Question

The error in two readings of A are $0.01$ and $-0.03$, then mean absolute error is?

Answer 1

Step 1: Given data

The two errors in the readings of A are $∆x_1=0.01$ and $∆x_2=-0.03$.

Step 2: Formula used

The absolute error is calculated by the subtraction of the actual value and the measured value of a quantity.

If the actual value is ${\mathrm{x}}_{₀}$ and the measured value is $\mathrm{x}$, the absolute error is expressed as $∆\mathrm{x}={\mathrm{x}}_{₀}-\mathrm{x}$, where $∆\mathrm{x}$ is the absolute error.

The mean absolute error(MAE) is the mean or average of all absolute errors, $\mathrm{MAE}=\frac{1}{n}\sum _{i=1}^n \left|∆x_{\mathit{i}}\right|$
where $n$ is the number of observations.

Step 3: Calculate Mean absolute error

Here, number of observations are two, so $n=2$.

The mean absolute error (MAE) is,

$\begin{array}{rcl}\mathrm{MAE}& =& \frac{1}{2}\left[\left|∆x_1\right|+\left|∆x_2\right|\right]\\ & =& \frac{1}{2}\left[\left|0.01\right|+\left|-0.03\right|\right]\\ & =& \frac{1}{2}\left|0.04\right|\\ & =& 0.02\end{array}$

Therefore, the mean absolute error of A is $0.02$.