[tunelling]

Hi,

I need to calculate the standard deviation of some results from a chemistry experiment.

Could someone please explain how to use the standard deviation equation. I've had a look at some webpages but I think they assume that you have a good understanding of maths, which I don't.

[Arkcon]

Humpf.  Funny.  Most people these days just plug their numbers into the Excel formula, or their calculator and just roll with it.  It is pretty impressive that you even care about this topic.  OK.  Let's try to work with what you have.  List your data.  If it's hundred's of numbers, then just lost some.  Copy, as best you can, the formula you've searched for.  And try to guess where to plug in the values.

[Arkcon]

Oh, and for an explanation of what a standard deviation is, did you see this wikipedia example.  It is pretty clear:

http://en.wikipedia.org/wiki/Standard_deviation#Example

[Mr Peanut]

Could someone please explain how to use the standard deviation equation.

One thing that is sometimes not clear for some is the distinction between the standard deviation and its estimate from a sample of the population. The standard deviation is (as wiki points out) the root mean square deviation from the mean for the values of ALL of the members of the population.

When making measurements we rarely measure all of the values. Instead we measure a subset called a "sample". The actual standard deviation (the population standard deviation) is estimated from the sample using the "sample standard deviation".

The sample standard deviation is almost a root mean square but instead of dividing by the population count we divide by the sample count minus the degrees of freedom (typically N-1 where N is the sample count).

[flask]

Simple Example

[pjaj]

One definition of the standard deviation is "The root of the mean of the squares of the differences from the average"
At first glance quite a mouthful, but read it out slowly and it is an explanation of how to calculate the SD.

1) calculate the average of the N data items ("the average")
2) tabulate the differences of each point from this average ("the differences")
3) square each difference, add them up and divide by N ("the mean of the squares of the differences")
4) take the square root of this average ("The root ... ") = The standard deviation.

This only works for the whole data set. If you only have a sample then the formula differs, as explained in the Wikipedia entry and a previous post.

The Wikipedia article also shows how the formula for the above calculation can be algebraically manipulated (under "Simplification of the formula") to give more useful versions that simplify the above calculation.

Note that the squaring step removes the distinction between positive and negative differences.
If you just added up the differences the answer should be zero in all cases!

Or, as others have said, you can blindly plug the numbers into Excel!

[darrenhenchback]

Well I think it's bloody awesome that you want to understand standard deviations rather than to just calculate them by shoving the numbers into a calculator (or worse, Microsoft Excel  ). Standard deviation is a measure of the spread of data. You can have a bunch of numbers that are all really close to each other, for example:

1,2,3,4,5,6,6,6,7,7,8

There are 11 numbers here

Step #1: work out the Mean  . This is done by adding the value of all the numbers and dividing that by the number of numbers (i.e. 11). So (1+2+3+4+5+6+6+6+7+7+8) divided by 11.
= 55/11
= 5

Step #2: from each of the above numbers, subtract the mean (so take away 5 in this case, and it's totally cool to get minus numbers here)... here's what you get  :

-4, -3, -2, -1, 0, 1, 1, 1, 2, 2, 3

Step #3: square each number and you get...

16, 9, 4, 1, 0, 1, 1, 1, 4, 4, 9

Step #4: add all these numbers up and you get...

50

Step #5: divide this number by the number of numbers (which as we know is 11) MINUS 1. So divide by 10 in this case, and we get ...

5.

Step #6: get the square root of the resulting number. So the standard deviation here is 2.24

Aint that cool ? Try working out the standard deviation now for a whole load of other numbers, so you can understand it better. The bigger the spread in the data, the bigger the value for standard deviation. Why? Because the bigger the spread, the more different the numbers will be from the mean. So you'll get much bigger numbers in step 2. The numbers in step 2 then get squared and added together, so go figure ^^

[ashishbandhu]

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calculator.tutorvista.com/math/351/standard-deviation-calculator.html