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§ Statistics

Statistical Investigation

§ Statistics

Statistical Investigation

CCSS.6.SP3 min read

A statistical investigation is a systematic process of forming a research question, collecting relevant data, analysing patterns, and drawing evidence-based conclusions. This process follows four key stages: hypothesis formation, data collection, analysis using statistical tools, and evaluation of results. Statistical investigations form the foundation of data-driven decision making across science, business, and social research.

§ 01

Why it matters

Statistical investigations underpin critical decisions in medicine, where clinical trials involving thousands of participants determine drug effectiveness. Market researchers use these methods to survey samples of 1,000-2,000 consumers to predict purchasing behaviour for millions. Government census data, collected from all 67 million UK residents every 10 years, informs policy decisions worth billions of pounds. In GCSE and A-level coursework, students conduct investigations analysing everything from reaction times to plant growth rates. Schools use statistical investigations to evaluate teaching methods, comparing test scores from different approaches across year groups of 100-300 students. Weather forecasters analyse decades of temperature and rainfall data to predict climate patterns, whilst social media companies investigate user engagement patterns from billions of daily interactions to optimise platforms.

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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 "What is your favourite colour?" a statistical question?

Answer: Yes (answers vary)

  1. Check if answers can vary Yes (answers vary) A statistical question expects variability in the answers.
Easy§ 02

You want to know if students prefer football or basketball. 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 300 students. You survey 20. Is this a census or sample?

Answer: Sample

  1. Compare surveyed to total 20 < 300 Only 20 out of 300 students were surveyed, not all.
  2. Determine type Sample (not everyone included) A census includes everyone; a sample includes a subset.
§ 04

Common mistakes

  • Confusing statistical and non-statistical questions — asking 'How tall is the school flagpole?' (one fixed answer) instead of 'How tall are Year 9 students?' (variable answers).
  • Sampling only 15 students from the library to represent all 800 students in the school, creating convenience bias that skews results towards academic preferences.
  • Treating a sample of 50 students as a census when the school population is 1,200, leading to incorrect generalisation of findings to the entire population.
§ 05

Frequently asked questions

What is the difference between a census and a sample?
A census collects data from every member of the population (like surveying all 400 Year 10 students), whilst a sample collects from a subset (like surveying 80 randomly selected Year 10 students). Censuses are more accurate but expensive and time-consuming for large populations.
How do you identify sampling bias?
Sampling bias occurs when the sample doesn't represent the population fairly. For example, surveying only students at the tuck shop about healthy eating preferences would likely underrepresent health-conscious students who avoid the tuck shop, creating biased results.
What makes a question statistical?
A statistical question expects varying answers from different respondents. 'What is your favourite subject?' is statistical because answers will vary. 'How many terms are in a school year?' is not statistical because it has one fixed answer.
What sample size is needed for reliable results?
Sample size depends on population size and desired accuracy. For a school of 600 students, a random sample of 60-100 students typically provides reasonable reliability. Larger samples reduce uncertainty but increase cost and time requirements.
How do you avoid bias in data collection?
Use random sampling methods, ensure questions are neutral and clear, collect data at different times and locations, and consider who might be excluded. Stratified sampling ensures all subgroups (like different year groups) are proportionally represented in the sample.
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See also

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Where to next?

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