Samples

## Samples

A population consists of all the items or people that are being considered.

A census is a survey of all the items or people in the population.

A sample is a survey of some of the population. In a random sample, each item or person in the population has an equal chance of being selected for inclusion in the survey.

Random sampling can be carried out by using a random number generator (as found on a calculator, or by using dice). Generate random numbers based on the population size and select (from a list) those items or people that require to be surveyed.

Note that some random number generators may only provide single digits. In this instance, group the numbers together to form the required size, throwing away any unusable numbers. For example, for a population of 500 and a generated list of

2 5 4 5 7 8 4 6 9 4 2 0 3 1 6 4 3 2 6 8 9...

Group the numbers into 3s

254 578 469 420 316 432 689 …

And ignore numbers higher than 500 (or equal to 000):

254 469 420 316 432 …

## Example 1

A survey is to be taken for the students in Year 11. There are 240 students in Year 11.

If 20% of these students need to be sampled, how many students should be included in the survey?

Select the Year 11 group of 240 students. 240 x 20% = 48 students.

## Example 2

A survey was undertaken of Year 11 students in a school. The survey interviewed students in one particular class by asking questions from the front of the class.

What are two problems with this survey?

Surveys should be unbiased. People should be selected at random.

Responses to surveys should not be subject to other influences as this introduces bias.

Answer: 1. The sample wasn't random. The selection of students was pre-determined by the composition of the class.

2. The nature of the interviews may have allowed answers to be influenced by other members of the class.