Question

Find the main absolute deviation of the following dataset.

{ 21, 25, 25, 26, 26, 27, 28, 30}
The mean absolute deviation is_____

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the mean absolute deviation, we first need to calculate the mean of the dataset.

Mean = (21 + 25 + 25 + 26 + 26 + 27 + 28 + 30) / 8 = 26.5

Next, we calculate the absolute deviations of each data point from the mean:
|21 - 26.5| = 5.5
|25 - 26.5| = 1.5
|25 - 26.5| = 1.5
|26 - 26.5| = 0.5
|26 - 26.5| = 0.5
|27 - 26.5| = 0.5
|28 - 26.5| = 1.5
|30 - 26.5| = 3.5

Now, we calculate the sum of the absolute deviations:
5.5 + 1.5 + 1.5 + 0.5 + 0.5 + 0.5 + 1.5 + 3.5 = 14

To find the mean absolute deviation, we divide the sum of the absolute deviations by the number of data points:
Mean Absolute Deviation = 14 / 8 = 1.75

Therefore, the mean absolute deviation of the dataset { 21, 25, 25, 26, 26, 27, 28, 30} is 1.75.