2  Population and Sample

2.1 Definitions

  • Statistics : The use of samples to describe, visualise, explain and predict the features of a population.

  • Population : The collection of all objects of interest.

  • Sample : A subset of a population.

  • Parameter : A number that represents a feature of a population.

  • Statistic : A number that estimates a population parameter based on a sample.

2.2 Common Symbols

Table 2.1 lists some common values and their matching symbols.

Table 2.1: Symbols for common values
Value Population Parameter Sample Statistic
Mean \(\mu\) \(\bar{x}\)
Standard Deviation \(\sigma\) \(s\)
Proportion \(p\) \(\hat{p}\)

2.3 Example

Forestry scientists are interested in the average height of trees in a forest. They measure the heights of 1000 randomly selected trees and determine the average height to be 17.5 metres. The population is all the trees in the forest. The sample is the randomly selected 1000 trees. The parameter is the unknown average height of the whole population. The statistic is the average height of the sample (17.5m), which is taken to be an estimate of the population average.