*27*

The **mean absolute percentage error (MAPE) **is commonly used to measure the predictive accuracy of models. It is calculated as:

**MAPE** = (1/n) * Σ(|actual – prediction| / |actual|) * 100

where:

**Σ**– a symbol that means “sum”**n**– sample size**actual**– the actual data value**prediction**– the predicted data value

MAPE is commonly used because it’s easy to interpret and easy to explain. For example, a MAPE value of 11.5% means that the average difference between the predicted value and the actual value is 11.5%.

The lower the value for MAPE, the better a model is able to predict values. For example, a model with a MAPE of 5% is more accurate than a model with a MAPE of 10%.

**How to Calculate MAPE in Python**

There is no built-in Python function to calculate MAPE, but we can create a simple function to do so:

import numpy as np def mape(actual, pred): actual, pred = np.array(actual), np.array(pred) return np.mean(np.abs((actual - pred) / actual)) * 100

We can then use this function to calculate the MAPE for two arrays: one that contains the actual data values and one that contains the predicted data values.

actual = [12, 13, 14, 15, 15,22, 27] pred = [11, 13, 14, 14, 15, 16, 18] mape(actual, pred) 10.8009

From the results we can see that the mean absolute percentage error for this model is **10.8009%**. In other words, the average difference between the predicted value and the actual value is 10.8009%.

**Cautions on Using MAPE**

Although MAPE is easy to calculate and interpret, there are two potential drawbacks to using it:

**1. **Since the formula to calculate absolute percent error is |actual-prediction| / |actual| this means that MAPE will be undefined if any of the actual values are zero.

**2. **MAPE should not be used with low volume data. For example, if the actual demand for some item is 2 and the forecast is 1, the value for the absolute percent error will be |2-1| / |2| = 50%, which makes it seem like the forecast error is quite high, despite the forecast only being off by one unit.