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.

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.