Interpolation is used when the position corresponding to a quartile does not fall directly on one observed value in the ordered dataset. The calculation then estimates a value between nearby observations rather than selecting an unrelated data point. This allows Q1 and Q3 to represent the intended 25th- and 75th-percentile positions consistently.
The interquartile range, calculated as Q3 minus Q1, measures the width of the dataset’s central 50 percent. A larger value indicates that this middle portion is more spread out, while a smaller value indicates greater concentration. Because it focuses on the interval between the quartiles, it supports comparisons of distributional spread.
The locations of Q1 and Q3 within an ordered dataset help indicate whether observations are distributed symmetrically or whether one side is more extended. Comparing the quartile interval with the dataset’s overall arrangement can reveal skewness, meaning an uneven distribution. This makes the quartiles useful for interpreting shape, not only numerical spread.
First, arrange all observations from smallest to largest. Next, locate the positions associated with the 25th and 75th percentiles. If either position falls between observations, interpolate according to the selected calculation procedure. The resulting values are Q1 and Q3, which can then be used to determine the interquartile range.
In a box plot, Q1 and Q3 form the lower and upper boundaries of the box, so the box displays the central 50 percent of observations. The distance between these boundaries corresponds to the interquartile range. Values lying unusually far beyond this central interval can be flagged as potential outliers.
Q1 and Q3 are useful when analysts need to summarize an ordered dataset with more information than a single central value. They show where the lower and upper portions of the distribution begin, support comparisons of spread through the interquartile range, and help interpret skewness or potential outliers in box plots.