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Statistics - Parameters and Statistics

The terms 'parameter' and (sample) 'statistic' refer to key concepts that are closely related in statistics.

They are also directly connected to the concepts of populations and samples.

Parameters and Statistics

Parameter: A number that describes something about the whole population.

Sample statistic: A number that describes something about the sample.

The parameters are the key things we want to learn about. The parameters are usually unknown.

Sample statistics gives us estimates for parameters.

There will always be some uncertainty about how accurate estimates are. More certainty gives us more useful knowledge.

For every parameter we want to learn about we can get a sample and calculate a sample statistic, which gives us an estimate of the parameter.

Some Important Examples

Parameter Sample statistic
Mean Sample mean
Median Sample median
Mode Sample mode
Variance Sample variance
Standard deviation Sample standard deviation

Mean, median and mode are different types of averages (typical values in a population).

For example:

  • The typical age of people in a country
  • The typical profits of a company
  • The typical range of an electric car

Variance and standard deviation are two types of values describing how spread out the values are.

A single class of students in a school would usually be about the same age. The age of the students will have low variance and standard deviation.

A whole country will have people of all kinds of different ages. The variance and standard deviation of age in the whole country would then be bigger than in a single school grade.