The demand and forecast of an item for five months are given in the table.

Month	Demand	Forecast
April	225	200
May	220	240
June	285	300
July	290	270
August	250	230

The Mean Absolute Percent Error (MAPE) in the forecast is ___________ % (round off to two decimal places)

Month Demand Forecast April 225 200 May 220 240 June 285 300 July 290 270 August 250 230

The correct answer is 8.07.

Step-by-Step Explanation:

Mean Absolute Percentage Error (MAPE) is a measure of prediction accuracy of a forecasting method in statistics. It is calculated using the following formula:

$$MAPE=\frac{1}{n}$$

where:
- $D_i$ is the actual demand for period i,
- $F_i$ is the forecasted demand for period i, and
- $n$ is the total number of periods ($n=5$ months).

Let's calculate the absolute percentage error for each month:

1. April:
Actual Demand ($D_1$) = 225, Forecast ($F_1$) = 200
Absolute Percentage Error = $\left|\frac{225-200}{225}\right|=\left|\frac{25}{225}\right|\approx 0.1111$

2. May:
Actual Demand ($D_2$) = 220, Forecast ($F_2$) = 240
Absolute Percentage Error = $\left|\frac{220-240}{220}\right|=\left|\frac{-20}{220}\right|\approx 0.0909$

3. June:
Actual Demand ($D_3$) = 285, Forecast ($F_3$) = 300
Absolute Percentage Error = $\left|\frac{285-300}{285}\right|=\left|\frac{-15}{285}\right|\approx 0.0526$

4. July:
Actual Demand ($D_4$) = 290, Forecast ($F_4$) = 270
Absolute Percentage Error = $\left|\frac{290-270}{290}\right|=\left|\frac{20}{290}\right|\approx 0.0690$

5. August:
Actual Demand ($D_5$) = 250, Forecast ($F_5$) = 230
Absolute Percentage Error = $\left|\frac{250-230}{250}\right|=\left|\frac{20}{250}\right|=0.0800$

Now, we compute the average of these absolute errors and multiply by 100 to get the percentage value:

$$MAPE=\frac{0.1111+0.0909+0.0526+0.0690+0.0800}{5}\times 100$$

$$MAPE=\frac{0.4036}{5}\times 100\approx 8.072\%$$

Rounding to two decimal places, we get 8.07 %.