Sigma Confusion ∑

Spyral

I'm doing an equation for a stats problem and I am confused

is ∑xy the same as ∑x * ∑y ??

does ∑xy mean add up all of x values and add them to all of the y values or does it mean add up all of x and multiply it by all of y added up ?

ie my problem is ∑xy -[∑x * ∑y / n ]

djpbarry

Spyral wrote: »

does ∑xy mean add up all of x values and add them to all of the y values or does it mean add up all of x and multiply it by all of y added up ?

I would imagine it means the sum of the products of the two data sets. If

X = {x1, x2, x3 .... xn}

and

Y = {y1, y2, y3 ... ym}

then:

∑XY = (x1 * y1) + (x2 * y2) + (x3 * y3) ... (xn * ym).

Spyral

thanks. But that doenst seem right.

djpbarry

Spyral wrote: »

thanks. But that doenst seem right.

In what way? What do X and Y represent?

Fremen

Sigma notation usually has an index which shows you what you're summing over. Check what that says in your formula, it might help.

The usual interpretation for what you've written is that with ∑xy you multiply corresponding entries, then sum up the products (like djpbarry said, except that n and m need to be equal for the sum to make sense).

∑x * ∑y means you add up all the X values, add up all the Y values seperately and then multiply the two sums.

djpbarry

Fremen wrote: »

...(like djpbarry said, except that n and m need to be equal for the sum to make sense)...

Yeah, sorry Spyral; I forgot to point that out.

Spyral

Sigma notation usually has an index which shows you what you're summing over. Check what that says in your formula, it might help.

The usual interpretation for what you've written is that with ∑xy you multiply corresponding entries, then sum up the products (like djpbarry said, except that n and m need to be equal for the sum to make sense).

∑x * ∑y means you add up all the X values, add up all the Y values seperately and then multiply the two sums.

thanks guys.. its just that any maths books or webpages have ranges of values and are talking about adding series it seems.

I also had a word with my lectuer. ∑xy is mulptiply x1 and y1, x2 and y2 and so on, add all of them up.

∑x * ∑y is add up all x's x1+x2+x3 etc and do the same for y then multiply them

djpbarry

Spyral wrote: »

I also had a word with my lectuer. ∑xy is mulptiply x1 and y1, x2 and y2 and so on, add all of them up.

∑x * ∑y is add up all x's x1+x2+x3 etc and do the same for y then multiply them

So are you ok now or is there still a problem?