our bar graph, the more sales we can see. And so, we’d expect the bar that represents the most sales to be the tallest. The third bar’s the tallest, so this must represent the item that sold the most. We know these are the pens, so we can label this bar to help us remember what it represents.
The next clue we’re given is that erasers were least popular. In other words, they sold the least amount. Which of our bars might represent the least sales? We’d expect the bar on our bar graph that shows the lowest sales to be the shortest. And we can see straightaway that the final bar on our graph is the shortest. It shows the least popular item. So, let’s label this bar erasers.
Remember our question asked us, how many rulers did the store sell? So far, we know that the bar that represents rulers isn’t the third or fourth bar. It must be one of the first two. Let’s look at our final clue. We’re told more pencils were sold than rulers. We’ve already labelled the pens and erasers, so the pencils and rulers must be the first two bars. But which is which?
If more pencils were sold than rulers, we’d expect the bar that represents pencils to be taller. And the taller of these two bars is the first. So, this must be the one that represents the number of pencils that were sold. This means the only remaining bar must be the one that represents the rulers that were sold. And now we can solve the problem.
How many rulers did the store sell? First, we can find the bar that represents rulers, which is the second one. And then, we can read across from the top of our bar all the way to the scale on the left-hand side, on the 𝑦-axis. We can see that it’s the same height as the number 30. We used the clues that we were given to work out which bar represented which item. The second bar along represents the number of rulers. And so, the number of rulers that the store sold in one week is 30.