Lesson

Businesses, organisations and governments all gather data and conduct surveys to help them make decisions about what people want. The Australian Census, which is conducted by the Australian Bureau of Statistics, is an example of a large-scale data collection. Every Australian citizen is required to fill in a survey so we get a picture of the characteristics of the Australian population. This lesson will explore techniques for collecting data as well as the practicalities and implications of obtaining data through sampling.

In a **census**, every member of a population is questioned. In maths, a **population** does not necessarily refer to the population of a country. It just means every member of a group. It may be a school's population, a sports club's population and so on.

Collecting data from every member of a population is the most accurate way of gathering information, but it is not always the most practical and can be very expensive or time consuming. Typically, a ** sample survey** is instead done on a subset of the population to make it quicker and less expensive.

Hannah has chosen to collect information using a sample instead of a census.

a

What are the advantages to doing a sample? Select all that apply.

A

It is cheaper to conduct.

B

There will be no sampling bias.

C

It's more accurate.

D

It takes less time.

Worked Solution

b

What are the disadvantages to doing a sample? Select all that apply.

A

It's less accurate.

B

It takes more time.

C

It's more expensive to conduct.

D

There can be sampling bias.

Worked Solution

For each of the following, determine whether they are a census or a sample.

a

Lucy has asked everyone in her office what snacks should be provided in the office.

Worked Solution

b

James asks a few of his friends how they did in the test to see if he is above average in his class.

Worked Solution

c

Joanne finds the height of the entire class to try to find the average height of 15 year old students in Australia.

Worked Solution

Idea summary

In a **census**, every member of a population is surveyed. In an unbiased **sample**, a representative proportion of the population is surveyed.

The most important thing when taking a sample is that it is representative of the population. In other words, we want to try and ensure there is no bias that may affect our results. There are different ways to collect a sample. Let's take a closer look at some of them now.

**Random sampling**

An example of random sampling is numbers being drawn out in the lottery. Every number has an equal probability of being chosen. Each individual is chosen at random (by chance). In other words, each individual has the same probability of being chosen.

**Stratified sampling**

Stratification is the process of dividing a group into subgroups with the same characteristics before we draw our random sample. Then we look at the size of each subgroup as a fraction of the total population. The number of items from each subgroup that are included in the sample should be in the same ratio as the amount they represent of the total population.

**Systematic sampling**

To use systematic sampling, a starting point is chosen at random, and then items are chosen at regular intervals. Such as selecting every nth item from a list. For example, we may call every tenth business in the phone book or select every fifth bottle from a production line.

In a group of 360 students, 90 are primary students and 270 are secondary students. A stratified sample of 120 is to be selected from the group based on year level.

How many primary students should be selected?

Worked Solution

The local mayor wants to determine how people in her town feel about the new construction project. Determine the type of sampling each of the following scenarios describe.

a

Selecting every 50th name from an alphabetical list of residents.

Worked Solution

b

Giving each resident a random number between 1 and 10 and then selecting everyone with the number 3.

Worked Solution

c

Selecting 10\% of the residents from each suburb.

Worked Solution

Idea summary

The most important thing when taking a sample is that it is representative of the population. Different sampling techniques aim to obtain a representative sample, but some may be more practical to carry out in different scenarios.

Sampling methods:

Random - selects people through a purely chance selection

Systematic - selects people at regular intervals on an ordered list

Stratified - selects a proportional amount of people from the different strata in a population

analyses single sets of data using measures of location, and range