How do you find the standard deviation of a set of statistics?

Answer 1

Ok, you ready for this....find the mean....that's done by adding all the numbers and dividing by however many numbers you have. Then take each number and subtract the mean from it and saqure that number. Once you've done each number add those numbers together and divide it by the amount of numbers you have and then take the square root.

ex: you set of numbers is 2, 4, 6, 8
the mean = 20/4=5
so do 2-5 and square it to get 9
4-5 then squre it to get 1
6-5 square to get 1
8-5 square it to get 9
add em all up so 9+1+1+9=20 and then take the square root of 20 ....if you do it with a calculator it gives you a decimal number if you don't use a calculator it should give you 2*square root of 5

Hope that helps.

Answer 2

Standard deviation (sigma) is defined as:
σ = sqrt[Σ(x-xbar)^2/(n -1)]

where xbar is the mean of the sample
and n is the size of the sample
x is any individual value in the sample

This formula is a logical way to measure the extent of the spread of data about a mean value. Two drastically different samples can have the same mean, for instance examine these two sets with the same mean of 50...

{51,48,55,46} and {2,105,12,81}

The mean alone would not tell us very much information about the different samples. Though the values of the second clearly have a much wider distribution. This is where standard deviation comes in...

For both examples xbar=50 n=4

For the first sample

x xbar x-xbar (x-xbar)^2
51 50 1 1
48 50 -2 4
55 50 5 25
46 50 -4 16

σ = sqrt[(1+4+25+16)/3]
σ ~ 3.92

For the second sample

x xbar x-xbar (x-xbar)^2
2 50 - 48 2304
105 50 55 3025
12 50 -38 1444
81 50 31 961

σ = sqrt[(2304+3025+1444+961)/3]
σ ~ 50.77

Answer 3

The cheat way is to use the stats functions on Excel. I used to know the proper way, but many years ago.