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. What is the correlation coefficient of the set of data? Round your answer to the nearest thousandth.
Temperature
68
77
83
85
89
94
96
99
Number of Cones
403
447
457
465
489
503
543
576
A. 0.956
B. -0.972
C. 0.019
D. 0.508
I put it in a correlation coefficient calculator and got 0.9562.
The answer is A. 0.956
hey what is the answer guys
Answer is 0.956
To find the correlation coefficient of the given data set, you can follow these steps:
Step 1: Calculate the mean of both sets of data (temperature and number of cones) separately.
To find the mean of the temperature data:
(68 + 77 + 83 + 85 + 89 + 94 + 96 + 99) / 8 = 841 / 8 = 105.125
To find the mean of the number of cones data:
(403 + 447 + 457 + 465 + 489 + 503 + 543 + 576) / 8 = 3883 / 8 = 485.375
Step 2: Find the difference between each data point and the respective mean for both sets of data.
For the temperature data:
68 - 105.125 = -37.125
77 - 105.125 = -28.125
83 - 105.125 = -22.125
85 - 105.125 = -20.125
89 - 105.125 = -16.125
94 - 105.125 = -11.125
96 - 105.125 = -9.125
99 - 105.125 = -6.125
For the number of cones data:
403 - 485.375 = -82.375
447 - 485.375 = -38.375
457 - 485.375 = -28.375
465 - 485.375 = -20.375
489 - 485.375 = 3.625
503 - 485.375 = 17.625
543 - 485.375 = 57.625
576 - 485.375 = 90.625
Step 3: Calculate the product of the difference for each data point in both sets.
For each data point, multiply the difference in temperature by the difference in the number of cones and sum up the products.
(-37.125) * (-82.375) + (-28.125) * (-38.375) + (-22.125) * (-28.375) + (-20.125) * (-20.375) + (-16.125) * (3.625) + (-11.125) * (17.625) + (-9.125) * (57.625) + (-6.125) * (90.625) = 35,223.15625
Step 4: Calculate the product of the standard deviations for both sets of data.
Calculate the standard deviation of the temperature data:
First, calculate the variance by finding the sum of the squared differences between each data point and the mean, then divide by the number of data points minus one:
((-37.125)^2 + (-28.125)^2 + (-22.125)^2 + (-20.125)^2 + (-16.125)^2 + (-11.125)^2 + (-9.125)^2 + (-6.125)^2) / (8-1) = 2524.75
The standard deviation is the square root of the variance:
sqrt(2524.75) = 50.247
Calculate the standard deviation of the number of cones data:
First, calculate the variance:
((-82.375)^2 + (-38.375)^2 + (-28.375)^2 + (-20.375)^2 + (3.625)^2 + (17.625)^2 + (57.625)^2 + (90.625)^2) / (8-1) = 6976.75
The standard deviation is the square root of the variance:
sqrt(6976.75) = 83.538
Step 5: Divide the product of the differences (from step 3) by the product of the standard deviations (from step 4).
35223.15625 / (50.247 * 83.538) = 0.838925
Step 6: Round the result to the nearest thousandth.
The correlation coefficient is approximately 0.839.
Therefore, the answer to the question is not available among the given options.