To find the median of this data set, let's go through the following steps:

Step 1: Order the Data

First, arrange the data in ascending order: $36, 40, 42, 43, 43, 46, 47, 48, 48, 49, 53$

Step 2: Find the Median

Since there are 11 numbers in this data set (an odd number), the median is the middle value. This value is found at position $(11 + 1) / 2 = 6$ in the ordered list.

The 6th number in the ordered data is: $46$

Answer:

The median of this data set is 46.

Would you like to see the detailed calculation steps, or do you have any questions?

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Here are some related questions to deepen your understanding:

1. How would the median change if an additional data point (e.g., 50) were added?
2. What is the mean of this data set?
3. How do we find the median in a data set with an even number of elements?
4. What are the quartiles for this data set, and how are they calculated?
5. How does the choice of using a sample versus a population affect the interpretation of the median?

Tip: Remember, the median is less sensitive to outliers than the mean, which makes it a useful measure of central tendency, especially in skewed data sets.