What is the Difference Between Parameter and Statistic?

The main difference between a parameter and a statistic lies in the population they describe and the data they represent. Here are the key differences:

• Parameter: A parameter is a fixed, numerical value that describes an entire population. It is an unknown value that is often estimated using statistics derived from sample data. For example, the mean of the population's height or the proportion of the population's political affiliation are parameters.
• Statistic: A statistic is a known number that describes a sample, or a portion of the target population. It is a characteristic of the sample, and its value depends on the specific sample taken. For example, the average income of a sample of 1,000 individuals in a city or the percentage of people who like vanilla ice cream in a class of third graders are statistics.

To determine whether a given number is a parameter or a statistic, ask yourself the following questions:

1. Does the number describe a whole, complete population where every member can be reached for data collection?
2. Is it possible to collect data for this number from every member of the population in a reasonable amount of time?

If the answer is yes to both questions, the number is likely a parameter. If not, it is likely a statistic.

In summary, parameters describe the characteristics of an entire population and are often theoretical concepts, while statistics describe the characteristics of samples and are derived from actual data collected from a portion of the population.

Comparative Table: Parameter vs Statistic

Here is a table comparing the differences between parameters and statistics:

In summary, parameters describe the characteristics of a whole population, while statistics describe the characteristics of a sample. Parameters are fixed and unknown, while statistics are variable and known. Parameters are symbolized by Greek letters or upper-case Latin letters, while statistics are symbolized by lower-case Latin letters.