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Probability and StatisticsGrades 9–12

Data Collection

Good data collection begins with a precise question, defined population and variables, ethical design, and a plan to reduce error.

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A sophisticated analysis cannot rescue data gathered with a vague question, biased process, or unreliable measurement.

Begin with a research question

A strong question identifies the population, variables, and purpose. “Do students sleep enough?” is vague; “What proportion of Grade 12 students at this school report at least eight hours of sleep on weeknights?” is measurable.

The wording of the question determines what data are relevant and what conclusions are possible.

Population, sample, and unit

The population is the full group of interest. A sample is the subset actually observed. The observational unit is the individual person, object, event, or period on which variables are recorded.

Define inclusion and exclusion rules before collecting data so the target does not shift after results are seen.

Variables and operational definitions

Categorical variables place units into groups; quantitative variables record numbers with meaningful arithmetic. Quantitative variables may be discrete counts or continuous measurements.

An operational definition states exactly how a variable is measured. “Academic success” might mean course average, credit completion, or another defined outcome; these are related but not interchangeable.

Worked design example

Random assignment and random sampling solve different problems.

Measurement quality

Reliability concerns consistency; validity concerns whether the method measures the intended construct. A scale can produce consistent readings that are all miscalibrated, making it reliable but invalid.

Standardize instruments, training, timing, and instructions. Record missing data and deviations from protocol.

Common mistakes

Collecting first and defining the question later. This encourages selective analysis.

Confusing random assignment with random sampling. One supports causation; the other generalization.

Using an undefined construct. Operationalize what will actually be measured.

Treating missing responses as zero. Missingness needs its own code and analysis.

Ignoring consent and privacy because the project is small. Ethical obligations still apply.

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