Line graph

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GCSE Maths Statistics Representing Data

Line Graph

Here we will learn about line graphs, including drawing, reading and interpreting them.

There are also line graphs worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is a line graph?

A line graph is a way of displaying data to easily see a trend over time.

To draw a line graph, we need to plot individual items of data onto a set of axes, and then connect each consecutive data point with a line segment.

The $x$ -axis or horizontal axis is labelled as time, and the $y$ -axis or vertical axis is the variable that is being measured or tracked (ice cream sales, hours spent on homework, earnings, number of births etc).

The main benefit of this type of graph is that you can spot trends in the data over time.

This is a really useful tool in business to show sales trends or profits and losses over time or in science to show the growth rate of bacteria, change of pH or a change in temperature over time.

Patterns in data allow for more accurate predictions in the future.

What is a line graph?

How to draw a line graph

In order to draw a line graph:

Label the axes and add an axis title.
Plot each data point accurately.
Connect each pair of consecutive points with a straight line.

How to draw a line graph

Line graph worksheet

Get your free line graph worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Line graph worksheet

Get your free line graph worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on representing data

Line graph is part of our series of lessons to support revision on representing data. You may find it helpful to start with the main representing data lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Line graph examples

Example 1: population change

The data shows the population of England from $1980$ to $2005$ . Draw a line graph to show the data in the table.

Label the axes and add an axis title.

Here, the $x$ -axis is labelled as the Year, and the $y$ -axis is labelled as the Population (millions). Each axis value is spaced out equally, with enough room to place each data value in a more specific location, so the line graph is more accurate.

2Plot each data point accurately.

Plotting each point one at a time, we get the following plot:

3Connect each pair of consecutive points with a straight line.

Example 2: price fluctuations

The table shows the average price of fish and chips in the UK over $50$ years.

Draw a line graph to show this information.

Label the axes and add an axis title.

Here, the $x$ -axis is labelled as the Year, and the $y$ -axis is labelled as the Price (£). Each axis value is spaced out equally, with enough room to place each data value in a more specific location, so the line graph maintains the accuracy within the data.

Plot each data point accurately.

Plotting each point one at a time, we get the following plot:

Connect each pair of consecutive points with a straight line.

Example 3: hours of sleep

The following table of data values shows the amount of sleep in hours James had over one week.

Draw a line graph to represent this data.

Label the axes and add an axis title.

Plot each data point accurately.

Connect each pair of consecutive points with a straight line.

Reading and interpreting line graphs

The purpose of drawing a line graph (or time series) is to spot trends over a period of time. This is much easier when looking at a plotted set of data, rather than data within a table.

How to read a value from a line graph

To read a value from a line graph, you need to identify which axis you are starting from, and so the data value will be estimated from the other axis.

E.g.

Using the line graph from Example $1$ , we have the line graph that represents the population of England in millions between $1980$ and $2005$ .

If we wanted to estimate the population in $1992$ , we would find the value of $1992$ on the axis (here the $x$ -axis), draw a vertical line up to the coordinate on the line graph, and then draw a horizontal line from this coordinate to the $y$ -axis. This would state the estimate for the population in $1992$ to be around $47.9$ million people.

We can do the same if we wanted to find out which year the population exceeded $50$ million people, by locating the value $50$ on the $y$ -axis, and reversing the process.

Here, the answer would be around the year $2003$ .

How to interpret a line graph

Interpreting a line graph is a key skill. Here, we need to spot trends or changes in the data that are significant, if not just noticeable.

Looking at the same line graph from Example $1$ , we can state a clear trend in the data: the population of England between $1980$ and $2005$ has increased. This is because, every year, the value for the population is higher than the previous year.

Here, the red line is a line of best fit for the population data, and the blue arrow indicates an upward trend. You may have to draw a line of best fit to represent the correlation of the data.

Step-by-step guide: Line of best fit (coming soon)

There are limitations to this that we have to consider. We only have the data for every $5$ years. There may have been no population change at all between the year $2000$ and the year $2004$ , and then the population suddenly increased in $2005$ . We simply drew a straight line between $2000$ and $2005$ , which assumes the population change over these $5$ years was exactly the same every year, which is very unlikely!

This example of a limiting factor is one of the most common issues with a line graph (generalisations in the data / lack of accuracy / not enough data values etc).

Time series can show seasonal fluctuations, for example the sales of ice cream throughout a year is expected to be higher in the warm summer months than the cold winter months and so we would use a moving average.

Step-by-step guide: Moving averages (coming soon)

How to read a value from a line graph

In order to read a value from a line graph:

Locate the value on the appropriate axis.
Draw a horizontal / vertical line to the data point on the line graph.
Draw a horizontal / vertical line from the data point to the other axis.
Read the value from the axis.

How to read a value from a line graph

Reading line graphs examples

Example 4: reading line graphs – frequency of cars

The line graph shows the frequency of cars on a busy road between $5$ am and $11$ am. Estimate the number of cars on the road at $8$ : $30$ am.

Locate the value on the appropriate axis.

Draw a horizontal / vertical line to the data point on the line graph.

Here we will draw a vertical line to the data point on the line graph as time is on the $x$ -axis.

Draw a horizontal / vertical line from the data point to the other axis.

As we need to reach the $y$ -axis, we draw a horizontal line from the data point to the $y$ -axis.

Read the value from the axis.

Here, the value on the $y$ -axis is around $425$ .

The frequency of cars on the road at $8$ : $30$ am is $425$ .

Example 5: reading line graphs – vaccinations

The line graph shows the number of people who received their flu vaccine per month over one year. The data was recorded on the last day of the month. What month did the number of people receiving their flu vaccine reach over $100,000$ ?

Locate the value on the appropriate axis.

Draw a horizontal / vertical line to the data point on the line graph.

Here we will draw a horizontal line to the data point on the line graph as the frequency of vaccinations is on the $y$ -axis.

Draw a horizontal / vertical line from the data point to the other axis.

As we need to reach the $x$ -axis, we draw a vertical line from the data point to the $x$ -axis.

Read the value from the axis.

Here, the value on the $x$ -axis is between October and November. This means that the number of vaccines reached over $100,000$ in November as the previous data point recorded was on the last day in October.

The number of vaccinations exceeded $100,000$ per month in November.

Example 6: reading line graphs – download speed

The time series shows the download speed of a video in megabytes per second $(mbs^{-1}$ ). The download speed was recorded every second for the length of the download.

How many seconds did the download speed exceed $2mbs^{-1}$ ?

Locate the value on the appropriate axis.

As we need to exceed $2mbs^{-1}$ , we need to locate $2mbs^{-1}$ on the $y$ -axis.

Draw a horizontal / vertical line to the data point on the line graph.

Instead of drawing a horizontal line to the first point, we need to determine all the points that are above $2mbs^{-1}$ and so we draw a horizontal line across the entire plot.

Draw a horizontal / vertical line from the data point to the other axis.

Drawing a vertical line for each value where the line graph crosses our horizontal line, we get the following:

Read the value from the axis.

We have two values that we need to read from the axis.

These are $9.1$ and $10.5$ :

As the question asks us for the length of time the download speed exceeded $2mbs^{-1}$ , by calculating the range of these two values, we will calculate this value.

$10.5 - 9.1 = 1.4$ seconds.

The download speed exceeded $2mbs^{-1}$ for $1.4$ seconds.

Common misconceptions

$x$ or $y$ axis

A line graph does not have to be connected to the axis everytime. It all depends on the number the axis starts with.

Reading values from a table

The values read in between plotted points on the graph are estimates because no exact values were collected at the times between the data points given. Any value taken from the graph that isn’t an exact plotted point is therefore an estimate.

Time and the $x$ axis

The time must be plotted on the $x$ axis (horizontal axis).

Practice line graph questions

As time is always written on the $x$ -axis, the mass of bacteria is therefore written on the $y$ -axis. Plotting the points at the exact values and joining these together with straight lines, we get the solution:

As time is always written on the $x$ -axis, rainfall is written on the $y$ -axis. Plotting the points at the exact values and joining these together with straight lines, we get the solution:

Draw each line graph separately. We plot the points for Office $A$ first, and connect them using straight lines. We then draw the plot for Office $B$ on the same set of axes, and join these consecutive points with straight lines. Do not connect the two plots together. This gives us the solution:

Monday

Tuesday

Wednesday

Saturday

As you would expect ice cream sales to correlate with the amount of warm sunshine (the more warm sunshine, the greater the number of ice cream sales), Tuesday has a very low number of ice creams sold so it is most likely to have rained that day.

7.70^\circ C

11.3^\circ C

6.4^\circ C

10.8^\circ C

The highest temperature recorded during the day is the highest data point on the graph. This is at $1$ pm at Station $B$ , where the temperature was recorded at $10.8^\circ C$ .

£59,400

£7,425

£59.40

£215,325

Adding up the building costs for each item of data recorded, we get $4+10.9+8+5.3+10.5+8.8+3.4+8.5=59.4.$

The mean for these $8$ items of data is therefore: $59.4\div 8=7.425$

As the data is recorded in $£1000s, 7.425\times 1000=£7425$ per month.

Line graph GCSE questions

1. The line graph below shows the number of cushions sold in a furniture shop over $6$ weeks.

(a) Which week did the shop sell the most cushions?

(b) Which week did the shop sell the least cushions?

(3 marks)

Show answer

(a)

Week $3$

(1)

(b)

$1$

(1)

(b)

$[83-87]$

(1)

2. The graph below shows the recovery heart rate of an athlete immediately after sprinting $100m$ during his recovery. The results were taken by using a heart rate monitor.

(a) What was the heart rate of the athlete, $105$ seconds after the sprint had finished?

(b) The athlete sat up at one point during his recovery. During which $30$ second period did he sit up?

(c) Work out the difference in the heart rate from the moment the athlete finished the sprint to $3$ minutes into his recovery.

(d) The table below measures an athlete’s fitness level, based on their recovery heart rate at $1$ minute after exercise. Determine what category the athlete is placed in.

(5 marks)

Show answer

(a)

$90 bmp$

(1)

(b)

$2$ minutes to $2$ minutes $30$

(1)

(c)

$160 - [75-78]$

(1)

$[82-85]$

(1)

Poor

(1)

3. The table shows the height of a sunflower over $6$ months.

(a) Use the axes below to draw a line graph to represent the height of the sunflower over the $6$ months.

(b) Between which two consecutive months did the sunflower grow the most?

(4 marks)

Show answer

(a)

Axes labelled correctly.

(1)

All points plotted correctly.

(1)

All consecutive points connected using a straight line.

(1)

(b)

Months $4$ and $5$

(1)

Learning checklist

You have now learned how to:

Interpret and construct tables and line graphs for time series data

The next lessons are

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