Explainer: Line Graphs

In this explainer, we will learn how to use line graphs to analyze data, communicate information, and get insights from data.

A line graph is a graph that uses points connected by lines to show how something changes, often, over time. Let us see how this works by drawing a line graph using data from a store selling ice cream in a seaside town. The table below shows the number of ice creams sold on four days in a particular week in June.

To draw a line graph, the first thing we need to do is to draw and label our axes. In this case, we have data on the number of ice creams sold (which will be on our vertical axis) and the day of the week on which those ice creams were sold (which we put on our horizontal axis).

Once we have our axes in place, from our data we can mark the number of ice creams sold each day on our chart. Here, we have done this with a cross. You can see, for example, that above “Thursday” there is a cross in line with where the number 12 would be on the vertical axis (since 12 ice creams were sold on Thursday).

We then join the dots in our plot with straight lines to give us the completed line graph.

Notice that in this graph each of the lines joining two crosses goes up, from left to right. This means that the ice cream sales increased each day. Suppose we now add the fact that 10 ice creams were sold on the following Monday to our data.

Adding this extra information to our line graph we see that the line between the sales figures for Sunday and Mondays goes down from left to right. This means that sales decreased from Sunday to Monday.

Let us now look at some examples of how we can use line graphs to analyze and gain information from data.

Example 1: Reading Savings from a Line Graph

The line graph shows how much a person saved in each of the first four months of a year. In which month was the smallest amount of money saved?

Answer

To find out in which month the least money was saved, we can look on our line graph for the month that has the lowest point above it. In this case, you can see that the month of April has the lowest point above it. So, the smallest amount was saved in April.

Note

By drawing a line directly across from the dot above April to the vertical axis, we can find out how much was saved in April. The line goes across to the number 10 on the vertical axis, so £10 was saved in April.

We can do the same for each of the months on the line graph

Now let us look at another example of reading and analyzing data from a line graph.

Example 2: Reading Data from Line Graphs

The graph shows how much Isabella had in savings at the end of each month, over a 5-month period. Find the difference in amount between when her savings were highest and when they were lowest.

Answer

The first thing we must do is to find out what Isabella’s highest and lowest savings were. We can do this by looking for the highest data point on the line graph and the lowest data point on the line graph. The highest point is circled in blue and the lowest in pink, on the graph below.

The highest data point is above April and the lowest is above May. To find out what Isabella’s savings were at the end of April and the end of May, we draw a line across to the vertical axis for each of these two months. We can then read off her savings for the end of April and the end of May.

The blue dashed line from the dot above April goes across to midway between 20 and 24 on the vertical axis. So, Isabella had £22 in savings at the end of April. The pink dashed line from the point above May goes across to midway between 4 and 8 on the vertical axis, so Isabella had (only!) £6 savings at the end of May. If we subtract Isabella’s savings at the end of May from those at the end of April, we find that the difference between them is £££226=16. Isabella’s savings have therefore decreased by £16. This means that Isabella must have spent £16 of her savings in May.

Example 3: Interpreting Line Graphs

The graph shows Hannah’s total savings over seven weeks. Did she save more money from week 5 to week 6 than any other week?