There are two types of number data: Discrete and Continuous.
Discrete data can only take specific values and not the values in-between. For example, number of children in a class or shoe size.
Continuous data can take any value within your range of accuracy. For example, height or weight.
When you have a load of numbers in front of you it is known as raw data. This topic is about organising that raw data so it becomes easy to extract information from it.
The simplest way to collect data is to use a tally chart. If you are given a load of numbers in an exam and asked to design a table to tally them this is the design of table you should use:
|Data Value (or group):||Tally:||Frequency:|
Another way to collect data is using questionnaires.
There are two main points to remember about the questions in a questionnaire:
1. They must be specific and have specific answers. So,
- 'How do you feel about football?'
would not be a good question, whereas,
- 'Do you like watching football (Yes/No)?'
would be better.
2. They must be fair and not leading questions. For instance,
- 'Do you agree that the BBC has the best sports coverage?'
is not a good question, whereas,
- 'Which channel has the best sports coverage?' (with a list of options)
is a lot better.
Once you have gathered and organised your data you can begin analysing it.
The 4 main values used in analysing data for GCSE are Mean, Median, Mode and Range.
Before you work anything out, however, you must remember this golden rule:
Always rearrange the data in ascending order! .
Then learn these definitions:
- Mean is the total of all the items divided by the number of items.
- Median is the middle value.
- Mode is the most common value.
- Range is the difference between the smallest and the biggest value.
The mean gives you an idea of the average value but is not a good measure of average if there are any extreme values (a lot bigger or smaller than the others).
The median can be used if there are any extreme values as it is not affected by them. The value at the end could be anything as far as the median is concerned, the middle value is still the same. The other benefit about the median is that you know exactly half the values are above it and half are below.
Note: if there are an even number of items then there will be two middle values so the median will be halfway between them.
The mode is only useful in certain circumstances. For example, voting for something.
The range must be given as a single number and not written as '.... to ....'.
Check you've learnt this properly by dragging the correct type of value on to the question marks in the panels below. Mark your answer to see how you did:
Comparing two sets of data
When doing this, either compare their means and their ranges or their medians and their ranges. Simply state the values. Do not make wild and waffly statements about what you think is going on. It is best to deal in facts.
Grouped Data is slightly different because, as the data has been put into groups, you don't know what the original individual values were.
Mean - assume all the items in a group take the mid-point of the group so for each group you do mid-point x frequency. Add them all up and divide by the Total Frequency.
Median - you cannot find the median, only the group that it is in. (You can, however, get an estimate of the Median using a 'Cumulative Frequency' graph).
Modal group - the group with the highest frequency.