Finite Math Examples

$\begin{array}{c} x & y \\ 90.4 & 11 \\ 92.2 & 12 \\ 75.9 & 10 \\ 81.5 & 11 \\ 78.1 & 10 \\ 76.8 & 9 \end{array}$

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.

$\sum_{}^{} x = 90.4 + 92.2 + 75.9 + 81.5 + 78.1 + 76.8$

Step 3

Simplify the expression.

$\sum_{}^{} x = 494.90002$

Step 4

Sum up the $y$ values.

$\sum_{}^{} y = 11 + 12 + 10 + 11 + 10 + 9$

Step 5

Simplify the expression.

$\sum_{}^{} y = 63$

Step 6

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

$\sum_{}^{} x y = 90.4 \cdot 11 + 92.2 \cdot 12 + 75.9 \cdot 10 + 81.5 \cdot 11 + 78.1 \cdot 10 + 76.8 \cdot 9$

Step 7

Simplify the expression.

$\sum_{}^{} x y = 5228.5$

Step 8

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

$\sum_{}^{} x^{2} = {(90.4)}^{2} + {(92.2)}^{2} + {(75.9)}^{2} + {(81.5)}^{2} + {(78.1)}^{2} + {(76.8)}^{2}$

Step 9

Simplify the expression.

$\sum_{}^{} x^{2} = 41073.91017517$

Step 10

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

$\sum_{}^{} y^{2} = {(11)}^{2} + {(12)}^{2} + {(10)}^{2} + {(11)}^{2} + {(10)}^{2} + {(9)}^{2}$

Step 11

Simplify the expression.

$\sum_{}^{} y^{2} = 667$

Step 12

Fill in the computed values.

$r = \frac{6 (5228.5) - 494.90002 \cdot 63}{\sqrt{6 (41073.91) - {(494.90002)}^{2}} \cdot \sqrt{6 (667) - {(63)}^{2}}}$

Step 13

Simplify the expression.

$r = 0.8593393$