1. Statistics and Parameters
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A statistic is a measure that describes a characteristic of a sample. A parameter is a measure that describes a characteristic of a population.
Population: All college students in the US
Sample: 1000 college students
Example Statistic: Mean of the money spent on books in a year by the sample of 1000 students
Example Parameter: Mean of the money spent on books in a year by all college students in the US
A population consists of all of the members of a group of interest. Since it might be unrealistic to consider every member of a population, a sample is sometimes selected to represent the population. A sample is a subset of the population. The sample can then be analyzed to draw conclusions about the entire population.
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A stratified random sample of 1000 college students in the United States is surveyed about how much money they spend on books per year. |
Here, the population consists of all college students in the United States. The sample consists of only 1000 college students. Let's recall the definitions of a statistic and a parameter as well as their characteristics.
| Definition | Characteristics | |
|---|---|---|
| Statistic | A statistic is a measure that describes a characteristic of a sample. | A statistic can — and usually will — vary from sample to sample. |
| Parameter | A parameter is a measure that describes a characteristic of a population. | Parameters are fixed values that can be determined by the entire population, but are typically estimated based on the statistics of a carefully chosen random sample. A parameter will not change, for it represents the entire population. |
With the above definitions in mind, we can think of a possible statistic and a possible parameter.