# Developing a Probability Distribution from Empirical Data

In real-world situations, statisticians obtain data by means of observation and experimental methods. Data obtained in this manner is called empirical data.

A probability distribution obtained by means of observation and experimental methods is referred to as an empirical probability distribution , or a relative frequency distribution based on observation.

Example:

Let X be the number of movies a high school student watches in a given month.

A survey conducted at one particular high school in the month of December gives by the following table:

If we assume that the students at this high school are typical, and that December is a typical month, then

The probability that a high school student will watch 1 movie per month is 17%;

The probability that a high school student will watch 2 movies per month is 28%;

etc.

Use this empirical probability distribution to find the expected value for the number of movies a high school student will watch in a month.

Convert the percentages to decimals.

17% = 0.17

Use the weighted average formula.

So, we can expect the average high school student to watch 2.95 movies per month.