1. **Arrange the Data**: First, arrange the data in ascending or descending order.
2. **Determine the Number of Data Points**: Count the total number of data points in the set. Let's denote this value as \( n \).
3. **Identify the Middle Value(s)**:
- If \( n \) is odd, the median is the value at the position \( \frac{n + 1}{2} \).
- If \( n \) is even, the median is the average of the values at positions \( \frac{n}{2} \) and \( \frac{n}{2} + 1 \).
4. **Calculate the Median**:
- If \( n \) is odd, the median is the value at the position \( \frac{n + 1}{2} \).
- If \( n \) is even, the median is the average of the values at positions \( \frac{n}{2} \) and \( \frac{n}{2} + 1 \).
\[
\text{Median} = \begin{cases}
\text{Data}\left[\frac{n + 1}{2}\right] & \text{if } n \text{ is odd} \\
\frac{\text{Data}\left[\frac{n}{2}\right] + \text{Data}\left[\frac{n}{2} + 1\right]}{2} & \text{if } n \text{ is even}
\end{cases}
\]
Where:
- \( \text{Data}[i] \) represents the \( i \)th data point in the sorted list.
5. **Interpret the Median**: Once you've calculated the median, it represents the middle value of the dataset. It's often used as a measure of central tendency, indicating the value around which the data tend to cluster.
Let's consider an example to illustrate these steps:
Example:
Consider the following set of numbers: {2, 5, 8, 10, 12, 15, 17}
1. Arrange the data: {2, 5, 8, 10, 12, 15, 17}
2. Determine the number of data points: \( n = 7 \)
3. Since \( n \) is odd, the median is the value at the position \( \frac{n + 1}{2} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \).
4. Calculate the median: Median = 10
So, the median of the given dataset is 10.