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# Misunderstanding samples and sampling

Generalising from a sample that is too small may lead to conclusions about a larger population that lack credibility. There is, however, no need to sample every element in a population to make credible, reliable conclusions. Recognising the variation between samples and establishing when samples are representative of a population ensures sampling methods are efficient and effective.

Students may have strong beliefs about what makes a fair sample. They often have difficulty understanding the characteristics of an unbiased sample, the naturally occurring variation within samples and the need for samples to be representative.

As a starting point, classroom discussions should focus on possible bias. This might relate to:

• survey questions
• sample size
• sampling methods.

Biased samples favour one way of thinking over another. Activities should challenge studentsâ€™ notions of the nature of sampling and the purpose of a sample in relation to the questions asked. They should also consider the context of the data in order to appreciate how sampling can influence the claims made.

## Bias in survey questions

The way survey questions are posed and the choices given for responses to survey questions have the potential to introduce bias into survey results.

## Good survey questions

Teachers can help students to write good survey questions.

## Writing survey questions

Students use an online tool to construct a survey and collect data for an investigation.

## Bias from sample size

Bias is introduced when the sample size is not representative of the population from which it is taken.

## How big a sample?

The larger the sample size the more likely it is that the sample results will reflect the results from the population.

## Increasing sample size

This activity compares the distributions of smaller samples with larger samples to determine when a sample is representative of the larger population.

## Bias in sampling methods

Samples need to be representative of the larger population. It is important to identify when bias may be introduced through various sampling methods.

## Selecting sampling methods

Students need experience in using various sampling strategies to develop an appreciation of when a sample may be biased.

## Sampling methods activity

This is a three-stage activity that includes establishing student prior learning, developing fluency, and determining changes in student thinking in relation to sampling methods.