Ron Peart owns a stationery shop which also provides photo coping services. You are a Utech graduate and was hired as supervisor, and to impress Mr. Peart you started analyzing photo copy sales for the period February to December as shown below.
 
Month

Actual Photo copying sales

($1000’s)

February

13

March

16

April

10

May

15

June

17

July

11

August

15

September

12

October

14

November

16

December

12
 
Calculate the forecast for photocopy sales using 5-month moving average

To calculate the 5-month moving average for photocopy sales, we need to average the sales for every group of 5 consecutive months. We can start from June (since we need 5 months of data starting from February) and move forward one month at a time, calculating the average of the previous 5 months.

The formula for the 5-month moving average at month $ t $ is:

\[
\text{Moving Average at } t = \frac{\text{Sales in month } (t-4) + (t-3) + (t-2) + (t-1) + t}{5}
\]

Let's calculate the moving averages step by step:

1. **June** (for February to June):
   \[
   \frac{13 + 16 + 10 + 15 + 17}{5} = \frac{71}{5} = 14.2
   \]

2. **July** (for March to July):
   \[
   \frac{16 + 10 + 15 + 17 + 11}{5} = \frac{69}{5} = 13.8
   \]

3. **August** (for April to August):
   \[
   \frac{10 + 15 + 17 + 11 + 15}{5} = \frac{68}{5} = 13.6
   \]

4. **September** (for May to September):
   \[
   \frac{15 + 17 + 11 + 15 + 12}{5} = \frac{70}{5} = 14.0
   \]

5. **October** (for June to October):
   \[
   \frac{17 + 11 + 15 + 12 + 14}{5} = \frac{69}{5} = 13.8
   \]

6. **November** (for July to November):
   \[
   \frac{11 + 15 + 12 + 14 + 16}{5} = \frac{68}{5} = 13.6
   \]

7. **December** (for August to December):
   \[
   \frac{15 + 12 + 14 + 16 + 12}{5} = \frac{69}{5} = 13.8
   \]

### Summary of 5-Month Moving Averages:
- June: 14.2
- July: 13.8
- August: 13.6
- September: 14.0
- October: 13.8
- November: 13.6
- December: 13.8

Would you like further details or clarification on this calculation?

### 5 Related Questions:
1. What are the advantages of using a moving average for sales forecasting?
2. How does a 3-month moving average compare to a 5-month moving average in terms of responsiveness to changes?
3. How can we adjust the moving average method for seasonal patterns?
4. What other forecasting methods could be used in addition to moving averages?
5. How would a weighted moving average improve the accuracy of this forecast?

### Tip:
A longer moving average (e.g., 5 months) smooths out short-term fluctuations, while a shorter one (e.g., 3 months) reacts faster to recent changes.

Ron Peart owns a stationery shop which also provides photo copying services. You are a Utech graduate and were hired as supervisor. To impress Mr. Peart, you started analyzing photocopy sales for the period February to December as shown below. Calculate the forecast for photocopy sales using a 5-month moving average.

Calculate the 5-month moving average for photocopy sales at Ron Peart's stationery shop from February to December. This step-by-step guide explains how to use time series analysis to forecast sales, utilizing the moving average formula. Suitable for high school students in Grades 10-12.

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