Calculate the three -yearly moving averages and display these and the original figures on the same graph.
`{:("Year ", 2001, 2002, 2003, 2004, 2005, 2006, 2007),("Values "," "20," " 40," " 50," "70," " 80," " 100," " 130):}`

Answer

To calculate the three-yearly moving averages for the given data and display them along with the original figures, follow these steps:

### Step 1: Organize the Data
We have the following data for the years 2001 to 2007:

| Year | Values |
|------|--------|
| 2001 | 20 |
| 2002 | 40 |
| 2003 | 50 |
| 2004 | 70 |
| 2005 | 80 |
| 2006 | 100 |
| 2007 | 130 |

### Step 2: Calculate the Three-Yearly Moving Averages
To calculate the three-yearly moving averages, we will take the average of every three consecutive years.

1. For 2001, 2002, and 2003:
\[ \text{Moving Average} = \frac{20 + 40 + 50}{3} = \frac{110}{3} \approx 36.67 \]

2. For 2002, 2003, and 2004:
\[ \text{Moving Average} = \frac{40 + 50 + 70}{3} = \frac{160}{3} \approx 53.33 \]

3. For 2003, 2004, and 2005:
\[ \text{Moving Average} = \frac{50 + 70 + 80}{3} = \frac{200}{3} \approx 66.67 \]

4. For 2004, 2005, and 2006:
\[ \text{Moving Average} = \frac{70 + 80 + 100}{3} = \frac{250}{3} \approx 83.33 \]

5. For 2005, 2006, and 2007:
\[ \text{Moving Average} = \frac{80 + 100 + 130}{3} = \frac{310}{3} \approx 103.33 \]

### Step 3: Create a Table for Moving Averages
Now we can summarize the moving averages in a table:

| Year | Values | 3-Year Moving Average |
|------|--------|-----------------------|
| 2001 | 20 | |
| 2002 | 40 | 36.67 |
| 2003 | 50 | 53.33 |
| 2004 | 70 | 66.67 |
| 2005 | 80 | 83.33 |
| 2006 | 100 | 103.33 |
| 2007 | 130 | |

### Step 4: Prepare the Graph
1. **X-axis**: Years (2001 to 2007)
2. **Y-axis**: Values (0 to 140)
3. **Plot Original Values**: Mark the points for the original values at their respective years.
4. **Plot Moving Averages**: Mark the points for the moving averages at 2002, 2003, 2004, 2005, and 2006.
5. **Connect the Points**: Draw lines to connect the points for both original values and moving averages.

### Final Graph
The graph will display the original values and the three-year moving averages, allowing for a visual comparison of the trends over the years.