The table below shows the temperature (in degrees) for eight consecutive days as well as the respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature
Number of Cones
403
68
77
83
85
457
465
89
489
94
96
99
447
576
543
503
What is the correlation coefficient of the set of data? Round your answer to the nearest thousandth.
(1 point)
A-0.956
B--0.972
C-0.019
D-0.508
To find the correlation coefficient, we need to calculate the covariance and the standard deviation for both the temperature and the number of cones.
First, we calculate the mean for both the temperature and the number of cones.
Mean temperature: (403+68+77+83+85+457+465+89)/8 = 253.875
Mean number of cones: (94+96+99+447+576+543+503)/7 = 368.857
Next, we calculate the covariance using the formula: covariance = Σ [(x_i - mean temperature) * (y_i - mean number of cones)] / n-1
(x_i - mean temperature) : -149.875, -185.875, -176.875, -170.875, -168.875, 203.125, 211.125, -164.875
(y_i - mean number of cones): -274.857, -272.857, -269.857, 78.143, 207.143, 174.143, 134.143
Sum of [(x_i - mean temperature) * (y_i - mean number of cones)] = -2541188.571
n-1 = 8-1 = 7
covariance = -2541188.571 / 7 = -363027.025
Next, we calculate the standard deviation for both the temperature and the number of cones using the formula: standard deviation = √(Σ[(x_i - mean)^2]/(n-1))
(x_i - mean temperature)^2: 22869.156, 3435.156, 1906.156, 667.156, 489.156, 41475.156, 44515.156, 3450.156
(y_i - mean number of cones)^2: 73135.224, 72265.224, 71215.224, 61272.122, 42977.122, 34695.122, 21929.122
Sum of (x_i - mean temperature)^2 = 155416.184
Sum of (y_i - mean number of cones)^2 = 317488.038
standard deviation temperature = √(155416.184 / 7) = 61.188
standard deviation number of cones = √(317488.038 / 7) = 78.353
Finally, we calculate the correlation coefficient using the formula: correlation coefficient = covariance / (standard deviation temperature * standard deviation number of cones)
correlation coefficient = -363027.025 / (61.188 * 78.353) = -363027.025 / 4789.346 ≈ -0.955
Rounded to the nearest thousandth, the correlation coefficient is -0.955.
Thus, the answer is A. -0.956.