Chapter 7, Problem 1SE

Parameter vs. Statistic (Example 1) Explain the difference between a parameter and a statistic.

To determine

Describe the difference between a parameter and a statistic.

Answer to Problem 1SE

The difference between a parameter and statistic is that parameter shows the attributes of the population whereas a statistic is based on the random sample observed from the population. The statistic is the formula used to estimate the population parameter based on the given sample.

Explanation of Solution

A parameter is a statistical measure which characterizes certain aspect of the population. In practical world, the population parameter may not be known.

A statistic is a statistical measure which is measure of the characteristics based on the sample data. The statistic provides an estimate of the population parameter based on the given sample.

Example: There is research conducted to determine the percentage of class ${12}^{th}$ students who are taller than 180 cm from the city. A random sample size of 100 is collected from a random school.

The percentage of class ${12}^{th}$ students who are taller than 180 cm based on the whole city is the parameter whereas the percentage of class ${12}^{th}$ students who are taller than 180 cm based on the sample is statistic.

The sample on its own does not depict exactly all the characteristics of the population such that there exists a bias between the statistic and the parameter.