a. The range is calculated by subtracting the minimum value from the maximum value. In this case, the minimum value is 31 and the maximum value is 50. Therefore, the range is 50 - 31 = 19.
b. To calculate the mean absolute deviation (MAD), first we need to find the mean of the data set.
Mean = (39 + 41 + 31 + 50 + 37 + 40) / 6 = 238 / 6 = 39.67
Next, we find the absolute difference between each data point and the mean:
|39 - 39.67| = 0.67
|41 - 39.67| = 1.33
|31 - 39.67| = 8.67
|50 - 39.67| = 10.33
|37 - 39.67| = 2.67
|40 - 39.67| = 0.33
The sum of these absolute differences is 24.
MAD = 24 / 6 = 4
c. To calculate the sample variance, we first need to find the squared difference between each data point and the mean:
(39 - 39.67)^2 = 0.4489
(41 - 39.67)^2 = 1.7689
(31 - 39.67)^2 = 74.5089
(50 - 39.67)^2 = 109.3489
(37 - 39.67)^2 = 7.1689
(40 - 39.67)^2 = 0.1089
The sum of these squared differences is 193.3464.
Sample variance = 193.3464 / (6 - 1) = 38.66928
d. The sample standard deviation is the square root of the sample variance:
Sample standard deviation = √38.66928 = 6.22
Consider the following sample data:
39 41 31 50 37 40
a. Calculate the range.
b. Calculate MAD. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
c. Calculate the sample variance. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
d. Calculate the sample standard deviation. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
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