Collecting Data and Sampling

Key idea

Surveys, experiments and random sampling.

In depth

We usually study a sample because measuring a whole population is costly. A good sample is chosen so that every member has a known chance of selection (random sampling), so the sample resembles the population. Methods include simple random, stratified, cluster, and systematic sampling.

Worked example

To survey 1,000 students, give each a number and draw 50 at random with a random number generator.

Real-world uses

• Running a school survey, checking product quality on a line, polling voters

Common mistake

Taking a convenient sample such as friends, which rarely represents the group.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related intermediate topics in Probability & Statistics

• Bias in Sampling – Systematic errors that make samples unrepresentative.
• Histograms – Bars showing frequency of numerical intervals.
• Dot Plots and Stem-and-Leaf Plots – Show the shape of small datasets.
• Mean – The arithmetic average.
• Median – The middle value of an ordered list.
• Range – Difference between maximum and minimum.