A population is the complete group about which a statistical question is posed, while a sample is the subset actually observed; a sample may support conclusions about the population only when it reasonably represents that group. A variable is a characteristic recorded for each individual or object, with values that may be categorical or quantitative and, when appropriate, accompanied by units. This scope excludes formal sampling distributions, estimation, and confidence intervals; it establishes the terminology needed for interpreting data and later statistical inference.
To identify the population, sample, and variable, ask three questions:
Who or what is the entire group being studied?
This is the population.
Who or what is actually observed or measured?
This is the sample, which is a smaller part of the population.
What characteristic is recorded for each individual or object?
This is the variable.
A school wants to find the average amount of time Grade 9 students spend on screens each day. Researchers randomly choose 50 Grade 9 students and record each student’s daily screen time.
Step 1: Identify the population.
The question is about all Grade 9 students at the school.
Step 2: Identify the sample.
The researchers actually collect data from the 50 randomly chosen students.
Step 3: Identify the variable.
For each student, the researchers record daily screen time.
The variable is:
This is a quantitative variable because its values are numbers with a meaningful unit.
Because the 50 students were chosen randomly, their results may reasonably represent the larger population. The sample can then help the school learn about the population, although the sample and population are not the same group.
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