1 Answer

NewBoy · Answer 1 · 2022-05-02T19:37:56+0000

You have some data points labeled by
. They form the set {3, 5, 7}.

The mean,
$\bar x$ , is the average of these values:

$\bar x = \frac{3+5+7}3 = \frac{15}3 = 5$

Then in the column labeled
$x-\bar x$ , what you're doing is computing the difference between each data point
and the mean
$\bar x$ :

$x=3 \implies x-\bar x = 3 - 5 = -2$

$x=5 \implies x-\bar x = 5-5 = 0$

$x=7 \implies x-\bar x = 7 - 5 = 2$

These are sometimes called "residuals".

In the next column, you square these values:

$x=3 \implies (x-\bar x)^2 = (-2)^2 = 4$

$x=5 \implies (x-\bar x)^2 = 0^2 = 0$

$x=7 \implies (x-\bar x)^2 = 2^2 = 4$

and the variance of the data is the sum of these so-called "squared residuals".

Your comment on this question: