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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:

Number of Movies Watched 1 2 3 4 5
% of students 17 28 34 15 6

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.

E ( x ) = x i P ( x i )

= ( 1 ) ( 0.17 ) + ( 2 ) ( 0.28 ) + ( 3 ) ( 0.34 ) + ( 4 ) ( 0.15 ) + ( 5 ) ( 0.06 ) = 0.17 + 0.56 + 1.02 + 0.90 + 0.30 = 2.95

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

 

 

 

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