Plz give me the answer of this problem of economics?

Question

calculate Karl's coefficient of correlation from the following data:

1) sum of deviations of x = 5

2) sum of deviations of y = 4

3) sum of square of deviations of x = 40

4) sum of square of deviations of y = 50

5) sum of product of deviations of x and y = 32

6) No. of pairs of observation = 10

i need only the answer to check mine.

Answer 1

r = 32 / ((10-1) √(40*50/10²)) = 32*10 / (9√2000) =

= 32 / (9√20) ≈ 0.795046392

P.S. It's math-stat problem - not economics, but it has a lot of applications in economics.

Edit (in reply to e-mail):

Yeah, the problem is that different sources provide different formulas which sometimes are not equal each other mathematecally.

Latest I find in many sources (thus probability if it is right one is highest) looks following way (for unlimited samples):

r=A/B

A is sum of product of deviations

A=∑( ∏(x;y) )

B is product of roots from sum of squired deviations or just product of standart deviations (σ):

B=√ (∑(x²) ) * √ (∑(y²) ) = σ(x) * σ(y)

But for given samples (finite set):

A=∑( ∏(x;y) ) = 32

B=(n-1) * σ(x) * σ(y) = (10-1) * σ(x) * σ(y) = 9 * σ(x) * σ(y)

σ(x)= √(∑(x²) / n) = √(40 / 10)

σ(y)= √(∑(y²) / n) = √(50 / 10)

σ(x) * σ(y) = √(40*50 / 100) = √20

B=9√20

r=32 / (9√20) ≈ 0.7950463919999252253899284

http://upload.wikimedia.org/math/c/a/6/c...

http://changingminds.org/explanations/re...

http://davidmlane.com/hyperstat/A56626.h...

http://davidmlane.com/hyperstat/A51911.h...

http://en.wikipedia.org/wiki/Squared_dev...

http://en.wikipedia.org/wiki/Standard_de...

http://en.wikipedia.org/wiki/Correlation