Tukey’s “median of halves” method finds Q1 and Q3 by first sorting the sample and locating the overall median (Q2). When the sample size is odd, the overall median is excluded and the lower and upper halves are formed from the remaining values; when even, the data are split into two equal halves. Q1 is the median of the lower half and Q3 is the median of the upper half. The interquartile range (IQR) is Q3 − Q1, a robust measure of spread that resists outliers.
Use +, -, r or the buttons to add/remove/reset sample values. The sample is drawn from a strongly positively skewed population. Quartile bars (Q1, Q2, Q3) are black with labels above each bar.
Blue curve shows a positively skewed distribution on x=0 to 20. Black vertical lines mark population quartiles with labels Q1, Q2, Q3. Blue dots along the x-axis show sampled values.
Histogram uses integer-centered bins with width 0.99 (e.g., bin 5 covers 4.50 to 5.49). Black vertical lines and labels show sample quartiles updated as the sample changes.