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Chance of That

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You might like to note that the sample correlation $r_{xy}$ of a pair of lists of $N$ numbers $x_i$, $y_i$  is given by


$$r_{xy} = \frac{\sum^{N}_{i=1} \left((x_i-\bar{x})(y_i-\bar{y})\right)}{\sqrt{\sum^N_{i=1}(x-\bar{x})^2\sum^{N}_{i=1}(y_i-\bar{y})^2}}$$