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Four made-up shops have 1, 2, 3 and 4 staff, and their sales on one day are 2, 3, 7 and 8 thousand…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Four made-up shops have $1$ , $2$ , $3$ and $4$ staff, and their sales on one day are $2$ , $3$ , $7$ and $8$ thousand rupees. Find $S_{xx}$ , $S_{yy}$ , $S_{xy}$ and the correlation coefficient $r$ , to four decimal places.

Need a reminder? The key ideaShow

$S_{xy} = \sum (x - \bar{x})(y - \bar{y})$ , $S_{xx} = \sum (x - \bar{x})^2$ , $S_{yy} = \sum (y - \bar{y})^2$ and

\displaystyle r = \dfrac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}.

With sample standard deviations, $r$ is also $\dfrac{1}{n - 1}\sum z_x z_y$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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