It seems like you've uploaded an image of a problem related to calculating the range and standard deviation of a data set. Let me walk through it:

The data provided in the problem is:

$66.2, 86.8, 69.2, 53.4, 40.6, 86.8, 71.5, 55.4, 61.7$

1. Range Calculation:

The range of a data set is found by subtracting the smallest value from the largest value.

Let's find the maximum and minimum values in this set:

• Maximum: $86.8$
• Minimum: $40.6$

So, the range is:

$\text{Range} = \text{Maximum} - \text{Minimum} = 86.8 - 40.6 = 46.2$

2. Standard Deviation Calculation:

For a sample standard deviation, the formula is:

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$

Where:

• $n$ is the number of data points (in this case, 10).
• $x_i$ is each individual data point.
• $\bar{x}$ is the mean of the data set.

Steps to find the standard deviation:

1. Find the mean ($\bar{x}$): $\bar{x} = \frac{66.2 + 86.8 + 69.2 + 53.4 + 40.6 + 86.8 + 71.5 + 55.4 + 61.7}{10}$
2. Calculate the squared differences between each data point and the mean.
3. Sum those squared differences.
4. Divide the sum by $n-1$ (since it’s a sample).
5. Take the square root of that value.

Would you like me to perform the detailed standard deviation calculation step-by-step for you? Or would you like to proceed with this general method?