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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.

Standard Deviation Formula 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. Varience Formula 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.