a. To calculate the range, subtract the smallest value from the largest value in the population data:
Range = Largest value - Smallest value
= 40 - 12
= 28
b. To calculate the MAD (Mean Absolute Deviation), first find the mean of the population data:
Mean = (38 + 40 + 15 + 12 + 24) / 5
= 17.8 (rounded to 1 decimal place)
Next, calculate the absolute deviation of each value from the mean:
|38 - 17.8| = 20.2
|40 - 17.8| = 22.2
|15 - 17.8| = 2.8
|12 - 17.8| = 5.8
|24 - 17.8| = 6.2
Now, find the average of these absolute deviations:
MAD = (20.2 + 22.2 + 2.8 + 5.8 + 6.2) / 5
= 11.24 (rounded to 2 decimal places)
c. To calculate the population variance, first find the mean of the population data (as done in part b). Then, subtract the mean from each value, square the result, and find the average of these squared differences:
(38 - 17.8)^2 = 328.84
(40 - 17.8)^2 = 487.84
(15 - 17.8)^2 = 7.84
(12 - 17.8)^2 = 34.84
(24 - 17.8)^2 = 38.44
Population Variance = (328.84 + 487.84 + 7.84 + 34.84 + 38.44) / 5
= 179.08 (rounded to 2 decimal places)
d. To calculate the population standard deviation, take the square root of the variance calculated in part c:
Population Standard Deviation = √(179.08)
= 13.38 (rounded to 2 decimal places)
Consider the following population data:
38 40 15 12 24
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 population variance. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
d. Calculate the population standard deviation. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
1 answer
1 answer