Find the mean absolute deviation of the following dataset. Round your answer to the nearest tenth.
204, 211, 216, 300, 426, 567, 680
First, let's find the mean of the dataset:
(204 + 211 + 216 + 300 + 426 + 567 + 680) / 7 = 319.3
Next, we find the absolute deviations from the mean for each data point:
|204 - 319.3| = 115.3
|211 - 319.3| = 108.3
|216 - 319.3| = 103.3
|300 - 319.3| = 19.3
|426 - 319.3| = 106.7
|567 - 319.3| = 247.7
|680 - 319.3| = 360.7
Now, find the mean of these absolute deviations:
(115.3 + 108.3 + 103.3 + 19.3 + 106.7 + 247.7 + 360.7) / 7 ≈ 152.0
Therefore, the mean absolute deviation of the dataset is 152.0.
wrong
I apologize for the mistake. Let's recalculate the mean absolute deviation of the dataset.
First, let's find the mean of the dataset:
(204 + 211 + 216 + 300 + 426 + 567 + 680) / 7 = 323.71
Next, we find the absolute deviations from the mean for each data point:
|204 - 323.71| = 119.71
|211 - 323.71| = 112.71
|216 - 323.71| = 107.71
|300 - 323.71| = 23.71
|426 - 323.71| = 102.29
|567 - 323.71| = 243.29
|680 - 323.71| = 356.29
Now, find the mean of these absolute deviations:
(119.71 + 112.71 + 107.71 + 23.71 + 102.29 + 243.29 + 356.29) / 7 ≈ 157.9
Therefore, the mean absolute deviation of the dataset is 157.9.