Question

Use the festival data set below to calculate a 5-year weighted moving average (WMA) to predict the number of guests at the festival in 2022. Use the weights of 0.4, 0.3, 0.1, 0.1, and 0.1 for the 5-year WMA, where the first weight is used for the most recent year and the last weight is used for the least recent year. Round your answer to two decimal places, if necessary.

Answer 1

To predict the number of guests in 2022 using a 5-year Weighted Moving Average, multiply the number of guests from the previous five years by their respective weights (0.4, 0.3, 0.1, 0.1, 0.1) and sum the results. Assuming the last five years had 1000, 1100, 1200, 1300, and 1400 guests respectively, the prediction for 2022 is 1280 guests.

Step-by-step explanation:

To calculate a 5-year weighted moving average (WMA) to predict the number of guests at a festival in 2022, we need the actual number of guests from the previous five years. Since that data isn't provided, let's assume we have the following numbers of guests for the years 2017 through 2021: 1000, 1100, 1200, 1300, and 1400 respectively. We will use the weights of 0.4, 0.3, 0.1, 0.1, and 0.1 for the years 2021 to 2017 respectively, with the largest weight applied to the most recent year, 2021.

The 5-year WMA is calculated as follows:

1. Multiply the number of guests in 2021 (1400) by its weight (0.4).
2. Multiply the number of guests in 2020 (1300) by its weight (0.3).
3. Multiply the number of guests in 2019 (1200) by its weight (0.1).
4. Multiply the number of guests in 2018 (1100) by its weight (0.1).
5. Multiply the number of guests in 2017 (1000) by its weight (0.1).
6. Sum these results to obtain the final weighted moving average.

Using these calculations:

• 1400 x 0.4 = 560
• 1300 x 0.3 = 390
• 1200 x 0.1 = 120
• 1100 x 0.1 = 110
• 1000 x 0.1 = 100

Sum: 560 + 390 + 120 + 110 + 100 = 1280

So, the prediction for the number of guests in 2022 using the 5-year WMA is 1280 guests.