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

The 5 scores above are the scores for the population since we are using all 5 scores.

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

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.

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