Consider the set of numbers

\[ \{1, 2, 2, 3, 3, 3, \ldots, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10\}, \]

where the number \(n\) appears \(n\) times for \(n=1 \) to 10. What is the (absolute value) of the difference between the mode and the median of this set?

**Details and assumptions**

The **mode** of a set is the value that appears most often. The **median** of a set is the middle value when the data is arranged in numerical order.

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