What is the mean absolute deviation of the following dataset: 4.8, 5.9, 6.2, 10.8, 1.2, 6.4?
To calculate the mean absolute deviation (MAD), follow these steps:
1. Find the mean of the dataset:
(4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4) / 6 = 35.3 / 6 = 5.88
2. Find the absolute deviation of each data point from the mean:
|4.8 - 5.88| = 1.08
|5.9 - 5.88| = 0.02
|6.2 - 5.88| = 0.32
|10.8 - 5.88| = 4.92
|1.2 - 5.88| = 4.68
|6.4 - 5.88| = 0.52
3. Find the mean of the absolute deviations:
(1.08 + 0.02 + 0.32 + 4.92 + 4.68 + 0.52) / 6 = 11.54 / 6 = 1.923
Therefore, the mean absolute deviation of the dataset is 1.923.