Numerical measures, graphs and diagrams — Edexcel A-Level Statistics
Test yourself on Numerical measures, graphs and diagrams with PEARSON EDEXCEL A-Level practice questions.
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Numerical measures, graphs and diagrams explained
An outlier is a value that is unusual relative to the rest of the data, but deciding whether it is a genuine feature of the population or an error depends on how the data were collected.
Read the full explanation
First identify the population being studied and the sampling or measurement process. Then ask whether the value could plausibly arise from that population and process. For example, a household income of £2,000,000 in a sample of 200 local households may be genuine if the population includes wealthy residents, but a recorded age of 250 years is almost certainly a data-entry error. Use the context, units and collection method to judge whether the value is possible, whether it is plausible, and whether it should be retained, investigated or excluded. The nature of an outlier is therefore not decided by a numerical rule alone; it is decided by reference to the population and the way the data were obtained.
Your focus
- Identify the population and the original data collection process for a given data set.
- Judge whether an unusual value is possible and plausible given the population and collection process.
- Decide whether an unusual value should be retained, investigated or excluded, and justify that decision.
Numerical measures, graphs and diagrams exam tips
Marking Points
- Defines an outlier as a value that is unusual relative to the rest of the data set.
- Explains that the population defines which values are possible or plausible.
- Explains that the original data collection process (sampling method, measurement instrument, recording procedure) affects whether an unusual value is genuine or an error.
- Uses context, units and collection method to judge whether an unusual value should be retained, investigated or excluded.
- Recognises that a numerical rule alone cannot determine the nature of an outlier without reference to the population and collection process.
Examiner Tips
- 💡State the population and the data collection process before judging whether an unusual value is genuine or an error.
- 💡Use the context and units of the data to test whether a value is possible and plausible, rather than relying only on a numerical rule.
- 💡When asked to determine the nature of an outlier, explain whether it should be retained, investigated or excluded and justify that decision with reference to the population and collection process.
Common Mistakes
- Treating any value beyond a fixed numerical boundary as automatically an error; correction: the boundary flags a value for investigation, but the population and collection process determine whether it is genuine or erroneous.
- Ignoring the population when judging an outlier; correction: the same numerical value may be plausible in one population and impossible in another, so the population must be identified first.
- Assuming an outlier must always be removed; correction: an outlier may be a genuine and important feature of the population, so it should be investigated before any decision to exclude it.
- Confusing an outlier with a recording error; correction: an outlier is a value that is unusual relative to the rest of the data, while a recording error is a mistake in the collection process, and the two are not the same.