Question: User: 47.2 53.4 57.4 61.9 68.7 73.6 78.1 84.7 58 63.2 66 68.3 57 64.2 68.1 62.3 64.2 60.6 58.5 75.7 66.6 61.7 63.8 64 65 60.8 63.8 63.2 66 63.2 69.4 68.3 71.7 69.4 62.6 68.5 60.8 61.3 63.4 69.2 59.1 56.4 72 66.4 68.7 67.2 62.6 71.2 55.2 46.4 64.2 64.4 70.1 57 51 64 72.6 55.2 70.1 74 72.6 70.1 56 64.2 51 68.5 67 60.8 56.4 65.8
1. **Stating the problem:** We are given a list of numbers and we want to analyze them statistically. A common first step is to find the mean (average) of the data set.
2. **Formula for the mean:** The mean $\bar{x}$ of $n$ numbers $x_1, x_2, ..., x_n$ is given by:
$$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$
3. **Count the numbers:** There are $n=60$ numbers in the list.
4. **Sum the numbers:** Adding all numbers:
$$\sum x_i = 47.2 + 53.4 + 57.4 + 61.9 + 68.7 + 73.6 + 78.1 + 84.7 + 58 + 63.2 + 66 + 68.3 + 57 + 64.2 + 68.1 + 62.3 + 64.2 + 60.6 + 58.5 + 75.7 + 66.6 + 61.7 + 63.8 + 64 + 65 + 60.8 + 63.8 + 63.2 + 66 + 63.2 + 69.4 + 68.3 + 71.7 + 69.4 + 62.6 + 68.5 + 60.8 + 61.3 + 63.4 + 69.2 + 59.1 + 56.4 + 72 + 66.4 + 68.7 + 67.2 + 62.6 + 71.2 + 55.2 + 46.4 + 64.2 + 64.4 + 70.1 + 57 + 51 + 64 + 72.6 + 55.2 + 70.1 + 74 + 72.6 + 70.1 + 56 + 64.2 + 51 + 68.5 + 67 + 60.8 + 56.4 + 65.8$$
Sum is approximately $\sum x_i = 3997.6$
5. **Calculate the mean:**
$$\bar{x} = \frac{3997.6}{60}$$
6. **Simplify:**
$$\bar{x} = \cancel{\frac{3997.6}{60}} = 66.6267$$
7. **Interpretation:** The average value of the data set is approximately $66.63$.
This is a basic statistical measure useful for understanding the central tendency of the data.