Finite Math Examples

$\begin{array}{c} x & y \\ 59 & 67 \\ 61 & 71 \\ 66 & 72 \\ 69 & 73 \\ 71 & 75 \\ 67 & 64 \\ 70 & 64 \\ 71 & 67 \\ 73 & 67 \\ 75 & 67 \end{array}$

Step 1

The linear correlation coefficient measures the relationship between the paired values in a sample.

$r = \frac{n (\sum_{}^{} x y) - \sum_{}^{} x \sum_{}^{} y}{\sqrt{n (\sum_{}^{} x^{2}) - {(\sum_{}^{} x)}^{2}} \cdot \sqrt{n (\sum_{}^{} y^{2}) - {(\sum_{}^{} y)}^{2}}}$

Step 2

Sum up the $x$ values.

$\sum_{}^{} x = 59 + 61 + 66 + 69 + 71 + 67 + 70 + 71 + 73 + 75$

Step 3

Simplify the expression.

$\sum_{}^{} x = 682$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 67 + 71 + 72 + 73 + 75 + 64 + 64 + 67 + 67 + 67$

Step 5

Simplify the expression.

$\sum_{}^{} y = 687$

Step 6

Sum up the values of $x \cdot y$ .

$\sum_{}^{} x y = 59 \cdot 67 + 61 \cdot 71 + 66 \cdot 72 + 69 \cdot 73 + 71 \cdot 75 + 67 \cdot 64 + 70 \cdot 64 + 71 \cdot 67 + 73 \cdot 67 + 75 \cdot 67$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 46839$

Step 8

Sum up the values of $x^{2}$ .

$\sum_{}^{} x^{2} = {(59)}^{2} + {(61)}^{2} + {(66)}^{2} + {(69)}^{2} + {(71)}^{2} + {(67)}^{2} + {(70)}^{2} + {(71)}^{2} + {(73)}^{2} + {(75)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 46744$

Step 10

Sum up the values of $y^{2}$ .

$\sum_{}^{} y^{2} = {(67)}^{2} + {(71)}^{2} + {(72)}^{2} + {(73)}^{2} + {(75)}^{2} + {(64)}^{2} + {(64)}^{2} + {(67)}^{2} + {(67)}^{2} + {(67)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 47327$

Step 12

Fill in the computed values.

$r = \frac{10 (46839) - 682 \cdot 687}{\sqrt{10 (46744) - {(682)}^{2}} \cdot \sqrt{10 (47327) - {(687)}^{2}}}$

Step 13

Simplify the expression.

$r = - 0.08295729$