Calculating a Mean
The mean of a series of variables is the arithmetical average of those numbers. It is determined by summing the numbers, then dividing that sum by the number of variables (count) included in that sum.
The formula for calculating a mean often appears like this:
However, any character of the alphabet may be substituted for X. For example, the following are also formulas for calculating a mean:
Now, apply the formula to calculate the mean for the following distribution of scores:
X1 = 79
X2 = 85
X3 = 92
X4 = 87
X5 = 93
X6 = 99
Looking at our formula, we know that we want to determine the value of
. We know the individual values of X and we know that n = 6 (there are 6 variables in this distribution). First, we must sum the values of the variables (79 + 85 + 92 + 87 + 93 + 99). Adding these we get 535, SX. Next the formula tells us that we must divide that sum by the count, n, which equals 6. So, 535 divided by 6 equals 89.17.
Following the formula mathematically, it would appear like this: