Quartile
A quartile is one of three values (Q1, Q2, Q3) that split an ordered data set into four equal-sized groups, found using a position formula such as k(n+1)/4.
See it move
Quartiles split sorted data into four equal-sized groups using the position formula k(n+1)/4. For 7 customers' spend sorted €20 to €50, Q1's position is 1×(7+1)/4 = 2, the 2nd value, €25. Q3's position is 3×8/4 = 6, the 6th value, €45. The interquartile range is Q3 − Q1 = €45 − €25 = €20, describing the middle 50% of customers without letting the extremes distort the picture.
The formula
Variables
- Quartile value (k = 1, 2 or 3)
- Quartile number (1, 2 or 3)
- Number of observations in the sorted data
Locates which ranked observation (or which pair to interpolate between) corresponds to a given quartile, once the data is sorted.
Check yourself
Nine employees' monthly bonuses, sorted, are: €1,000, €1,200, €1,400, €1,600, €1,800, €2,000, €2,200, €2,400, €2,600. Using the position formula k(n+1)/4, what is Q1?