# Mean Absolute Percentage Error

I am trying to work on some Excel exercises I found to prepare for an upcoming course and I stumbled upon some questions and terms that I am not familiar with. Anyone know how to do these questions? I don't know what MAPE means or what "forecasting" is.. Not familiar with the strange formulas in this question either...Hopefully someone knows something about this.

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## 1 Answer

Suppose that you weigh $9$ people, using a not very good scale S.

Let $w_1,w_2,\dots,w_9$ be the actual weights of the people, say measured using a high precision scale, and let $m_1,m_2,\dots,m_9$ be their measured weights using our low quality scale.

Then the mean absolute percentage error (MAPE) made by scale S is $$\frac{1}{9}\left(\frac{|w_1-m_1|}{w_1}+\cdots+\frac{|w_9-m_9|}{w_9}\right).$$ Note that in general $|x|$, the absolute value of $x$, measures the magnitude of $x$. Formally, it is defined by $|x|=x$ if $x\ge 0$, and $|x|=-x$ if $x\lt 0$. For example, $|4|=4$ and $|-4.7|=4.7$.

So $|w_1-m_1|$ measures the "error" made in weighing the first person. And $\dfrac{|w_1-m_1}{w_1}$ measures the relative error made in weighing. Often, we are more interested in relative error than in error, since an error of $5$ pounds in the weight of a $300$ pound person is not very important, while a $5$ pound error in the weight of a year-old child might be. For the MAPE, we find the average relative error.

The MAPE is often expressed as a percentage, that is, $0.057$ would be reported as $5.7\%$.

Suppose we are making predictions (forecasts) about monthly sales, January to September. Then the $w_i$ would be the actual sales. The $m_i$ would be the predicted sales. Then the MAPE is a measure of by what fraction our monthly forecasts were off, on average.

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oh man I love you! Thank you for explaining it so well to me and taking the time to do it so fast too! – Raynos Nov 20 '12 at 5:12