# Population distribution

The population distribution is the probability distribution using all elements of a population.

Suppose there are 5 students in a math class and their scores on the final exam are the followings:

80          85          85         90           92

Notice that we are only using 5 scores! Nonetheless, the 5 scores above are the scores for the population since we are using all 5 scores.

A population does not need to have 10,000,000 items in order for it to be called a population! It could have just 5 items as long we use all the elements.

## Calculating the population distribution for the 5 scores above

Let x be the score of a student. We can make a frequency distribution table of scores as shown in the table below.

 x f Relative Frequency 80 1 1/5  = 0.20 85 2 2/5  = 0.40 90 1 1/5 = 0.20 92 1 1/5 = 0.20 5 Sum = 1

Here is the population probability distribution

 x P(x) 80 0.20 85 0.40 90 0.20 92 0.20 ΣP(x) =1

## Calculating the mean using the population probability distribution

μ =  ΣxP(x) = 80 × 0.20 + 85 × 0.40 + 90 × 0.20 + 92 × 0.20 =  86.4

μ is a population parameter and it gives the average grade for the population distribution.

The value of μ or 86.4 is fixed or constant. In other words, there is only 1 value of the population mean.

The value of the standard deviation, which we do not compute here is also fixed or constant.

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