Question
Calculate the mean $\%$ error in five observation
$80.0,80.5,81.0,81.5,82$
✓
Answer
The mean percentage error can be calculated as,
$M P E=\frac{1}{n} \sum\left(\frac{x-\bar{x}}{x}\right) \times 100 \%$ $...(1)$
The mean value of the errors is calculated as,
Mean of the errors $=\frac{80+80.5+81+81.5+82}{5}$
$=81$
| $x$ | $x-\bar{x}$ | $\frac{x-\bar{x}}{x}$ |
| $80.0$ | $1.0$ | $0.0125$ |
| $80.5$ | $0.5$ | $0.0062$ |
| $81.0$ | $0$ | $0$ |
| $81.5$ | $0.5$ | $0.0061$ |
| $82.0$ | $1.0$ | $0.122$ |
| Sum$=0.037$ |
Substituting the values in equation $(1),$ we get
$M P E=\frac{1}{5} \times(0.037) \times 100 \%$
$=0.74 \%$
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