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Can anyone help me out with some maths?
    #6978369 -

Hey,

I have an economics exam soon, and there's a section on Economic Data Analysis which is really fucking easy, but because I don't have a maths background, I find some of the notation a little hard to get my head around.

For instance, the concept of Standard Deviation is easy to grasp. The steps of calculating standard deviation:

Quote:
  1. For each value xi calculate the difference between xi and the average value
  2. Calculate the squares of these differences.
  3. Find the average of the squared differences. This quantity is the variance σ2.
  4. Take the square root of the variance.




are also perfectly simple. However, the forumula   stumps me, even though I understand it when written in English. Could anyone walk me through it? That is, explain how it can be translated into the steps quoted. I'd be very much obliged.

Thanks! :sun:

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Re: Can anyone help me out with some maths? [Re: OJK]
    #6978731 -

i used to be the master of qmet but i forgot it all now. i think there may be a more simplified formula than that one though.


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I can flash/jtag/repair 360's, pm for details.

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Re: Can anyone help me out with some maths? [Re: iateshaggy]
    #6979406 -

the sigma(x-x_hat)^2 is merely a sum. All it is saying is that if you have N values, just subtract each value from the average and square it. Then add up all the resulting values. After that is done, divide by the number of terms, N. Take the square root.

So Xi is just a particular value of X. If you have say,
[3,2,1], youd have an N value of 3. And X1 would be 3, X2 would be 2, X3 would be 1. X_hat is equal to 2, as that is the average value. so youd just do
(X1-2)^2 + (X2-2)^2+(X3-2)^2
Then divide that result by 3, and take the square root.

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Re: Can anyone help me out with some maths? [Re: TheCow]
    #6980867 -

Nothing wrong with the above description, but I will provide another so that you can look at it from two directions:

Look at your data; you have N items. If we were looking at the weight of ten people, N would equal 10. The average weight of all ten people is X with the bar over it (X_hat). The actual weight of each individual is Xi, where i the "index" into the data. For example, the data might look like: X1=100 lbs, X2=120 lbs, X3=105 lbs, X4=240 lbs, ... X10=180 lbs.

The sigma (looks like a capital E, kind of) means summation. The bottom value (i=1) tells you were to start and the top value (N) tells you were to stop. The expression that comes after the sigma is what gets summed. In this case, it is telling us to sum (add together) the value of (Xi minus X_hat) for each value of i from 1 to N. We already know Xi for each value of i from 1 to 10 and we already know X_hat, so this is easy.

Assume that X_hat=140 lbs. The sum would look something like:

sum=(x1-x_hat)^2+(x2-x_hat)^2+(x3-x_hat)^2+ ... +(x10-x_hat)^2

or:

sum=(100-140)^2+(120-140)^2+(105-140)^2+ ... (180-140)^2

The ^2 means to the power of 2, or squared, or multiplied by itself (all mean the same thing). Thus (100-140)^2 is the same as [(100-140)*(100-140)], or [(-40)*(-40)]=1600. (The * means multiply)

The 1/N means to divide 1 by N (the number of data points). Once you get a value, you multiple it by the sum you just calculated in the previous step.

Finally, you take the square root of this value to get your standard deviation.


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Just another spore in the wind.

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Re: Can anyone help me out with some maths? [Re: Seuss]
    #6981172 -

That was a great explanation, it seems very clear now. Thanks guys!

:sun:

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Re: Can anyone help me out with some maths? [Re: OJK]
    #6984877 -

Yeah make sure you know this is the variance and std.dev of the population.

The commonly used unbiased sample std. dev has a slightly different formula. I can explain the why's if needed...

Make sure you know if you are working with sample or population...


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Be like water my friend!

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