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

Mean Deviation about the Mean — Continuous (Grouped) Data

When the data is grouped into class intervals, the mean deviation about the mean is computed exactly the same way as for a discrete frequency distribution, with one adjustment already familiar from computing the mean itself: every observation inside a class is treated as though it were located at that class's class mark (midpoint), $x_i = \dfrac{\text{lower limit}+\text{upper limit}}{2}$ .

Note

Mean Deviation about the Mean — Continuous/Grouped Data

$\text{MD}(\bar{x}) = \dfrac{\sum f_i\,|x_i - \bar{x}|}{N}, \qquad N=\sum f_i$

where $x_i$ is the class mark of the $i$ -th class and $\bar{x}$ is the mean of the grouped distribution (found first, by the direct/assumed-mean/step-deviation method, exactly as in the measures-of-central-tendency chapter).

The procedure is therefore: (1) find each class mark, (2) find the mean $\bar{x}$ of the whole distribution, (3) find the absolute deviation of each class mark from $\bar{x}$ , (4) multiply each absolute deviation by its class's frequency, (5) total the $f|x-\bar{x}|$ column, and (6) divide by $N$ . Worked Example 3 below carries out all six steps on one grouped table in full. …

Definition 1Class Mark (recap)

The midpoint of a class interval, (lower limit + upper limit)/2, used to represent every observation inside that class …

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