What is the mean absolute deviation of the following dataset: 4.8, 5.9, 6.2, 10.8, 1.2, 6.4? Round the answer to the nearest tenth. (1 point)
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
Step 1: Find the mean (average) of the dataset.
The mean is found by adding up all the numbers in the dataset and dividing by the total number of values.
4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4 = 35.3 (sum of all values)
35.3 / 6 = 5.88 (mean)
The mean is approximately 5.88.
Step 2: Find the absolute deviation for each value by subtracting the mean from each value and taking the absolute value.
|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
Step 3: Find the average of these absolute deviations.
(1.08 + 0.02 + 0.32 + 4.92 + 4.68 + 0.52) / 6 = 1.33
The mean absolute deviation (MAD) is approximately 1.33 when rounded to the nearest tenth.