Calculating Covariance missing understanding for one step

Question

I am following this

once I get to this point

I don't understand the transition/calculation to get -0.01

I mean to me that equals 0.00 so what have I missed?

Answer 1

I understand why you are confused. It seems to me that first they calculate $\sum\limits_{i=1}^9 (x_i-x_{\mathrm{avg}})$ which is obviously zero, but due to rounding errors on $x_{\mathrm{avg}}$, they end up with -0.01. Similarly, due to rounding errors on $y_{\mathrm{avg}}$ they end up by saying that $\sum\limits_{i=1}^9 (y_i-y_{\mathrm{avg}})$ is 0.04. These two numbers are then multiplied and also multiplied by $1/8$. But this would be $$ \frac18\Big(\sum_{i=1}^9(x_i-x_{\mathrm{avg}})\Big)\Big(\sum_{i=1}^9 (y_i-y_{\mathrm{avg}})\Big) $$ which is not the formula for the (sample) covariance. The formula for the covariance is $$ \frac18\sum_{i=1}^9(x_i-x_{\mathrm{avg}})(y_i-y_{\mathrm{avg}}) $$ which they correctly write at the top. Using this formula we would end up with -8.0694 approximately.