SP is the sum of the product of deviations of x and y and is given by
[tex]\Sigma (x-\bar{x})(y-\bar{y})[/tex]
Given the table below
x: 1 2 9
y: 4 4 1
The mean of x is given by (1 + 2 + 9) / 3 = 12 / 3 = 4
The mean of y is given by (4 + 4 + 1) / 3 = 9 / 3 = 3.
We find the SP using the table below.
[tex]\begin{center}
\begin{tabular}
{|c|c|c|c|c|}
x & y & $x-\bar{x}$ & $y-\bar{y}$ & ($x-\bar{x}$)($y-\bar{y}$)\\ [1ex]
1 & 4 & $1-4=-3$ & $4-3=1$ & $-3\times1=-3\\
2 & 4 & $2-4=-2$ & $4-3=1$ & $-2\times1=-2$\\
9 & 1 & $9-4=5$ & $1-3=-2$ & $5\times-2=-10\\[1ex]
& & & & \Sigma (x-\bar{x})(y-\bar{y})=-15
\end{tabular}
\end{center}[/tex]
Therefore, the value of SP for the given set of data is -15.
