Tutor’s Toolkit: Application of Number

Interpreting Information

I7	Select appropriate methods for obtaining the results you need,
Including grouping data when this is appropriate

Useful Web Links:

BBC Bitesize Revision: Maths: Discrete and continuous data
http://www.bbc.co.uk/schools/gcsebitesize/maths/datahandlingih/piechartsi_rev2.shtml

MathsDirect: Grouped Data
http://www.mathsdirect.co.uk/pure/purtutstagro.htm
This article describes how to group data.

I7.1	Grouping data

Scope: 

Students need to be able to:
•	organise discrete data into groups [NOE],
•	organise continuous data into groups [NOE].

What students need to know:

Sometimes it is necessary to collect a lot of data and organise it after we have seen it. This may happen with a scientific experiment or getting costs we aren’t sure about.
The most important distinction to make is between discrete and continuous data. 

Discrete data is when there are only a certain number of specific things the data can be. Most importantly, any amount in between the data points has no meaning. 

For example, shoe sizes are discrete data. We can have  but any further division is meaningless. You cannot buy a pair of sized shoes! Other examples would be numbers of people (we cannot have 4.2 people!), or even prices: £4.6265 is going to cause problems with the change!

Continuous data means that any value is (in principle) possible. The gaps in between do have a meaning. Basically, anything that you measure is going to be continuous. For example, people’s heights are continuous. Even though we measure 1.78m, a height of 1.78134m is possible (but very difficult to measure!).

When we come to group our data, choose groups which are sufficiently big to give few enough groups, 5 to 10 groups is ideal. Then make the groups start and finish at nice even points.

Example Question:
Group these shoe sizes:

2, 9, 4, 5, 3, 7, 8, 6, 9, 11, 4, 13, 5, 10, 12, 5.

Solution:

The largest is 13 and the smallest is 2. If we had 5 groups with 3 sizes in each, that would fit all of the data.

Shoe Size	
Frequency	

1-3	
2	

4-6	
6	

7-9	
4	

10-12	
3	

13-15	
1	

Each group shows all of the sizes included.

Example Question:
Group these heights:

1.36m, 1.87m, 0.98m, 1.43m, 1.76m, 1.48m, 1.12m, 1.78m, 1.47m, 1.51m, 1.83m, 1.67m, 1.34m, 1.18m, 1.37m, 1.71m

Solution:

The largest is 1.87m and the smallest is 0.98m. We can have 6 groups, each with 0.2m going form 0.8m to 1.0m to 1.2m and so on.

The important point here is that we need to be clear which group the dividing points would go into. So, we can decide that the group starts at 0.8m and goes up 1.0m but 1.0m is NOT included. We write it like this: 0.8m  h < 1.0m. Any letter will do, but h for height seems appropriate.

Check the frequency yourself. Notice that 1.36m is between 1.2m and 1.4m, so it goes in the third group.

Height (h)	
Frequency	

0.8m  h < 1.0m	
1	

1.0m  h < 1.2m	
2	

1.2m  h < 1.4m	
3	

1.4m  h < 1.6m	
4	

1.6m  h < 1.8m	
4	

1.8m  h < 2.0m	
2