Analysis of four different samples of an alloy yielded 12.12, 12.14, 12.10 and 12.22% of metal. The mean deviation of the result is :
0.0375
Mean deviation is the average of the absolute deviations from the mean, so the calculation has three steps.
Step 1 — find the mean. \(\bar{x} = \frac{12.12 + 12.14 + 12.10 + 12.22}{4} = \frac{48.58}{4} = 12.145\)%.
Step 2 — take the absolute deviation of each reading.
\(|12.12 - 12.145| = 0.025\); \(|12.14 - 12.145| = 0.005\); \(|12.10 - 12.145| = 0.045\); \(|12.22 - 12.145| = 0.075\).
Step 3 — average those deviations. \(\text{mean deviation} = \frac{0.025 + 0.005 + 0.045 + 0.075}{4} = \frac{0.150}{4} = 0.0375\).
Two checks are worth making. The answer must be positive, because absolute values are used — a negative figure could only arise from forgetting the modulus, and the signed deviations always sum to zero. And it must be smaller than the largest single deviation (0.075), since it is an average of values including much smaller ones.
The value 0.1500 is the sum of the deviations rather than their mean, so it is the result of omitting the final division by four.
Hence the mean deviation is 0.0375.
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