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Evaluate the representativeness of a sample

Representativeness means that a sample’s composition and distribution of relevant characteristics are reasonably similar to those of the population it is intended to describe, so conclusions about the population are justified. Evaluating representativeness involves examining how the sample was selected—such as whether population members had a fair chance of selection—and detecting convenience, voluntary-response, or undercoverage bias; a large sample can still be unrepresentative, while a random sample may differ from the population by chance.

Detailed Explanation: Evaluate the representativeness of a sample

A sample is representative when it has characteristics similar to the whole population and is selected fairly.

To evaluate a sample:

  1. Identify the population. Who do we want to describe?
  2. Examine how the sample was selected.
    • A random sample gives population members a fair chance of being chosen.
    • A convenience sample uses people who are easiest to reach.
    • A voluntary-response sample uses people who choose to participate.
    • Undercoverage happens when some groups have little or no chance to be selected.
  3. Compare important characteristics of the sample with those of the population.
  4. Decide whether conclusions about the population are reasonable.

Worked example

A school has 200 eighth-grade students. The school knows that 120 students usually eat breakfast at school and 80 do not.

The principal wants to find out whether students like the school breakfast. She asks for volunteers during lunch. Forty students volunteer, and 30 of them usually eat breakfast at school.

Is this sample representative of all eighth-grade students?

Step 1: Identify the population.

The population is all 200 eighth-grade students.

Step 2: Compare the groups.

In the population:

120200=60%\frac{120}{200}=60\%

of students eat breakfast at school.

In the sample:

3040=75%\frac{30}{40}=75\%

of students eat breakfast at school.

The sample contains a larger percentage of students who already eat school breakfast than the population does.

Step 3: Examine the selection method.

The students volunteered. This is a voluntary-response sample. Students who like school breakfast may have been more willing to participate than students who dislike it.

Step 4: Make a conclusion.

The sample is probably not representative. Its composition differs from the population, and the volunteers may have stronger opinions about school breakfast. Therefore, the principal should not assume that the sample’s opinion represents all eighth-grade students.

A larger sample would not automatically fix this problem. The sample must also be selected fairly.

Learn by doing: Evaluate the representativeness of a sample

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    Statistics Data Organization - Sample and Population to Is Representative

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