Students will be able to:
understand the difference between a population and a sample.
establish whether a sample is representative of a population.
generate random samples that represent the entire population.
Representative samples reflect the characteristics of the entire population. The best way to determine a representative sample is to make sure the sample is randomly chosen.
POPULATIONS, SAMPLES, AND REPRESENTATIVE SAMPLES
A population is an entire group of objects—people, animals, plants—from
which data can be collected. A sample is a subset of the population. When
you ask a statistical question about a population, it is often more efficient
to gather data from a sample of the population.
A representative sample of a population has the same characteristics as the
population. Generating a random sample is one reliable way to produce a
representative sample of a population.
You can generate multiple random samples that are different but that are each
representative of the population.
DIAGRAM: A POPULATION AND A RANDOM SAMPLE
The diagram shows a population of 12 numbered people with different colors.
Population (left to right):
1 (blue), 2 (red), 3 (green), 4 (red), 5 (green), 6 (green),
7 (red), 8 (red), 9 (red), 10 (blue), 11 (blue), 12 (red).
The random sample is made up of individuals 2 (red), 5 (green),
9 (red), and 12 (red). Arrows connect those selected members of the
population to the four-person sample.