The relative average, also known as the average absolute deviation relative to the mean, is calculated by following a few steps based on the data's average deviation. Here's how to find it:
Steps to Calculate the Relative Average
Here's a breakdown of how to compute the relative average using the provided references:
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Calculate the Mean (Average): First, find the mean (ˉx) of your data set using all the high-quality data points. The mean is the sum of all data points divided by the number of data points.
- Example: If your high-quality data is [2, 4, 6, 8], the mean is (2 + 4 + 6 + 8) / 4 = 5.
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Calculate the Deviations: For each individual data point (xi), calculate the absolute deviation (d) from the mean (ˉx). This is done by subtracting the mean from each data point and taking the absolute value: d = |xi - ˉx|.
- Example: Using the data above and the mean of 5, the deviations would be:
- |2 - 5| = 3
- |4 - 5| = 1
- |6 - 5| = 1
- |8 - 5| = 3
- Example: Using the data above and the mean of 5, the deviations would be:
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Calculate the Average Deviation: Find the average of these deviations. Add up all the deviations, and divide by the total number of data points.
- Example: Using the deviations we calculated above, the average deviation is (3 + 1 + 1 + 3)/4 = 2.
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Calculate the Relative Average: Divide the average deviation by the mean of your original data. The result is the relative average.
- Example: Using our mean of 5 and the average deviation of 2, the relative average is 2 / 5 = 0.4 or 40%.
Summary
Here's a summary in a table format for easier reference:
| Step | Description | Formula |
|---|---|---|
| 1. Calculate the Mean | Find the average of your data set. | ˉx = (Σxi) / n |
| 2. Calculate the Deviations | Find how far each data point is from the mean. | d = |
| 3. Calculate Average Deviation | Find the average of the calculated deviations from step 2. | average d = (Σd) / n |
| 4. Calculate the Relative Average | Divide the average deviation by the mean to get the relative average. | (Average d) / ˉx |
In essence, the relative average tells you how much, on average, the individual data points deviate from the mean, expressed as a proportion of the mean itself.
