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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 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.

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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.

§ 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.

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Worked examples

Beginner§ 01

Is "How many pets do students in our class have?" 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 cats or dogs. 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 800 students. You survey 20. Is this a census or sample?

Answer: Sample

  1. Compare surveyed to total 20 < 800 Only 20 out of 800 students were surveyed, not all.
  2. Determine type Sample (not everyone included) A census includes everyone; a sample includes a subset.
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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.
§ 05

Frequently asked questions

What makes a question statistical versus non-statistical?
A statistical question expects answers that vary from person to person or situation to situation. 'How many siblings do students have?' is statistical because responses range from 0 to 5 or more. 'How many sides does a triangle have?' is non-statistical because it always equals 3.
When should researchers use a sample instead of a census?
A sample works when the population is large (over 200 people), time is limited, or costs are high. Surveying 300 students from a school of 1,200 provides reliable data while being more practical than questioning all 1,200 students.
How do you identify sampling bias in data collection?
Sampling bias occurs when the selected group doesn't represent the whole population. Surveying only students who ride the bus about transportation preferences excludes 60-70% of students who use other methods, creating skewed results.
What data types are commonly collected in statistical investigations?
Statistical investigations collect categorical data (favorite colors, yes/no responses) or numerical data (heights measured in inches, test scores from 0-100). Categorical data gets counted and displayed in bar graphs, while numerical data gets averaged and shown in histograms.
How do researchers draw reliable conclusions from statistical investigations?
Reliable conclusions require adequate sample sizes (typically 30+ for numerical data), unbiased collection methods, and appropriate analysis techniques. Researchers compare medians, calculate ranges, and look for patterns that exceed normal variation before making claims about the broader population.
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See also

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Where to next?

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