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How Do You Find the Absolute Median Deviation?

Published in Statistical Dispersion 2 mins read

The absolute median deviation, a robust measure of statistical dispersion, is found through a series of steps involving the median and absolute differences. Here's a breakdown of the process, incorporating the information from the provided reference:

Steps to Calculate Absolute Median Deviation

  1. Find the Median: First, order your data set from smallest to largest. The median is the middle value. If you have an even number of data points, average the two middle values to find the median.
  2. Subtract the Median: Next, subtract the calculated median from each value in your original data set. This gives you the deviations of each data point from the center.
  3. Take Absolute Values: Take the absolute value of each deviation you calculated in the previous step. The absolute value ensures that all deviations are positive, regardless of whether the original data points are above or below the median.
  4. Sum the Absolute Differences: Add all the absolute deviations together.
  5. Divide by Number of Data Points: Finally, divide the total sum of absolute deviations by the total number of data points in your original set. This gives you the absolute median deviation.

Example

Let's say you have the following data set: [4, 6, 2, 8, 5].

  1. Order: [2, 4, 5, 6, 8]
  2. Median: The median is 5 (the middle number).
  3. Subtract Median: [2-5, 4-5, 5-5, 6-5, 8-5] which results in [-3, -1, 0, 1, 3].
  4. Absolute Values: [|-3|, |-1|, |0|, |1|, |3|] which results in [3, 1, 0, 1, 3].
  5. Sum Absolute Differences: 3 + 1 + 0 + 1 + 3 = 8
  6. Divide by Data Points: 8 / 5 = 1.6.

Therefore, the absolute median deviation for this dataset is 1.6.

Practical Insights

  • The absolute median deviation is less sensitive to outliers than the standard deviation, making it a useful measure when dealing with data that may contain extreme values.
  • It provides a measure of the typical distance of data points from the median.

Summary

Step Description
1. Find Median Order the data and find the middle value.
2. Subtract Median Subtract median from each value.
3. Absolute Values Take the absolute value of each difference.
4. Sum Absolute Differences Sum up all absolute differences.
5. Divide by Data Points Divide the sum by the number of data points.

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