Discussion
The mean deviation about the mean for the following data
| x | : | 2 | 4 | 6 | 10 |
| f | : | 7 | 4 | 5 | 4 |
Answer: B
The mean deviation about the mean is 2.5.
\[ \begin{aligned} N &= 7 + 4 + 5 + 4 = 20 \\ \bar{x} &= \frac{14 + 16 + 30 + 40}{20} = 5 \\ \sum f|x - \bar{x}| &= 7(3) + 4(1) + 5(1) + 4(5) = 50 \end{aligned} \]
So MD = \(\frac{50}{20} = 2.5\). Dividing by the 4 distinct values instead of N, or measuring deviations from a wrong mean, gives the other options.
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