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How to Find Mean Deviation About Median?

Published in Statistics 3 mins read

The mean deviation about the median quantifies the average absolute difference between each data point and the median of the dataset. Here's how to calculate it:

Steps to Calculate Mean Deviation About Median

  1. Find the Median: Determine the median of the given data set.

    • For ungrouped data: Arrange the data in ascending order.

      • If the number of data points (n) is odd, the median is the middle value, i.e., the (n+1)/2 th value.
      • If the number of data points (n) is even, the median is the average of the two middle values, i.e., the average of the n/2 th and (n/2 + 1) th values.

    • For grouped data: Use the formula:

      Median = l + [ (N/2 - cf)/f ] * h

      Where:

      • l = lower limit of the median class
      • N = total frequency
      • cf = cumulative frequency of the class preceding the median class
      • f = frequency of the median class
      • h = class size

  2. Calculate Absolute Deviations: Subtract the median from each data value and take the absolute value of each difference. This ensures all deviations are positive. Represent the data values as xi and the median as M. The absolute deviation for each data point is |xi - M|.

  3. Sum the Absolute Deviations: Add all the absolute deviations calculated in the previous step. Mathematically, this is represented as ∑ |xi - M|.

  4. Calculate the Mean Deviation: Divide the sum of the absolute deviations by the total number of data points (n). This gives you the mean deviation about the median. The formula is:

    Mean Deviation about Median = (∑ |xi - M|) / n

Example

Let's say we have the following data set: 4, 6, 8, 10, 12

  1. Median: The median is 8, as it's the middle value when the data is arranged in ascending order.

  2. Absolute Deviations:

    • |4 - 8| = 4
    • |6 - 8| = 2
    • |8 - 8| = 0
    • |10 - 8| = 2
    • |12 - 8| = 4

  3. Sum of Absolute Deviations: 4 + 2 + 0 + 2 + 4 = 12

  4. Mean Deviation: 12 / 5 = 2.4

Therefore, the mean deviation about the median for this data set is 2.4.

Key Considerations

  • The mean deviation about the median provides a measure of the spread or dispersion of data around the central value (median).
  • It uses absolute values to avoid the canceling out of positive and negative deviations, providing a more accurate representation of variability.

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