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