Understanding Mean Absolute Percentage Error Visually

Welcome to understanding MAPE - Mean Absolute Percentage Error!MAPE is a statistical measure that helps us understand how accurate our predictions are by expressing the error as a percentage.Let's break down what each part of this formula means.MAPE consists of three main components that work together to give us our final percentage.Let's look at some simple examples to understand how MAPE is calculated.In our first example, when the actual value is 100 and we predict 90, our percentage error is 10 percent.For our second example, an actual value of 50 with a prediction of 55 gives us a 10 percent error as well, even though the absolute difference is smaller.And in our third example, with an actual value of 200 and a prediction of 180, we again get a 10 percent error, showing how MAPE normalizes errors across different scales.Now, let's look at some key characteristics that make MAPE useful for measuring prediction accuracy.Now that we understand what MAPE is, let's explore how to visualize these percentage errors.To understand how percentage error is calculated, we first need to visualize the differences between actual and predicted values.Let's plot our actual values in blue. These represent the true values we're trying to predict.We can connect these points to see the trend of actual values over time.Now, let's add our predicted values in red. Notice how they differ from the actual values.Similarly, we can connect our predicted values to see the predicted trend.The absolute error at each point is shown by the vertical distance between the actual and predicted values.Let's look more closely at point three as an example. The vertical line represents the absolute difference between the actual and predicted values.Notice how the size of these errors varies across different points. Some predictions are closer to the actual values than others.These absolute differences will be used to calculate percentage errors in our next step.Now that we understand absolute differences, let's see how they convert to percentages.Consider two scenarios with the same absolute error of 10 units, but very different scales.The formula for percentage error divides the absolute difference by the actual value and multiplies by one hundred.When we visualize these percentages, we can see how the same absolute error leads to different percentage errors.Let's look at how percentage errors can become extreme with small actual values.When we visualize these percentage errors, we can see how small actual values can lead to much larger percentage errors.These examples highlight important considerations when working with percentage errors.Now that we have our individual percentage errors, let's calculate their mean to find the MAPE.We'll add each percentage error one by one and calculate the running average.Now that we understand how to calculate MAPE, let's look at how to interpret these values.MAPE values can be categorized into different quality levels based on their percentage ranges.Let's look at some real-world examples across different industries.However, MAPE has an important limitation when dealing with values close to zero.Notice how the same absolute error of 10 results in very different MAPE values depending on the actual value's scale.Despite this limitation, MAPE is particularly useful for comparing different forecasting methods.When comparing methods, the one with the lowest MAPE generally indicates the most accurate forecasting approach.Remember to consider both the MAPE value and the context when interpreting forecast accuracy.