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The Standard Deviation :: Standard Deviation Calculation ShortCut Method
This method might be a bit faster to calculate. Calculate the Standard Deviation for the following data using the calculator to the right (round to 1 decimal points). Click on the Check Answer button to see how you did.
Data:
9, 10, 12, 15, 17, 20, 21
1
Add up all the values.
Sum
104
2
Square this sum
Sum Squared
10816
3
Count the total number of values.
n
7
4
Divide Sum Squared by the the total number of values
Avg. Sum Squared
1545.14
5
Square each individual value.
6
9
^{2}
81
7
10
^{2}
100
8
12
^{2}
144
9
15
^{2}
225
10
17
^{2}
289
11
20
^{2}
400
12
21
^{2}
441
13
Add up all these squared values.
Sum of Squares
1680
14
Subtract Sum of Squares  Avg. Sum Squared
134.86
15
Divide this by the total number of values minus 1.
sample variance
22.48
16
Take the square root of the variance.
sample standard deviation
4.74
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November 15, 2011  sakura wrote:
how is this a shortcut? i already know how to use a calculator. the point of a shortcut was to find a way to get the standard deviation without having to go through the pain of having to square each individual value every single time! when you're working with 30+ numbers this is unbelievably irritating, calculator or no. this isn't a shortcut!
May 28, 2009  brandee dungan wrote:
i do not understand where or how to get sample variance value. everything else makes since.