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§ Statistics·Grades 6–10

Statistical Investigation Worksheets

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Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable statistical investigation worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from classify a question as statistical or not at the easy level through to identify sampling bias and its impact at the advanced level.

CCSS.6.SPLK20.10

What is 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.

Common mistakes to watch for

  • ✗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.

Questions teachers ask

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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Beginner

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Concepts
Classify a question as statistical or not
Range
simple yes/no classification
Steps
1 step
Example
Is "What is your favourite colour?" a statistical question?

Easy

Generate →
Concepts
Identify what data to collect for a survey
Range
categorical preferences
Steps
1–2 steps
Example
How would you find out if students prefer cats or dogs?

Medium

Generate →
Concepts
Distinguish census vs sample
Range
school populations 200–1000
Steps
1–2 steps
Example
A school has 500 students. You survey 50. Census or sample?

Hard

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Concepts
Identify sampling bias and its impact
Range
convenience/biased samples
Steps
2 steps
Example
Why might surveying only your friends give biased results?

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