To solve this, we need to calculate the mean, median, and sample standard deviation of the given data set. Here’s the dataset provided:

$x = [27.1, 19.4, 12.6, 11.5, 13.3, 7.1, 29.1, 1.9, 19.6, 9.4]$

Step 1: Calculating the Mean

The mean $\bar{x}$ is calculated by summing all values and dividing by the total number of values.

$\bar{x} = \frac{\sum x}{n}$

Step 2: Finding the Median

To find the median, we arrange the values in ascending order and then locate the middle value. Since there are 10 values, the median will be the average of the 5th and 6th values in the sorted list.

Step 3: Calculating the Sample Standard Deviation

The sample standard deviation $s$ is calculated using the formula:

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

Let me proceed with these calculations.Here are the results for the dataset provided:

1. Mean: 15.10 (rounded to two decimal places)
2. Median: 12.95
3. Sample Standard Deviation: 8.64

Would you like further details on any of these calculations or additional help?

Here are a few related questions that may help you understand this topic better:

1. How does the sample standard deviation differ from the population standard deviation?
2. What is the effect of outliers on the mean and median?
3. How can you determine if a dataset is symmetric based on mean and median?
4. What are some common uses of standard deviation in real-life scenarios?
5. How would you interpret a high versus low standard deviation?

Tip: Remember, the median is less affected by outliers compared to the mean, making it a robust measure of central tendency.