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Statistical Investigation

CCSS.6.SP3 min read

Statistical investigations form the backbone of data handling skills in GCSE mathematics, yet many Year 10 students struggle to distinguish between a proper statistical question and a simple factual query. Teaching students to design effective investigations requires systematic practice with real scenarios they can relate to.

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§ 01

Why it matters

Statistical investigation skills prepare students for A-level mathematics and countless real-world applications. Market researchers use these methods to survey 1,200 consumers about product preferences rather than questioning all 67 million UK residents. Medical studies employ stratified sampling to test treatments on 500 patients across different age groups, ensuring reliable results. In business, companies analyse customer satisfaction through systematic surveys of 300-800 respondents, using these findings to make £millions in strategic decisions. Students who master hypothesis formation, sampling methods, and bias identification develop critical thinking skills essential for university coursework and careers in psychology, economics, medicine, and data science. The UK National Curriculum emphasises these concepts in Year 10 and Year 12 because statistical literacy has become fundamental in our data-driven society.

§ 02

How to solve statistical investigation

Statistical Investigation

  • Form a clear hypothesis or question.
  • Collect data using a suitable method (survey, experiment, observation).
  • Analyse using charts, averages, and spread.
  • Draw conclusions and evaluate reliability.

Example: Hypothesis: Year 8 students sleep more than Year 10. Collect sleep data, compare medians.

§ 03

Worked examples

Beginner§ 01

Is "How many days are in a week?" a statistical question?

Answer: No (only one correct answer)

  1. Check if answers can vary No (only one correct answer) A statistical question expects variability in the answers.
Easy§ 02

You want to know if students like reading or gaming more. What data would you collect?

Answer: Survey students and count preferences

  1. Identify the data type needed Categorical data (preferences) We need to count how many prefer each option.
  2. Choose collection method Survey students and count preferences A survey or poll is the most practical method.
Medium§ 03

A school has 1000 students. You survey 20. Is this a census or sample?

Answer: Sample

  1. Compare surveyed to total 20 < 1000 Only 20 out of 1000 students were surveyed, not all.
  2. Determine type Sample (not everyone included) A census includes everyone; a sample includes a subset.
§ 04

Common mistakes

  • Students confuse factual questions with statistical ones, thinking 'What is the population of Manchester?' is statistical when it has one correct answer (547,000), unlike 'How many hours do Manchester teenagers spend online?' which varies by person.
  • Many pupils incorrectly calculate sample sizes, believing they need 50% of a population when surveying 30 students from a Year 9 cohort of 180 provides sufficient data for most school investigations.
  • Students often ignore sampling bias, selecting only their friends for surveys about screen time, yielding results like '8 hours daily' when a random sample might show '4.2 hours daily'.
  • Pupils frequently write vague hypotheses such as 'boys are better at sport' instead of testable statements like 'Year 8 boys can run 100m faster than Year 8 girls by at least 2 seconds'.
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§ 05

Frequently asked questions

What makes a question statistical rather than factual?
A statistical question expects variability in answers across different people or situations. 'How tall are Year 7 students?' is statistical because heights vary from 140cm to 165cm, whilst 'How many centimetres in a metre?' has one correct answer (100cm).
When should we use a sample instead of a census?
Use samples when surveying the entire population is impractical or expensive. For a school of 800 students, surveying 80-100 provides reliable data about lunch preferences, whilst questioning all 800 wastes time and resources unnecessarily.
How can we avoid sampling bias in school investigations?
Use random sampling methods rather than convenience sampling. Instead of surveying friends in your form group, assign each student a number and use random selection. Stratified sampling ensures representation across different year groups or house systems.
What sample size do we need for reliable results?
For school populations under 500, aim for 20-30% of the group. For larger populations over 1000, samples of 100-300 usually suffice. The key is random selection rather than just large numbers.
How do we write a proper hypothesis for investigation?
Make predictions specific and measurable. Rather than 'Year 11 students are stressed', write 'Year 11 students sleep fewer than 7 hours nightly during exam periods'. This allows clear testing through data collection and numerical comparison.
§ 06

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