Find the main absolute deviation of the following data set round your answer to the nearest tenth 204, 211, 216, 300, 426, 567, 680
To find the main absolute deviation of a data set, we need to find the absolute value of the difference between each data point and the mean of the data set, then take the average of these absolute differences.
First, we need to find the mean of the data set:
(204 + 211 + 216 + 300 + 426 + 567 + 680) / 7 = 349.6
Next, we find the absolute value of the difference between each data point and the mean:
|204 - 349.6| = 145.6
|211 - 349.6| = 138.6
|216 - 349.6| = 133.6
|300 - 349.6| = 49.6
|426 - 349.6| = 76.4
|567 - 349.6| = 217.4
|680 - 349.6| = 330.4
Now, we find the average of these absolute differences:
(145.6 + 138.6 + 133.6 + 49.6 + 76.4 + 217.4 + 330.4) / 7 ≈ 169.6
Rounded to the nearest tenth, the main absolute deviation of the data set is 169.6.