a. The range is calculated by subtracting the smallest value from the largest value:
Range = 51 - 8 = 43
b. To calculate the MAD (Mean Absolute Deviation), we first need to find the mean of the data. The mean is calculated by summing all the values and dividing by the number of values:
Mean = (27 + 51 + 8 + 19 + 13) / 5 = 23.6
Next, we find the absolute deviation of each data point by subtracting the mean from each data point:
|27 - 23.6| = 3.4
|51 - 23.6| = 27.4
|8 - 23.6| = 15.6
|19 - 23.6| = 4.6
|13 - 23.6| = 10.6
Then, we calculate the sum of the absolute deviations:
Sum of Absolute Deviations = 3.4 + 27.4 + 15.6 + 4.6 + 10.6 = 61.6
Finally, we divide the sum of absolute deviations by the number of values to find the MAD:
MAD = 61.6 / 5 = 12.32
c. To calculate the population variance, we need to find the squared deviations from the mean for each data point. Then, we calculate the mean of these squared deviations:
(27 - 23.6)^2 = 13.44
(51 - 23.6)^2 = 755.84
(8 - 23.6)^2 = 239.36
(19 - 23.6)^2 = 21.16
(13 - 23.6)^2 = 112.36
Sum of Squared Deviations = 13.44 + 755.84 + 239.36 + 21.16 + 112.36 = 1142.16
Population Variance = Sum of Squared Deviations / Number of Values = 1142.16 / 5 = 228.43
d. The population standard deviation is the square root of the population variance:
Population Standard Deviation = √(228.43) ≈ 15.10
Consider the following population data:
27 51 8 19 13
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