What is the mean absolute deviation of the following dataset: 4.8, 5.9, 6.2, 10.8, 1.2, 6.4? Round your answer to the nearest tenth.
First, we need to calculate the mean of the dataset:
Mean = (4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4) / 6
Mean = 34.3 / 6
Mean = 5.72
Next, we calculate the absolute deviation for each data point:
|4.8 - 5.72| = 0.92
|5.9 - 5.72| = 0.18
|6.2 - 5.72| = 0.48
|10.8 - 5.72| = 5.08
|1.2 - 5.72| = 4.52
|6.4 - 5.72| = 0.68
Now, we calculate the mean absolute deviation:
Mean Absolute Deviation = (0.92 + 0.18 + 0.48 + 5.08 + 4.52 + 0.68) / 6
Mean Absolute Deviation = 11.86 / 6
Mean Absolute Deviation ≈ 1.98
Therefore, the mean absolute deviation of the dataset is approximately 1.98.