1. The problem involves computing sums and averages from the given data set: 30, 20, 40, 20, 30, 60, 80, 20, 40, 20. 2. To find the sum, use the formula: $$\text{Sum} = \sum_{i=1}^n x_i$$ where $x_i$ are the data points. 3. Calculate the sum: $$30 + 20 + 40 + 20 + 30 + 60 + 80 + 20 + 40 + 20 = 360$$ 4. To find the average (mean), use the formula: $$\text{Average} = \frac{\text{Sum}}{n}$$ where $n$ is the number of data points. 5. There are 10 data points, so: $$\text{Average} = \frac{360}{10} = 36$$ 6. Therefore, the sum of the data is 360 and the average is 36. This process helps summarize data by total and central tendency, useful in many fields like statistics and data analysis.