The task asks you to calculate the median of the given data set to two decimal places. The data values are:

$5.7, 28.8, 7.8, 23.8, 1.5, 6.8, 12.8, 11.5, 9.2, 16.9$

Steps to find the median:

1. Arrange the data in ascending order: $1.5, 5.7, 6.8, 7.8, 9.2, 11.5, 12.8, 16.9, 23.8, 28.8$

2. Identify the median:

   • Since there are 10 values (an even number), the median is the average of the 5th and 6th values in the ordered list.
   • The 5th value is $9.2$ and the 6th value is $11.5$.

3. Calculate the median: $\text{Median} = \frac{9.2 + 11.5}{2} = \frac{20.7}{2} = 10.35$

Thus, the median of the data is 10.35.

Would you like any further details or explanations?

Related Questions:

1. How do you calculate the median for an odd number of data points?
2. What is the difference between the median and the mean?
3. How would the median change if an additional extreme value were added to this data set?
4. How do you calculate the mode, and is there one for this set?
5. How can the median be used in real-world applications like economics or healthcare?

Tip: The median is a good measure of central tendency when there are outliers in the data since it is not affected by extreme values as much as the mean.