How do we find the median if the number of observations in a data set is odd?

To find the median in a data set with an odd number of observations, follow these steps:

1. Arrange the Data: First, sort the data set in ascending order. This means you need to list the numbers from the smallest to the largest.
2. Count the Observations: Determine the total number of observations in the data set. Since the number is odd, it will always be in the form of 2n + 1, where n is a whole number.
3. Locate the Median Position: To find the position of the median, use the formula (n + 1) / 2, where n is the total number of observations. This will give you the index of the median value in your sorted data.
4. Identify the Median: Once you have the position, simply find the value at that index in your sorted list. This value is the median of the data set.

For example, consider the data set: [3, 1, 2, 5, 4]. First, sort it to get [1, 2, 3, 4, 5]. There are 5 observations, which is odd. The median position is (5 + 1) / 2 = 3. The value at the 3rd position in the sorted list is 3, which is the median.