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!