Question

work out the median of these numbers:

\\13, -8, 8, 9, 3, -13\\

Explanation:

🆕 New Concept Discovered: Finding the Median
The middle value in an ordered list

Step 1: Order the numbers

To find the median, we must first arrange the numbers in order from smallest to largest (ascending order).

Our original list of numbers is:

$$ 13, -8, 8, 9, 3, -13 $$

Arranging them from smallest to largest, keeping in mind that negative numbers with larger absolute values are smaller:

$$ -13, -8, 3, 8, 9, 13 $$

Step 2: Find the middle values

Count how many numbers are in the data set:

$$ n = 6 $$

Since there is an even number of values, there is no single middle number. Instead, we locate the two middle numbers, which are the 3rd and 4th values in our ordered list:

$$ -13, -8, \mathbf{3}, \mathbf{8}, 9, 13 $$

The two middle numbers are \(3\) and \(8\).

Step 3: Calculate the mean of the two middle values

To find the median of an even set of numbers, we find the average (mean) of the two middle values by adding them together and dividing by \(2\):

$$ \text{Median} = \frac{3 + 8}{2} $$

$$ \text{Median} = \frac{11}{2} = 5.5 $$

Answer:

\(5.5\) (or \(\frac{11}{2}\))