Suppose you have the following dataset that lists the number of children in each family by surname:
Abbot 2
Darnowsky 5
Engel 4
Fuhrman 2
Galarneau 3
Hu 3
Jones 1
Kjorstad 3
Smith 2
This would be a calculation of frequencies of numbers of children:
# Frequency
1 1
2 3
3 3
4 1
5 1
Total: 9
One family has one child, three families have two children, three have three, one family has four and one family has five children.
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Assuming the products are created from a dataset which contains each value once or more times by multiplying the each value by its frequency in the dataset, then the result of sum of products (of values by their frequencies) divided by sum of frequencies is the mean average of the all the values in the dataset.
In statistics, an underlying assumption of parametric tests or analyses is that the dataset on which you want to use the test has been demonstrated to have a normal distribution. That is, estimation of the "parameters", such as mean and standard deviation, is meaningful. For instance you can calculate the standard deviation of any dataset, but it only accurately describes the distribution of values around the mean if you have a normal distribution. If you can't demonstrate that your sample is normally distributed, you have to use non-parametric tests on your dataset.
Usually mu is the symbol for the mean of a probability distribution. It is sometimes used as the average of a dataset (also called the mean of the dataset), although I prefer to use "x bar".
mean = sum of dataset / number of items in dataset = (3 + -10 + -2 + 13 + 11) / 5 = 15/5 = 3
You need to have all the values within the range to calculate the arithmetic mean .