Standard Deviation

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  • Created by: Jonjo
  • Created on: 04-04-12 11:06

\bar{x} \!\, (http://upload.wikimedia.org/wikipedia/en/math/5/3/8/5380f6f9098d18b8282bbf241ce9db13.png) = Mean 

Σ = Sum of

When dealing with a set of data you might use the mean and range. This is not always appropriate, as two sets of data can give you the same mean and range but be completely different!

Example:

1 2 4 8 10  Mean: 5 Range: 9

1 1 3 10 10 Mean:5 Range 9

They have the same mean and range but are spread out in a completely different way. To be able to make this difference more obvious we use Standard Deviation.

Standard Deviation shows how close the numbers in a set of data are to the mean. Theoretically, it would make sense to just take the mean away from each number. 

Example:

1 2 3 8 10

 1-5 =-4           2-5=-3           4-5=-1

Comments

Joe Kay

Amazing!!

mital

really nice....

Oliver

 (http://farm8.staticflickr.com/7228/6898524794_2c4b786e16_t.jpg)

Can this be the same as Sum x^2/n - mean of x^2? (That's what it says in my revision guide)

Oliver

^ the mean of x gets squared.

Jonjo

Oliver wrote:

 (http://farm8.staticflickr.com/7228/6898524794_2c4b786e16_t.jpg)

Can this be the same as Sum x^2/n - mean of x^2? (That's what it says in my revision guide)

Sorry this response may be a little late! :) I believe you are talking about the Alternative formula? This works too... It is Sum x^2/n - (sum of x/n)^2 

So yes, you are correct.

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