Today I have learned something new and it was a merely nightmare for me to comprehent, but I guess I was not as bad as I've always expected... There you go:
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 every number to get the list of deviations. Create a list of these numbers. It's OK to get negative numbers here. Next, square the resulting list of numbers (read: multiply them with themselves).
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.
6 Easy Steps for Standard Deviation:
- List numbers in ascending order.
- Find out the mean: sum of numbers divided by quantity of numbers.
- Find out the deviation: each number subtracted from the mean.
- Square each deviation.
- Find out the sum of all squared deviations.
- Find out the Standard Deviation: Sum of all squared deviations divided by quantity of numbers (or less than 1 of quantity of numbers for Variance SD).
I know this sounds confusing, but just check out this example:
- List of Numbers: 1, 3, 4, 6, 9, 19
- Mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7
- List of Deviations: -6 (1-7), -4 (3-7), -3 (4-7), -1 (6-7), 2 (9-7), 12 (19-7)
- Squares of Deviations: 36 (6x6), 16 (4x4), 9 (3x3), 1 (1x1), 4 (2x2), 144 (12x12)
- Sum of Squared Deviations: 36+16+9+1+4+144 = 210
- For Population Standard Deviation: Sum of squared SD divided by the quantity of numbers: 210 / 6 = 35
- For Population Standard Deviation: Square Root of this number: Square Root (35) = 5.91
- For Variance Standard Deviation: Divided by one less than the sum of the list: 210 / 5 = 42
- For Variance Standard Deviation: Square root of this number: square root (42) = about 6.48
Good luck and have fun...