In statistics, a population is all people, objects or events defined by a set number of characteristics.
When dealing with data representing an entire population, we use the following symbols for population parameters:

Mean: $\mu$ (Greek symbol mu)

Standard Deviation: $\sigma$ (Greek symbol sigma)

Examples

Examples of populations can include dogs in Melbourne, marbles in a sack or visits to a zoo.

Sample

In practice, it is often not practical to collect data about an entire population, especially when those populations are very large. In these cases, we often take data from only a portion of the population, which we call the sample.
When dealing with data gathered from a sample, we use the following symbols for sample statistics:

Mean: $\bar{X}$

Standard Deviation: $s$

Example

If we wanted to find the most common breed of dog in Australia, it may be impractical to gather data on every single dog. Instead, we may choose to collect a sample of 200 dogs from each state and territory.

Random Numbers/Random Samples in Statistics

When taking a sample of a population, it is often easier, or more likely that the individuals, objects or events that are sampled will have a particular trait, if unaccounted for this can produce inaccurate results.

Example

If a university wanted to find the average level of education for Australian citizens, the easiest group for them to survey would be university students, however because university students receive a higher than average level of education, the results would be inaccurate as they do not give a good picture of the entire population.

To overcome this, the concept of random sampling is important. Random sampling means that any individual within a population has an equal chance of being selected. This makes it more likely that the selected sample will have the needed diversity.
Random numbers work on a similar concept: for 2-dimensional data, each number has an equal chance of being selected, and the corresponding result recorded.

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