 TOPICS # Quartile

One of the four divisions of observations which have been grouped into four equal-sized sets based on their statistical rank. The quartile including the top statistically ranked members is called the first quartile and denoted . The other quartiles are similarly denoted , , and . For data points with of the form (for , 1, ...), the hinges are identical to the first and third quartiles.

The following table summarizes a number of common methods for computing the position of the first and third quartiles from a sample size (P. Stikker, pers. comm., Jan. 24, 2005). In the table, denotes the nearest integer function.

 method 1st quartile 1st quartile 3rd quartile 3rd quartile odd even odd even Minitab    Tukey (Hoaglin et al. 1983)    Moore and McCabe (2002)    Mendenhall and Sincich (1995)    Freund and Perles (1987)    Hinge, Interquartile Range, Percentile, Quantile, Quartile Deviation, Quartile Variation Coefficient

## Explore with Wolfram|Alpha ## References

Freund, J. and Perles, B. "A New Look at Quartiles of Ungrouped Data." American Stat. 41, 200-203, 1987.Hoaglin, D.; Mosteller, F.; and Tukey, J. (Ed.). Understanding Robust and Exploratory Data Analysis. New York: Wiley, pp. 39, 54, 62, 223, 1983.Kenney, J. F. and Keeping, E. S. "Quartiles." §3.3 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 35-37, 1962.Mendenhall, W. and Sincich, T. L. Statistics for Engineering and the Sciences, 4th ed. Prentice-Hall, 1995.Moore, D. S. and McCabe, G. P. Introduction to the Practice of Statistics, 4th ed. New York: W. H. Freeman, 2002.Whittaker, E. T. and Robinson, G. The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 184-186, 1967.

Quartile

## Cite this as:

Weisstein, Eric W. "Quartile." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Quartile.html