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
To find the mean absolute deviation, we need to find the mean of the dataset first.
Mean = (4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4) / 6 = 35.3 / 6 = 5.9
Next, we need to find the absolute deviation for each data point. Absolute deviation is the absolute value of the difference between each data point and the mean.
Absolute Deviation for 4.8 = |4.8 - 5.9| = 1.1
Absolute Deviation for 5.9 = |5.9 - 5.9| = 0
Absolute Deviation for 6.2 = |6.2 - 5.9| = 0.3
Absolute Deviation for 10.8 = |10.8 - 5.9| = 4.9
Absolute Deviation for 1.2 = |1.2 - 5.9| = 4.7
Absolute Deviation for 6.4 = |6.4 - 5.9| = 0.5
Now, we find the mean of the absolute deviations.
Mean Absolute Deviation = (1.1 + 0 + 0.3 + 4.9 + 4.7 + 0.5) / 6 = 11.5 / 6 ≈ 1.9
Therefore, the mean absolute deviation of the dataset is approximately 1.9.
To find the mean absolute deviation (MAD), follow these steps:
Step 1: Calculate the mean (average) of the dataset.
Add up all the values and divide the sum by the number of values in the dataset.
4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4 = 35.300000000000004
35.300000000000004 ÷ 6 = 5.883333333333333
The mean of the dataset is approximately 5.9 (rounded to the nearest tenth).
Step 2: Find the absolute deviation for each data point.
Subtract the mean from each data point and ignore the sign.
|4.8 - 5.9| = 1.1
|5.9 - 5.9| = 0
|6.2 - 5.9| = 0.3
|10.8 - 5.9| = 4.9
|1.2 - 5.9| = 4.7
|6.4 - 5.9| = 0.5
Step 3: Calculate the mean of the absolute deviations.
Add up all the absolute deviations and divide the sum by the number of values in the dataset.
1.1 + 0 + 0.3 + 4.9 + 4.7 + 0.5 = 11.5
11.5 ÷ 6 = 1.9166666666666667
The mean absolute deviation (MAD) for this dataset is approximately 1.9 (rounded to the nearest tenth).