Download Standard Deviation Example

Standard Deviation Example
AP Statistics
Remember our formula for standard deviation:
So, if we have the following data: 3,4,7,9,8,0,0,0,11,1
First we calculate the mean:
(3+4+7+9+8+0+0+0+11+1)
=
10
4.3
Then we start by subtracting the mean from each of our observations:
-1.4, -.3, 2.7, 4.7,
3.7, -4.3,
-4.3,
-4.3,
6.7,
-3.3
Then we square each of them: 1.96, .09, 7.29, 22.09, 13.69, 18.49, 18.49, 18.49, 44.89, 10.89
Then we add each of these together (definition of the summation notation):
1.96+.09+7.29+22.09+13.69+18.49+18.49+18.49+44.89+10.89=156.37
Then we divide by n-1. N is 10, so we divide by 9. 156.37/9=17.37
Finally, we take the square root of 17.37, which is approximately equal to 4.17.
Thus, our standard deviation is approximately 4.17.
We can conclude from this that the data points are typically about 4.17 from the mean in this
dataset.
IF YOU ARE STILL STRUGGLING, THE FOLLOWING WEBSITE PROVIDES SOME MORE
EXAMPLES: https://www.mathsisfun.com/data/standard-deviation-formulas.html. Note,
however, that we will use the sample standard deviation formula for now (meaning that we use
n-1 instead of n). Some of the examples on the website use the population formula rather than
the sample formula.