Mean, Median, Mode, Standard Deviation, and Variance

When working with a set of numbers, measures of central tendency can be used to determine the average, middle, or most occurring numbers. Standard deviation and variance can also be calculated.

Suppose you have the following set of numbers:

4, 2, 7, 4, 3, 1, 8, 5, 6

To calculate the mean, or average, you must divide their sum by the number of numbers:

4 + 2 + 7 + 4 + 3 + 1 + 8 + 5 + 6 = 40

40 / 9 = 4.44

To find the median, you must place all of the numbers in order and find the number in the middle:

1, 2, 3, 4, 4, 5, 6, 7, 8

If there are two numbers in the middle, then the median will be their average; however, the median is only one number in this case.

To find the mode, you must determine which number occurs the most:

1 = 1x

2 = 1x

3 = 1x

4 = 2x

5 = 1x

6 = 1x

7 = 1x

8 = 1x

To find the standard deviation, you must use the following equation:

In this case, the standard deviation is 2.297.

To find the variance, you simply square the standard deviation, producing, in this case, 5.278.