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Business Mathematics and Basic Statistics · Ch 7 — Measures of Dispersion

Mean Deviation about the Median — Discrete Data

3

Mean Deviation about the Median — Discrete Data

The mean deviation can equally be measured about the median instead of the mean — averaging the absolute distances of every observation from the middle value of the data set rather than from its arithmetic average. For a data set that contains extreme values (a few very large or very small observations), the median-based measure is often preferred, because the median itself is far less affected by such extremes than the mean is.

Note

Mean Deviation about the Median — Individual Observations

For nn individual observations with median MM,

MD(M)=∑∣xi−M∣n\text{MD}(M) = \dfrac{\sum |x_i - M|}{n}

For a discrete frequency distribution, the median MM is first located using the cumulative frequency method (exactly as in the measures-of-central-tendency chapter), and then every deviation is weighted by its frequency:

Note

Mean Deviation about the Median — Discrete Frequency Distribution

MD(M)=∑f ∣x−M∣N\text{MD}(M) = \dfrac{\sum f\,|x-M|}{N} …

Definition 1Mean Deviation about the Median

The average of the absolute deviations of every observation from the median MM; MD(M)=∑∣x−M∣/n\text{MD}(M)=\sum|x-M|/n for individual data, or ∑f∣x−M∣/N\sum f|x-M|/N fo …

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