How to find the sum of $(x-\bar x)(y- \bar y)$

Question

Please I need help. I need the correct steps how to calculate: Sum $(x-\bar x)(y- \bar y)$?

My numbers are: $x$: 2,4,6,8,10 $y$: 3,5,7,10,12

My results are: $\Sigma x=30$

$\Sigma y=37$

$\bar x= 6$

$\bar y= 7.4$

I think $(x-\bar x)^2$ = 40 and $(y-\bar y)^2$ = 53.38

Standard deviation = 3.16228

Sum of $(x-\bar x)(y-\bar y)^2$)?

Canot figure out what I'm doing wrong? Any help/guide will be appreciated.

Wait, $\sum(x_i-\overline x)^2$ or is it $\sum(x_i-\overline x)(y_i-\overline y)$? Note that while the two sums are related, you cannot get one by calculating only the other... — abiessu, Sep 08 '16 at 21:34
Update your question with what you have done so we can help further. — unseen_rider, Sep 08 '16 at 21:44
Plugging in all the numbers, I get 45.6. What exactly is it that is causing you trouble? — Bobson Dugnutt, Sep 08 '16 at 22:11
How did you get 45.6? I'm getting (30-6)(37-7.4) = 710.4 what I'm doing wronge? — Sar, Sep 08 '16 at 22:37

tomi · Answer 1 · 2016-09-09T06:43:38.750

1

When we say $\Sigma (x-\bar x)(y-\bar y)$, you need to calculate $(x-\bar x)(y-\bar y)$ for each data point and add them all up:

$(2-6)(3-7.4)+(4-6)(5-7.4)+(6-6)(7-7.4)+(8-6)(10-7.4)+(10-6)(12-7.4)$

You said: "My results are: X=30 Y=37 Xbar= 6 Ybar= 7.4"

You should have said: "My results are: $\Sigma x=30$, $\Sigma y=37$, $\bar x= 6$, $\bar y= 7.4$"

edited Sep 09 '16 at 06:43

answered Sep 08 '16 at 22:51

tomi

1 Answers1