Module 1 (M1) - Handling data - Presenting and interpreting data - Line graphs and scattergraphs

Part ofMathsM1: Handling data

Data can be presented in many ways that make it quicker and easier to read.
In this section we will look at some of these ways. It is important to choose the best way to present data.

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Line graphs

A line graph can be used to show how one quantity changes as another is changed, e.g. how temperature changes over time or how a spring extends as the mass is increased.

It is plotted as a series of points, which are joined with straight lines.The ends of the line graph do not have to join to the axes.

Example

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  1. An image of a line graph. A vertical axis has been drawn to the left. The axis has been labelled with numbers. The values are increasing in units of five from zero to twenty. It is subdivided into intervals of zero point five. The axis has also been labelled, temperature, measured in degrees Celsius. The horizontal axis has been labelled with letters representing the first letter of each month. Each label is aligned with a vertical gridline. Between each label is a gap of width equalling five subdivisions. The axis has also been labelled, Month. Twelve data points have been plotted on the axes with crosses at; January, three. February, five. March, seven. April, seven. May, ten. June, fifteen. July, eighteen. August, fifteen. September, fifteen. October, fifteen. November, twelve. December, six. The data points have been joined by eleven line segments, passing through the data points in order. Written above: a line graph to show average temperature in the UK.

    What is the average temperature in May?

Line graph showing midday temperature over a period of 7 days

Line graph showing midday temperature over a period of 7 days

You can tell at a glance that the temperature was at its highest on Monday and that it started to fall in the middle of the week before rising again at the end of the week.

  1. What was the lowest temperature, and on what day did it occur?

  2. On what day was the midday temperature 26°C?

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Scatter graphs

Scatter graphs are a good way of displaying two sets of to see if there is a correlation, or connection.

Example

The number of umbrellas sold and the amount of rainfall on 9 days is shown on the scatter graph and in the table.

Scatter graph of umbrellas sold vs rainfall
Umbrellas sold11025013247815
Rainfall (mm)324005611

The graph shows that there is a positive correlation between the number of umbrellas sold and the amount of rainfall. On days with higher rainfall, there were a larger number of umbrellas sold.

Types of correlation

Positive correlation

The points lie close to a straight line, which has a positive gradient.

This shows that as one variable increases the other increases.

Scatter graph illustrating positive correlation

Negative correlation

The points lie close to a straight line, which has a negative gradient.

This shows that as one variable increases, the other decreases.

Scatter graph illustrating negative correlation

No correlation

The points do not lie close to any straight line.

This shows that there is no connection between the two variables.

Scatter graph illustrating no correlation

The scatter graph shows the temperature on 12 days in the summer and the number of ice creams sold by Jude’s Gelati on those days.

Temperature vs ice creams sold graph
  1. How many ice creams were sold when it was 23°C?
  2. Describe the relationship between the temperature and the number of ice creams sold.

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Test yourself

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