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), we first need to calculate the mean of the dataset.
Mean = (4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4) / 6
= 35.3 / 6
= 5.88 (rounded to the nearest hundredth)
Next, we find the deviations of each data point from the mean and take their absolute values:
|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
Now, we calculate the mean of these deviations:
MAD = (1.08 + 0.02 + 0.32 + 4.92 + 4.68 + 0.52) / 6
= 11.54 / 6
= 1.923 (rounded to the nearest thousandth)
Therefore, the mean absolute deviation of the dataset is approximately 1.9.
Thank ku
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To find the mean absolute deviation, follow these steps:
Step 1: Calculate the mean of the dataset.
- Add all the numbers in the dataset: 4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4 = 35.3
- Divide the sum by the number of data points: 35.3 / 6 = 5.88
Step 2: Calculate the absolute deviation for each data point.
- Subtract the mean from each data point and take 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 mean of the absolute deviations.
- Add all the absolute deviations: 1.08 + 0.02 + 0.32 + 4.92 + 4.68 + 0.52 = 11.54
- Divide the sum by the number of data points: 11.54 / 6 ≈ 1.92
Therefore, the mean absolute deviation of the dataset is approximately 1.92.