Standard Deviation — manual calculation

How to Calculate the Standard Deviation

February 22, 2013

Of course the calculator can make short work of this, but doing it by hand a few times can help increase the understanding of what the standard deviation is all about.

First, you need to determine the mean. The mean of a list of numbers is the sum of those numbers divided by the quantity of items in the list (read: add all the numbers up and divide by how many there are).

Then, subtract the mean from each number to get the list of deviations. Create a list of these numbers. It’s OK to get negative numbers here. Next, square each of these deviations.

Add up all of the resulting squares to get their total sum. Divide your result by one less than the number of items in the list.

To get the standard deviation, just take the square root of the resulting number

I know this sounds confusing, but just check out this example:

your list of numbers: 1, 3, 4, 6, 9, 19

mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7

list of deviations  <The deviations are the values you get by taking the mean from each of the original numbers>: -6, -4, -3, -1, 2, 12

squares of deviations: 36, 16, 9, 1, 4, 144

sum of the squares of the deviations: 36+16+9+1+4+144 = 210

divided by one less than the number of items in the list: 210 / 5 = 42

The standard deviation is the square root of this number: square root (42) = about 6.48

Another example:Standard Deviation calc

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