When calculating the upper and lower quartiles in a data set, whether or not to include the median depends on how you define your quartiles and the specific method you are using to find them.
1. Excluding the Median: Many traditional methods for calculating quartiles exclude the median from the data set when finding the upper and lower quartiles. In this approach, the lower quartile (Q1) is calculated as the median of the lower half of the data (the values below the median), and the upper quartile (Q3) is the median of the upper half of the data (the values above the median).
2. Including the Median: Some statisticians opt to include the median as part of the data set when determining the quartiles, particularly if the data set has an odd number of observations. In this case, the median is counted as part of both halves, which can lead to different calculations for Q1 and Q3.
Example: Consider the following data set: [1, 3, 5, 7, 9]. The median (Q2) is 5.
- If you exclude the median, the lower half is
[1, 3](Q1 = 2) and the upper half is[7, 9](Q3 = 8). - If you include the median as part of the data set, you would get
[1, 3, 5]for the lower half (Q1 = 3) and[5, 7, 9]for the upper half (Q3 = 8).
In summary, there is no universally correct answer to whether the median should be included when finding quartiles. It depends on the method you choose for quartile calculation. Always clarify your approach based on the context in which you are working.