Discrete data results from counting the number of coins in pupils' pockets, number of peas in a pod, or the number of lengths swum in a sponsored swim.

Grouped discrete data arises from a discrete variable (usually numerical) where the data has been grouped into sets, e.g. the numbers of pupils with shoe sizes 3–5, 6–8, 9–11, etc.

Discrete means separate. Therefore discrete data is a variable that can only take separate values e.g. eye colour, how you travel to school. Sets are formed for each discrete variable.

Discrete data is normally recorded on a block graph or bar chart. There should be gaps between the bars to show that data is discrete.

Continuous data results from measurements such as lengths of caterpillars or weights of crisp packets, and may be organised in touching but non-overlapping groups. For example, the heights of pupils (x cm) can be grouped into 130 < x ≤ 140, 140 < x ≤ 150, etc.(In English this reads as the height of the pupil is greater than 140 cm and smaller than or equal to 150 cm.) In this way, whatever height is measured it can still belong to a single specific group.

Continuous data is a variable that can take any value on a continuum. For example if we are measuring the height of a sunflower shoot the measurement for one shoot could measure anywhere from 1 mm – 100 mm including 1.1 mm

Continuous data is usually illustrated in a histogram, line graph or ‘cumulative frequency’ graph.

What this might look like in the classroom

Activity 1
As a class, collect the following information for each pupil in the group:

Number of siblings

Shoe size

Height in centimetres

Foot length in centimetres

Hand span

Decide on a sensible way to record the information and present it in a form which makes it easy to analyse. Before you start to collect the data ask pupils to make a hypothesis about what they think they will find out.

Number of siblings

A degree of sensitivity might be required when it comes to deciding how to record the number of brothers and sisters. For example you might have a tally chart that includes: brothers, step brothers, sisters, and step sisters. The results for this discrete data can be placed into a frequency table and then into a block graph.

Shoe size

Shoe size is an unusual example of discrete data as it includes half sizes, and also because foot length in centimetres measures the same thing, but provides continuous data.

Height

Example hypothesis – most people in this class will be between 120 cm < h ≤ 130 cm. Most KS2 classes will yield a set of results for height between 100 cm and 160 cm. It is sensible for this to be grouped into class widths of 10 cm: For example: 100 cm < h ≤ 110 cm, 110 cm < h ≤ 120 cm, 120 cm < h ≤ 130 cm, and so on up to 150 cm < h ≤ 160 cm. As it is continuous data careful discussion might be needed about how to represent the groups and ensure that it is clear where a measurement of 130 cm should be placed. When the data has been collected and presented you will be able to prove or disprove your initial hypothesis.

Hand span

This is also continuous data. Pupils might like to collect the information and then suggest the size of each of the groups so they can put their information into a frequency table.

Taking this mathematics further

Cross curricular links Data is everywhere in our society these days. To help children become confident in this area, it is important that their experiences stretch beyond the mathematics lesson. Science and geography are obvious areas where this can happen.

In science, for example, bar charts can be created to show different types of materials found in the classroom, line graphs can be created to show the temperature of hot water as it cools. In geography children can make bar charts and line graphs to show, for example, temperatures and rainfall in countries around the world. A bar chart could show grouped discrete data for annual temperatures and rainfall for a selection of countries, a line graph could show how these vary for one country over a period of say, a year.

Making connections

There are several steps that need to be taken through an exercise in data handing. This is called The data handling cycle. These are:

Identify a problem/situation.

Make a hypothesis about the situation.

Design a data collection method that is fair and not biased.

Collect the data

Display the data appropriately

Analyse the data

Say if your hypothesis is true or false and give reasons (using your presentation and analysis of the data you found.

Evaluate your project and say how you might do it differently next time.

Pupils need to be aware of the difference between discrete and continuous data in simple terms such as shoe sizes in a class (discrete), the growth of a seed over a two week period (continuous). Basically, discrete data can only take particular values, and continuous data can take any value in a given range.

Children need to appreciate that distinguishing between the types of data informs them how to group correctly, which then allows them to analyse the data more easily. Also, distinguishing between the types of data is necessary in order to choose the correct way of representing the data. For example, if the data is discrete and a bar−graph is used to represent it, there should be a gap between the bars.

Related information and resources from the NCETM

Exploring data: This resource offers statistic and data handling information for all levels of mathematics teaching.