Population distribution
Recommended for You
Not sure where to start? These are the lessons and games we recommend most to students, parents and teachers on Basic-mathematics.com. Each lesson explains the topic in plain language, walks you through worked examples step by step, and ends with practice so you can check your understanding. Pick one below, or use the menu to find lessons on fractions, algebra, geometry, statistics and more.
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.Share this page