Lower and Upper Quartiles
Quartiles split an ordered data set into four equal parts. The lower quartile is the value below which about one quarter of the data lie, and the upper quartile is the value below which about three quarters of the data lie.
Method
- Order the data from smallest to largest.
- Find the median of the full list.
- Split the data into two halves:
- the lower half contains the values below the median,
- the upper half contains the values above the median.
If the number of values is odd, do not include the median in either half.
- Find the median of each half:
- the median of the lower half is the lower quartile,
- the median of the upper half is the upper quartile.
Important checks
- Make sure the data are in the correct order before starting.
- If the list has an odd number of values, handle the middle value consistently.
- Quartiles should be written as exact values from the data when possible.
Final check
Your answers should make sense in order: lower quartile ≤ median ≤ upper quartile. If that is not true, recheck the ordering and the splitting step.