thirdQuartile

The third quartile, commonly denoted Q3, is the value in a dataset below which 75% of the observations fall. It is the upper quartile or the 75th percentile, marking the boundary between the middle and the upper portion of the data.

Calculation methods vary. A common approach is to take the median of the upper half of the data (the values above the overall median). Another method uses percentile interpolation to locate the 75th percentile in the sorted data, which can yield a fractional value. Because different definitions exist, Q3 is sometimes reported with the specific method used.

Relation to IQR and box plots: Q1 is the 25th percentile, Q3 is the 75th percentile, and the interquartile range IQR = Q3 − Q1 measures the spread of the middle 50% of the data. Box plots typically display Q1, the median, and Q3 as the box boundaries, providing a compact view of distribution and skew.

Example: for the data set 1, 2, 3, 4, 5, 6, 7, 8, the upper half is 5, 6, 7, 8. The median of this half is (6 + 7) / 2 = 6.5, so Q3 = 6.5 under this common upper-half method. Note that other conventions can yield slightly different values.

In practice, thirdQuartile is used to summarize distribution shape, identify potential outliers (often defined as values greater than Q3 + 1.5 IQR), and support descriptive analyses alongside Q1 and the median.