Answer :
A. The range is 88.8 - 64.3 = 24.5 (rounded to 1 decimal place).
B. The sample mean is calculated by adding up all the values in the sample and dividing by the number of values in the sample. In this case, the sample mean is (78.5 + 88.8 + 76.2 + 73.0 + 79.5 + 66.9 + 72.4 + 86.6 + 67.6 + 73.5 + 72.6 + 72.6 + 80.0 + 69.1 + 79.1 + 73.9 + 72.3 + 83.3 + 64.3 + 69.1)/20 = 74.97 (rounded to 2 decimal places).
How do we determine the sample variance?
C. To calculate the sample variance, subtract the mean from each value, square the difference, add up the squared differences, and divide by the number of values in the sample minus 1. In this case, the sample variance is
[(78.5 - 74.97)^2 + (88.8 - 74.97)^2 + (76.2 - 74.97)^2 + (73.0 - 74.97)^2 + (79.5 - 74.97)^2 + (66.9 - 74.97)^2 + (72.4 - 74.97)^2 + (86.6 - 74.97)^2 + (67.6 - 74.97)^2 + (73.5 - 74.97)^2 + (72.6 - 74.97)^2 + (72.6 - 74.97)^2 + (80.0 - 74.97)^2 + (69.1 - 74.97)^2 + (79.1 - 74.97)^2 + (73.9 - 74.97)^2 + (72.3 - 74.97)^2 + (83.3 - 74.97)^2 + (64.3 - 74.97)^2 + (69.1 - 74.97)^2]/(20-1) = 42.5 (rounded to 2 decimal places).
The sample standard deviation is the square root of the sample variance. In this case, the sample standard deviation is sqrt(42.5) = 6.52 (rounded to 2 decimal places).
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