the table shows the number of flowers in four bouquets and the total cost of each bouquet. what is the…

Answer:

0.28

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient $r$ is $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$. Let $x$ be the number of flowers and $y$ be the total cost.

Step2: Calculate sums

For the given data:

$x$	$y$	$xy$	$x^{2}$	$y^{2}$
8	12	96	64	144
12	40	480	144	1600
6	15	90	36	225
20	20	400	400	400

$\sum x=8 + 12+6 + 20=46$, $\sum y=12 + 40+15 + 20=87$, $\sum xy=96+480+90+400 = 1066$, $\sum x^{2}=64 + 144+36+400=644$, $\sum y^{2}=144+1600+225+400 = 2369$, and $n = 4$.

Step3: Substitute into the formula

$n(\sum xy)=4\times1066 = 4264$, $(\sum x)(\sum y)=46\times87=4002$, $n\sum x^{2}=4\times644 = 2576$, $(\sum x)^{2}=46^{2}=2116$, $n\sum y^{2}=4\times2369 = 9476$, $(\sum y)^{2}=87^{2}=7569$.

The numerator is $n(\sum xy)-(\sum x)(\sum y)=4264 - 4002=262$.

The denominator: [ \begin{align*} &\sqrt{(2576 - 2116)(9476 - 7569)}\ =&\sqrt{460\times1907}\ =&\sqrt{877220}\ \approx&936.5 \end{align*} ]

$r=\frac{262}{936.5}\approx0.28$.