How would I work out the Standard Deviation and the RMSD of
X 3 4 5 6 7 8 9
f 2 5 8 14 9 4 3
Please show me the steps
Have you checked this out as a start?
Standard derivation at Wikipedia
is your data set and N is the number of data points.
First find the mean (average) value, .
Then calculate for each data point.
Then calculate for each data point.
Now add all the together to get .
Now divide this by N to get . ( is called the "variance.")
Now take the square root. . This is your standard deviation.
-Dan
I think there is something that says you can divide by N-1 as well, probably because if you have only one value, the standard derivation would become 0 if you divided by 1, while it rather should be undefined (as in division by 0 undefined ).
There is also an alternative way of calculation the standard derivation where you calculate the average value "at the same time" (though it really does the same):
is your data set and n is the number of data points.
Calculate the sum of the values:
The average value is obtained by the fraction
Calculate the sum of the squares of the values:
Calculate what the sum of the squares would have been ( ) if every value had been the same as the average value:
Now let's se how much is missing to obtain the actual sum of the squares:
Now if we divide the difference by n we'll get the variance:
So, the standard derivation
And let's say you only want to divide by n-1:
This method is useful if you have a set of numbers which you already have calculated the standard derivation for with this method, and want to ad a new number to the set and at the same time fast calculate the new standard derivation. Just be sure to store and so you are able to quickly update them when a new number is added.
/Kristofer
By the way, what does "-Dan" mean?