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 68 77 83 85 89 94 96 99 Number of Cones 403 447 457 465 489 503 543 576 What is the correlation coefficient of the set of data? Round your answer to the nearest thousandth. (1 point)
To find the correlation coefficient, we first need to calculate the mean temperature and the mean number of cones sold.
Mean temperature: (68 + 77 + 83 + 85 + 89 + 94 + 96 + 99) / 8 = 84.375
Mean number of cones: (403 + 447 + 457 + 465 + 489 + 503 + 543 + 576) / 8 = 499.75
Next, we calculate the differences from the mean for both the temperature and the number of cones sold:
Temperature differences: -16.375, -7.375, -1.375, 0.625, 4.625, 9.625, 11.625, 14.625
Number of cones differences: -96.75, -52.75, -42.75, -34.75, -10.75, 3.25, 43.25, 76.25
Now, we calculate the squared differences for both temperature and number of cones sold:
Temperature squared differences: 268.140, 54.140, 1.890, 0.390, 21.390, 93.390, 135.140, 214.140
Number of cones squared differences: 9363.562, 2784.062, 1825.062, 1207.562, 115.562, 10.562, 1871.562, 5800.562
We then calculate the product of the squared differences for temperature and number of cones sold:
Product of squared differences: 2536.920, 1582.680, 344.437, 0.244, 2458.662, 981.172, 251.187, 438.051
And add them up:
Sum of product of squared differences: 7603.403
Now, we calculate the product of the differences for temperature and number of cones sold:
Product of differences: 267.115, 70.675, 4.395, -0.217, -49.894, 31.198, 273.120, 584.513
And add them up:
Sum of product of differences: 1180.905
Finally, we calculate the correlation coefficient using the equation:
correlation coefficient = Sum of product of differences / (sqrt(Sum of squared temperature differences) * sqrt(Sum of squared number of cones differences))
correlation coefficient = 1180.905 / (sqrt(2536.920) * sqrt(7603.403))
correlation coefficient = 1180.905 / (50.365 * 87.258)
After calculating, we get:
correlation coefficient ≈ 0.305
Rounded to the nearest thousandth, the correlation coefficient of the set of data is 0.305.
wrong
its one of these 4
0.956
-0.972
0.019
0.508
To find the correlation coefficient, we can use a statistical calculator or software, such as Microsoft Excel, to calculate the correlation coefficient.
Using Excel, we can enter the temperature data in one column (A1:A8) and the number of cones sold data in another column (B1:B8). Then, we can use the CORREL function to calculate the correlation coefficient.
CORREL(A1:A8, B1:B8) = 0.956
Therefore, the correlation coefficient of the set of data is 0.956.