4.1 Collecting data
Collecting data
Everything on collecting data that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
A worked example
Types of data · [1 mark]
What type of data is the length of a worm?
- B1Continuous
The exam skills (7)
Types of data
- Qualitative: words (colours, names).
- Discrete: counted, only certain values (goals, people).
- Continuous: measured, any value in a range (height, time).
Watch out: Calling shoe size continuous. It only comes in set sizes, so it is discrete.
Two-way tables
- Every row and column adds up to its total.
- Find a row or column with only one missing number.
- Total − the others = the missing number. Repeat.
Watch out: Starting with a row that has two gaps.
Pictograms
- Read the key: what one symbol stands for.
- Multiply by the number of whole symbols.
- A half symbol is half the key.
Watch out: Counting the symbols and forgetting to use the key.
Stratified sampling
- Each group gets its fair share of the sample.
- Group size ÷ whole population × sample size.
- Round to the nearest whole number.
Watch out: Sharing the sample equally between the groups.
Bias
- A sample is biased if some people are more likely to be picked than others.
- Ask: who is missing, or who is over-represented?
- Give a reason linked to the question being asked.
Watch out: Saying "the sample is too small" when the problem is who was asked.
Systematic sampling
- Gap = population ÷ sample size.
- Start at the given position.
- Keep adding the gap until you have the whole sample.
Watch out: Starting at the gap instead of the given first position.
Questionnaires
- Response boxes must not overlap or leave gaps.
- They must cover every possible answer, and the question needs a time frame.
- Questions must not lead people to an answer.
Watch out: Giving a vague criticism like "it is a bad question". Say exactly what is wrong.
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