Does the formula change for Variance and Deviation
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Does the formula change for Variance and Deviation

[From: ] [author: ] [Date: 11-05-11] [Hit: ]
.[xminusx]² for i= 1...........
On my online math class, they set up a table for finding variance and standard deviation

x sub i ~ x sub i-mean ~ (x sub i-mean)^2

Even though they set up the table like this, they sometimes subtract the x term from the mean instead. Is there a reason for this, or are they just messing up?

-
Both will give the same result because
(xsubi - mean)^2 = (mean - xsubi)^2

-
The variance is calculated by figuring out

The Average of the
................▬
[x minus x ]² for i= 1.....n if there are n data points
...i

Now
When they set up the table they probably

do this

column 1 column 2 column 3 column 4
x.....................x-mean xsubi - x mean (xsubi - x mean)²

list ................list the mean...........subtract ................figure squares
values...........same number...column2 from col 2........of column 3


Then you are probably told to ADD up all numbers in column 4
then divide by n

That is the variance.

It is possible to just do column 3
where mean is subtracted from x term



There is a short cut formula too that you may be
encountering.

In the table above you are figuring out the variance as
Σ(x - µ)²
————— where µ means x sub i mean
.....n

but it can be shown that this is the same
algebraically as

Σx² - nµ²
————
.....n

-
The table is:

xi----------(xi - xmean)----------(xi - xmean)^2

To each value of X, xi, subtract the mean (called media deviation: di = xi - xmean) and after di^2.

Now, you wrote "they sometimes subtract the x term from the mean instead.".

What do you mean with this?

It must be done with each value xi!.

If you want, write here the link of your website.

-
They're probably just messing up, but it doesn't matter. You're calculating the square of (x_i - mean) and that's the same as the square of (mean - x_i). They're negatives of each other.
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