Mean Absolute Deviation Practice
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Question
Find the mean absolute deviation of the following dataset.
{21,25,25,26,26,27,28,30} (1 point)
The mean absolute deviation is
.
2.5.
To find the mean absolute deviation, first find the mean of the dataset:
(21 + 25 + 25 + 26 + 26 + 27 + 28 + 30) / 8 = 27
Next, find the absolute difference between each data point and the mean:
|21 - 27| = 6
|25 - 27| = 2
|25 - 27| = 2
|26 - 27| = 1
|26 - 27| = 1
|27 - 27| = 0
|28 - 27| = 1
|30 - 27| = 3
Now, find the mean of these absolute differences:
(6 + 2 + 2 + 1 + 1 + 0 + 1 + 3) / 8 = 2.5
Therefore, the mean absolute deviation of the dataset is 2.5.
wrong
I apologize for the error. Let's correct the calculation:
To find the mean absolute deviation, we first need to find the mean of the dataset:
(21 + 25 + 25 + 26 + 26 + 27 + 28 + 30) / 8 = 212 / 8 = 26.5
Next, find the absolute difference between each data point and 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, find the mean of these absolute differences:
(5.5 + 1.5 + 1.5 + 0.5 + 0.5 + 0.5 + 1.5 + 3.5) / 8 = 14.5 / 8 = 1.8125
Therefore, the mean absolute deviation of the dataset is 1.8125.