Finite Math Examples

\begin{matrix} x & p 1 & 12 3 & 119 6 & 973 8 & 2350 \end{matrix}

$\begin{array}{c} x & p \\ 1 & 12 \\ 3 & 119 \\ 6 & 973 \\ 8 & 2350 \end{array}$

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}}}

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

Step 2

Sum up the

x

$x$ values.

\sum x = 1 + 3 + 6 + 8

$\sum_{}^{} x = 1 + 3 + 6 + 8$

Step 3

Simplify the expression.

\sum x = 18

$\sum_{}^{} x = 18$

Step 4

Sum up the

y

$y$ values.

\sum y = 12 + 119 + 973 + 2350

$\sum_{}^{} y = 12 + 119 + 973 + 2350$

Step 5

Simplify the expression.

\sum y = 3454

$\sum_{}^{} y = 3454$

Step 6

Sum up the values of

x \cdot y

$x \cdot y$ .

\sum x y = 1 \cdot 12 + 3 \cdot 119 + 6 \cdot 973 + 8 \cdot 2350

$\sum_{}^{} x y = 1 \cdot 12 + 3 \cdot 119 + 6 \cdot 973 + 8 \cdot 2350$

Step 7

Simplify the expression.

\sum x y = 25007

$\sum_{}^{} x y = 25007$

Step 8

Sum up the values of

x^{2}

$x^{2}$ .

\sum x^{2} = {(1)}^{2} + {(3)}^{2} + {(6)}^{2} + {(8)}^{2}

$\sum_{}^{} x^{2} = {(1)}^{2} + {(3)}^{2} + {(6)}^{2} + {(8)}^{2}$

Step 9

Simplify the expression.

\sum x^{2} = 110

$\sum_{}^{} x^{2} = 110$

Step 10

Sum up the values of

y^{2}

$y^{2}$ .

\sum y^{2} = {(12)}^{2} + {(119)}^{2} + {(973)}^{2} + {(2350)}^{2}

$\sum_{}^{} y^{2} = {(12)}^{2} + {(119)}^{2} + {(973)}^{2} + {(2350)}^{2}$

Step 11

Simplify the expression.

\sum y^{2} = 6483534

$\sum_{}^{} y^{2} = 6483534$

Step 12

Fill in the computed values.

r = \frac{4 (25007) - 18 \cdot 3454}{\sqrt{4 (110) - {(18)}^{2}} \cdot \sqrt{4 (6483534) - {(3454)}^{2}}}

$r = \frac{4 (25007) - 18 \cdot 3454}{\sqrt{4 (110) - {(18)}^{2}} \cdot \sqrt{4 (6483534) - {(3454)}^{2}}}$

Step 13

Simplify the expression.

r = 0.93924602

$r = 0.93924602$