1. The problem provides a list of 30 data points, each with an index and a corresponding value. 2. We want to analyze or summarize this data, for example by calculating the mean (average) value. 3. The formula for the mean of $n$ values $x_1, x_2, \ldots, x_n$ is: $$\text{mean} = \frac{1}{n} \sum_{i=1}^n x_i$$ 4. We sum all the values and then divide by the number of values (30). 5. Summing the values: $$100.01 + 99.19 + 99.84 + 99.23 + 99.78 + 98.60 + 100.22 + 99.06 + 99.96 + 99.89 + 99.67 + 99.38 + 99.34 + 98.96 + 99.75 + 99.12 + 99.40 + 99.14 + 99.88 + 99.20 + 99.11 + 99.49 + 99.66 + 99.03 + 99.69 + 98.99 + 99.48 + 99.62 + 99.51 + 99.19 = 2983.37$$ 6. Dividing by 30: $$\text{mean} = \frac{2983.37}{30} = 99.4457$$ 7. Therefore, the average value of the data set is approximately $99.45$. 8. This gives a good summary measure of the central tendency of the data.