Consider the following data:



Monthly Profit of a GymMonth

Jan-12

Feb-12

Mar-12

Apr-12

May-12

Jun-12

Jul-12

Aug-12

Sep-12

Profit ($)

5,3505,350

5,1035,103

4,8244,824

4,4374,437

5,0805,080

5,3585,358

5,8195,819

6,0916,091

5,8375,837

Step 3 of 5 :  

Determine the three-period weighted moving average for the next time period with weights of 33 (most recent), 22 (second recent), and 11 (oldest time period). If necessary, round your answer to one decimal place.

To calculate the three-period weighted moving average for the next time period, we'll use the given weights: 3 for the most recent period, 2 for the second recent period, and 1 for the oldest period. The formula for a weighted moving average is:

\[
WMA = \frac{(W_1 \times P_1) + (W_2 \times P_2) + (W_3 \times P_3)}{(W_1 + W_2 + W_3)}
\]

Where:
- $W_1, W_2, W_3$ are the weights (3, 2, 1 respectively),
- $P_1, P_2, P_3$ are the profits for the most recent periods.

Let's calculate the weighted moving average using the data for July, August, and September 2012.

1. Profit for July 2012: $P_3 = 5,819$
2. Profit for August 2012: $P_2 = 6,091$
3. Profit for September 2012: $P_1 = 5,837$

Now, apply the formula:

\[
WMA = \frac{(3 \times 5,837) + (2 \times 6,091) + (1 \times 5,819)}{3 + 2 + 1}
\]

Let's compute this.The three-period weighted moving average for the next time period is approximately $5,918.7 (rounded to one decimal place).

Would you like further details or have any questions? Here are some related questions you might find helpful:

1. How is the weighted moving average different from a simple moving average?
2. What are the advantages of using a weighted moving average in forecasting?
3. How would the weighted moving average change if we adjusted the weights?
4. Can the weighted moving average method be applied to different time periods?
5. What impact does the choice of weights have on the outcome of the moving average?

**Tip:** When calculating weighted moving averages, always ensure the weights sum to the total number of periods for accurate forecasting.

Learn how to calculate a three-period weighted moving average (WMA) for gym profits using specific weights for time periods. This problem involves analyzing monthly gym profits from January to September 2012 and applying weights of 3, 2, and 1 to the most recent, second recent, and oldest time periods respectively.

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