Statistical Investigation
A statistical investigation is a systematic process of forming a question, collecting data, analyzing patterns, and drawing conclusions based on evidence. The process begins with identifying whether a question is statistical (meaning answers will vary) or non-statistical (having a single correct answer). Statistical investigations form the foundation for understanding how data-driven decisions are made across multiple fields.
Why it matters
Statistical investigations appear throughout scientific research, business decisions, and public policy formation. Medical researchers use statistical investigations to test drug effectiveness, often requiring sample sizes of 1,000 or more participants to ensure reliable results. Marketing companies investigate consumer preferences by surveying representative samples rather than entire populations — a company might survey 2,500 customers instead of their 2.5 million user base. Weather forecasters collect temperature data from thousands of weather stations to predict patterns and issue warnings. Political pollsters survey approximately 1,200 registered voters to predict election outcomes for millions of voters. These investigations help distinguish between random variation and meaningful patterns, enabling informed decision-making in medicine, business, education, and government policy.
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.
Worked examples
Is "How many pets do students in our class have?" a statistical question?
Answer: Yes (answers vary)
- Check if answers can vary → Yes (answers vary) — A statistical question expects variability in the answers.
You want to know if students prefer cats or dogs. What data would you collect?
Answer: Survey students and count preferences
- Identify the data type needed → Categorical data (preferences) — We need to count how many prefer each option.
- Choose collection method → Survey students and count preferences — A survey or poll is the most practical method.
A school has 800 students. You survey 20. Is this a census or sample?
Answer: Sample
- Compare surveyed to total → 20 < 800 — Only 20 out of 800 students were surveyed, not all.
- Determine type → Sample (not everyone included) — A census includes everyone; a sample includes a subset.
Common mistakes
- Treating non-statistical questions as statistical ones. The question 'What is the capital of Texas?' has one answer (Austin), while 'How tall are students in Grade 7?' expects varied responses from 58 to 72 inches.
- Confusing census with sample data collection. Surveying 50 students from a school of 800 represents a sample (6.25%), not a census which would require all 800 students.
- Ignoring sampling bias in data collection. Surveying only students in the library about study habits creates bias, as library users likely study 2-3 hours more per week than the general student population.