This website has many features that depend on JavaScript, please make sure that your browser setting has JavaScript enabled! or turned on.

# Statistics Formulas Quick Reference

## Arithmetic mean (AM)

The arithmetic mean (or simply "mean") of a sample x_1,x_2,... ,x_n is the sum the sampled values divided by the number of items in the sample:

Visit the Mean page on Wikipedia for more details

## The Median

### For an odd number of values

As an example, we will calculate the sample median for the following set of observations: 1, 5, 2, 8, 7.

Start by sorting the values: 1, 2, 5, 7, 8.

In this case, the median is 5 since it is the middle observation in the ordered list.

The median is the ((n + 1)/2)th item, where n is the number of values. For example, for the list {1, 2, 5, 7, 8}, we have n = 5, so the median is the ((5 + 1)/2)th item. median = (6/2)th itemmedian = 3rd itemmedian = 5

### For an odd number of values

As an example, we will calculate the sample median for the following set of observations: 1, 6, 2, 8, 7, 2.

Start by sorting the values: 1, 2, 2, 6, 7, 8. In this case, the arithmetic mean of the two middlemost terms is (2 + 6)/2 = 4. Therefore, the median is 4 since it is the arithmetic mean of the middle observations in the ordered list.

We also use this formula MEDIAN = {(n + 1 )/2}th item . n = number of values

As above example 1, 2, 2, 6, 7, 8 n = 6 Median = {(6 + 1)/2}th item = 3.5th item. In this case, the median is average of the 3rd number and the next one (the fourth number). The median is (2 + 6)/2 which is 4.

Visit the Median page on Wikipedia for more details

## The Standard Deviation

the standard deviation (SD) (represented by the Greek letter sigma, σ) measures the amount of variation or dispersion from the average.

In other words, the standard deviation σ (sigma) is the square root of the variance of X; i.e., it is the square root of the average value of (X − μ)2. In the case where X takes random values from a finite data set x1, x2, ..., xN, with each value having the same probability

Visit the Standard Deviation page on Wikipedia for more details

## The Variance

measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical. Variance is always non-negative: a small variance indicates that the data tend to be very close to the mean (expected value) and hence to each other, while a high variance indicates that the data are very spread out around the mean and from each other.