Question

Find the median of a data set

Answer 1

To find the median of a data set, follow these steps:

1. **Organize the Data**: Arrange the numbers in the data set in ascending order (from smallest to largest).

2. **Determine the Size of the Data Set**: Count the number of values (n) in the organized list.

3. **Find the Median**:
- If n is odd: The median is the middle number in the ordered list. You can find it using the formula:
\[
\text{Median} = \text{Value at position } \left( \frac{n + 1}{2} \right)
\]
- If n is even: The median is the average of the two middle numbers. You can find it using the formula:
\[
\text{Median} = \frac{\text{Value at position } \left( \frac{n}{2} \right) + \text{Value at position } \left( \frac{n}{2} + 1 \right)}{2}
\]

### Example

Let's find the median of the following data set:

\[ 3, 1, 4, 2, 5 \]

**Step 1: Organize the Data**
\[ 1, 2, 3, 4, 5 \]

**Step 2: Determine the Size of the Data Set**
- Here, n = 5 (which is odd).

**Step 3: Find the Median**
- Since n is odd, we use the first formula:
\[ \text{Median} = \text{Value at position } \left( \frac{5 + 1}{2} \right) = \text{Value at position } 3 \]
- The 3rd value in the ordered list is 3.

So, the median of the data set is **3**.

If you provide a specific data set, I can help you calculate its median as well!