When calculating the upper and lower quartiles in a data set, whether to include the median depends on how we define the quartiles, but generally, the median is not counted when finding quartiles.
The lower quartile (Q1) is the median of the lower half of the data set, while the upper quartile (Q3) is the median of the upper half. If you have an odd number of data points, then the median will not be included in either half when you calculate Q1 and Q3. However, if the data set has an even number of values, you can choose to include or exclude the median based on your preference or the specific method you are using.
In summary, for consistency and clarity, it’s common practice to exclude the median when determining the lower and upper quartiles of a data set. This approach ensures that the lower half only considers values below the median and the upper half only considers values above it.