To solve this problem, we need to compute both the three-month moving average and the five-month moving average for the sales data, specifically from June to December.

Given Sales Data:

• January: 300
• February: 600
• March: 1,000
• April: 2,000
• May: 4,000
• June: 7,000
• July: 22,000
• August: 44,000
• September: 58,000
• October: 65,000

1. Three-Month Moving Average:

To calculate the three-month moving average, we take the average of the sales for the three months preceding each target month.

June:

• Average of March, April, May: $\frac{1000 + 2000 + 4000}{3} = \frac{7000}{3} \approx 2333.33$

July:

• Average of April, May, June: $\frac{2000 + 4000 + 7000}{3} = \frac{13000}{3} \approx 4333.33$

August:

• Average of May, June, July: $\frac{4000 + 7000 + 22000}{3} = \frac{33000}{3} = 11000$

September:

• Average of June, July, August: $\frac{7000 + 22000 + 44000}{3} = \frac{73000}{3} \approx 24333.33$

October:

• Average of July, August, September: $\frac{22000 + 44000 + 58000}{3} = \frac{124000}{3} \approx 41333.33$

2. Five-Month Moving Average:

For the five-month moving average, we average the sales for the five months preceding each target month.

June:

• Average of January, February, March, April, May: $\frac{300 + 600 + 1000 + 2000 + 4000}{5} = \frac{7900}{5} = 1580$

July:

• Average of February, March, April, May, June: $\frac{600 + 1000 + 2000 + 4000 + 7000}{5} = \frac{14600}{5} = 2920$

August:

• Average of March, April, May, June, July: $\frac{1000 + 2000 + 4000 + 7000 + 22000}{5} = \frac{36000}{5} = 7200$

September:

• Average of April, May, June, July, August: $\frac{2000 + 4000 + 7000 + 22000 + 44000}{5} = \frac{79000}{5} = 15800$

October:

• Average of May, June, July, August, September: $\frac{4000 + 7000 + 22000 + 44000 + 58000}{5} = \frac{135000}{5} = 27000$

Summary of Forecasts:

Three-Month Moving Average:

• June: 2333.33
• July: 4333.33
• August: 11000
• September: 24333.33
• October: 41333.33

Five-Month Moving Average:

• June: 1580
• July: 2920
• August: 7200
• September: 15800
• October: 27000

Would you like further details or have any questions?

Related Questions:

1. How does the moving average method help in forecasting sales?
2. What are the limitations of using a simple moving average for forecasting?
3. Can the moving average method be applied to data with a clear seasonal pattern?
4. What is the difference between a three-month and a five-month moving average in terms of sensitivity to recent changes?
5. How would the inclusion of more data points affect the moving average calculation?

Tip:

The more periods you include in a moving average, the smoother the forecast becomes, but it may be less sensitive to recent changes in the data.