POPULATIONS AND SAMPLES
A population consists of all members (people, objects or events) of a specified group about which information is sought.
Examples
A sample is a representative subset of the population and it consists of some members (people, objects or events) of the population that we collect to make inferences.
Examples
If the sample is random and large enough, the information collected from the sample can be used to make inferences about the population.
Note: Populations consist of very large numbers of members; the example with the cats above is used for visualisation purposes.
| Population parameters | Sample statistics |
|
population mean = μ standard deviation = σ population size = N (large size) population proportion = p |
sample mean = x̄ standard deviation = s
sample size = n (manageable size) sample proportion = p̂ |
| * hard and costly to collect the data | * easy and cost effective to collect the data |
Population proportion, p, and Sample proportion, p̂
The population proportion is constant; it's value does not change.
| Population |
|
If the group of children shown above represents the population of children in a tutoring class, for example, then the proportion of girls is
where X is the number of girls in the population and N is the population size.
The sample proportion is variable; it's value changes from sample to sample.
In the table below there are some examples of sample proportions corresponding to the size of the sample.
| Sample | Sample proportion, p̂ |
|
|
x = 3 girls n = 5 children
|
|
|
x = 1 girl n = 5 children
|
Simple random sampling
A simple random sample is a subset of a population with the following properties:
* every member of the population is chosen entirely by chance;
* every member of the population has an equal chance of being selected;
* all samples have the same size, n;
* every possible sample of size n has an equal chance of being selected.
Methods
Simple random sampling has the advantage that is easy to perform. It works well for a small sample size.
Simple random sampling can be done using
* the lottery type of selection. Each number is written an a ball and put in a lottery machine and selected one by one.
