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

Explanation:

Step1: Calculate the means

Let (x) be the number of flowers and (y) be the total cost. (\bar{x}=\frac{8 + 12+6+20}{4}=\frac{46}{4} = 11.5) (\bar{y}=\frac{12 + 40+15+20}{4}=\frac{87}{4}=21.75)

Step2: Calculate the numerator of the correlation - coefficient formula

(n = 4) (\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})=(8 - 11.5)(12-21.75)+(12 - 11.5)(40 - 21.75)+(6 - 11.5)(15 - 21.75)+(20 - 11.5)(20 - 21.75)) (=(-3.5)(-9.75)+(0.5)(18.25)+(-5.5)(-6.75)+(8.5)(-1.75)) (=34.125 + 9.125+37.125-14.875) (=65.5)

Step3: Calculate the denominator of the correlation - coefficient formula

(\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}=(8 - 11.5)^{2}+(12 - 11.5)^{2}+(6 - 11.5)^{2}+(20 - 11.5)^{2}) (=(-3.5)^{2}+(0.5)^{2}+(-5.5)^{2}+(8.5)^{2}) (=12.25 + 0.25+30.25+72.25) (=115) (\sum_{i = 1}^{n}(y_{i}-\bar{y})^{2}=(12 - 21.75)^{2}+(40 - 21.75)^{2}+(15 - 21.75)^{2}+(20 - 21.75)^{2}) (=(-9.75)^{2}+(18.25)^{2}+(-6.75)^{2}+(-1.75)^{2}) (=95.0625+333.0625 + 45.5625+3.0625) (=476.75) (\sqrt{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}\sum_{i = 1}^{n}(y_{i}-\bar{y})^{2}}=\sqrt{115\times476.75}=\sqrt{54826.25}\approx234.15)

Step4: Calculate the correlation coefficient (r)

(r=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}\sum_{i = 1}^{n}(y_{i}-\bar{y})^{2}}}=\frac{65.5}{234.15}\approx0.28)

Answer:

0.28