Questions: Find the median

Solution Steps

To find the median of a list of numbers, we need to sort the list (if it is not already sorted) and then find the middle value. If the list has an odd number of elements, the median is the middle element. If the list has an even number of elements, the median is the average of the two middle elements.

The given list of numbers is already sorted: \[ \{1, 2, 3, 5, 9, 9, 9, 11, 12, 12, 13, 13, 14, 14, 15, 16, 19, 19, 20, 21, 25, 29, 30, 32, 38, 40, 48, 52, 67, 86\} \]

The number of elements in the list is \( n = 30 \).

Since \( n \) is even, the median is the average of the two middle elements. The middle elements are at positions \( \frac{n}{2} \) and \( \frac{n}{2} + 1 \), which correspond to the 15th and 16th elements in the list.

The 15th element is \( 15 \) and the 16th element is \( 16 \).

The median is given by: \[ \text{Median} = \frac{15 + 16}{2} = \frac{31}{2} = 15.5 \]

Final Answer