Find the mean absolute deviation of the following dataset: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2. Round the answer to the nearest tenth. (1 point)
• 1.7
• 9.3
• 11.8
• 7.0
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
1. Find the mean of the dataset:
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7
Mean = 65.1 / 7
Mean = 9.3
2. Find the absolute deviation for each data point by subtracting the mean from each data point:
|8.4 - 9.3| = 0.9
|9.4 - 9.3| = 0.1
|14.2 - 9.3| = 4.9
|5.6 - 9.3| = 3.7
|8.3 - 9.3| = 1.0
|9.0 - 9.3| = 0.3
|10.2 - 9.3| = 0.9
3. Find the average of these absolute deviations to get the MAD:
MAD = (0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9) / 7
MAD = 10.8 / 7
MAD ≈ 1.5
Therefore, the mean absolute deviation of the given dataset is approximately 1.5. Since none of the answer choices are close to 1.5, it seems like there might have been a calculation error.