Determine the mean absolute deviation of the following dataset. Round your answer to the nearest tenth.
{134,138,150,155,158,165}
Responses
11.2
11.2
150
150
56
56
9.3
The mean absolute deviation is calculated by finding the mean, then subtracting each individual data point from the mean, taking the absolute value of each difference, and then finding the average of those absolute differences.
First, find the mean of the dataset:
(134 + 138 + 150 + 155 + 158 + 165) / 6 = 900 / 6 = 150
Next, calculate the absolute differences from the mean for each data point:
|134-150| = 16
|138-150| = 12
|150-150| = 0
|155-150| = 5
|158-150| = 8
|165-150| = 15
Now, find the average of these absolute differences:
(16 + 12 + 0 + 5 + 8 + 15) / 6 = 56 / 6 = 9.3
Therefore, the mean absolute deviation of the dataset {134,138,150,155,158,165} is 9.3.