Line Graphs

Julie has recorded the number of ice creams she sold in her truck depending on the temperature outside. She wants to identify if there is a possible connection between the two variables. What do you think she could do to analyse this correlation? Well, it is always helpful to view the comparison between a set of objects visually through a graph.

However, we now need to think about the type of graph we could potentially use to plot these two variables against each other. Any guesses? Let me give you a hint: line graphs! Throughout this topic, we aim to explore the concept of a line graph and analyse its behaviour. The main objective here is to observe whether any significant relationships arise between the given variables we are investigating. So, let's begin!

Definition of a Line Graph

A line graph is a tool used to graphically display information, linking two variables where one is usually plotted on the x-axis and the other on the y-axis. Each point is plotted based on its x- and y-values. All the points are then connected together through straight line segments. Below is an example of a line graph used to display the number of rainy days in Dubai per year.

Line graph displaying the number of rainy days in Dubai per year between 2008 and 2012, StudySmarter Originals

Say we are told to find the number of rainy days in a given year. In order to do this, we would simply need to find the y value of the plotted line on that given year.

For example, if we were looking to find the number of rainy days in 2011, we can see that the line for that year arrives at a y-value of 40. Hence, the number of rainy days that year would be 40.

A line graph may sometimes be referred to as a line chart. They are often used to illustrate patterns that may arise between a pair of data sets and make predictions about future data values. One data set is usually dependent on the other.

Components of a Line Graph

Let us return to our previous line graph above. There are seven vital components we need to consider when observing or plotting a given line graph.

Components of a graph, StudySmarter Originals

Types of Line Graphs

There are three main different types of line graphs, namely:

1. Simple line graph

2. Multiple line graph

3. Compound line graph

Each of these graphs has its own way of calculating key statistical figures in relation to the data they contain within them. Before we explore each type above, let us learn how to interpret a given line graph.

How to Read a Line Graph

Say we are given a line graph. We are told to decipher the information illustrated by this graph. In this case, we can carry out a 5-step process to do this.

1. Observe the title of the graph;

2. Recognise the axis labels;

3. Analyse the slope between each pair of consecutive points. Make note of any significant trends;

4. Determine the exact figures by looking at the corresponding data points;

5. Evaluate the mean, median, mode and range.

With that in mind, let us now the three types of line graphs mentioned above in turn.

Simple line graph

Multiple line graph

A multiple line graph consists of a diagram with more than one plotted line.

Let us bring back the graph displaying the number of ice creams sold by Julie's truck at different temperatures, but this time between the years 2016 and 2017. We shall assume that the previous graph represents the number of ice creams sold by Julie in the year 2016. The line graphs for 2016 and 2017 are displayed in a singular graph below and are represented by the blue line and pink line respectively.

Line graph showing the number of ice creams sold by Julie's truck at different temperatures between 2016 and 2017, StudySmarter Originals

Deciphering this graph is similar to the simple line graph case. However, the only difference here is that we would have to analyse more than one data set and deal with more numbers. Since we are dealing with more values, be careful not to make careless mistakes! Always list your data set so that your calculations are accurate.

Let us first take note of any distinct patterns on the graph above. There are two patterns here:

1. The greater the temperature, the more ice creams are sold. This is the same trend we found in our previous example.

2. The number of ice creams sold in 2017 is greater than the number of ice creams sold in 2016 for each temperature value. This is because each pink point happens to be plotted above each corresponding blue point. This essentially means that Julie received more business in 2017 compared to 2016.

Now let us find the total number of ice creams sold between these 5 temperatures for each year. From the previous example, we know that the total number of ice creams sold in 2016 is 275. We can apply the same method to find the total number of ice creams sold in 2017.

21 + 57 + 64 + 78 + 100 = 320

Say we are also told to find the total number of ice creams sold in both years. To do this, we simply need to add the total number of ice creams sold in 2016 and the total number of ice creams sold in 2017. This yields,

275 + 320 = 595

We will now evaluate the mean, median, mode and range of this graph.

Compound line graph

A compound line graph shows the layers of data showing what proportions make up the total values. These graphs are also known as stacked area graphs. The way these graphs are read is by finding the difference between the highest part of a specific area and the lowest part of that same area, at the same x-coordinate.

Let us show this with an example. The graph below shows the number of vehicles sold by a motor company in Dundee throughout 2018. The graph shows the quantity for 3 types of vehicles: cars, trucks and motorcycles. The graph is also divided into 4 sections (called quartiles) throughout the year: Quarter 1, Quarter 2, Quarter 3 and Quarter 4.

Number of vehicles sold by a motor company in Dundee in 2018, StudySmarter Originals

To analyse this type of graph, we simply need to identify the upper and lower bounds of each quartile. For example, say we are told to find the number of motorcycles sold in the 4th Quarter. Observe the section in which this quarter is displayed. The number of motorcycles sold in the 4th Quarter has an upper bound of 26 and lower bound of 21. The number of motorcycles sold is simply the difference between these two values.

26 – 21 = 5

Thus, 5 motorcycles were sold in the 4th Quarter of 2018. In the same manner, try working out the number of trucks and cars sold in the 2nd Quarter and 3rd Quarter. Remember to take note of the upper and lower bounds for each case!

How to Plot a Line Graph

We shall now move on to drawing line graphs. This follows a 5-step procedure, as listed below.

1. Construct the x and y-axes. Label each axis clearly. Ensure that the axis scales are divided into even intervals;

2. Come up with a brief and informative title for your graph. Make sure that it relays the purpose of your graph;

3. Plot the data on the graph with respect to the corresponding x and y-values given;

4. Connect each pair of successive points with a straight line segment;

5. If you are comparing several data sets, make a key to distinguish the line graph for each sample using different colours. It is often advised to only have a maximum of 4 data sets in one line graph to avoid confusion.

Let's show this with an example.

Advantages and Disadvantages of Line Graphs

Just like any other graph, line graphs also have their pros and cons. The table below describes the advantages and disadvantages of line graphs.

More Examples Involving Line Graphs

Let us end this discussion with two more worked examples applying line graphs.