Definition: Quartiles are the three values that cut an ordered data set into four parts with equal counts, called the first quartile, the median, and the third quartile.
What are quartiles?
Quartiles divide ordered data into four groups of about equal size. Q1 has about 25 percent of the values below it, Q2 is the median at 50 percent, and Q3 has about 75 percent below it.
How do you find them?
Sort the data. Split it at the median. Q1 is the median of the lower half, Q3 the median of the upper half.
For 12, 15, 21, 22, 26, 30, 34, 38, 41, the median is 26. The lower half is 12, 15, 21, 22, so Q1 = (15 + 21) / 2 = 18. The upper half is 30, 34, 38, 41, so Q3 = (34 + 38) / 2 = 36.
Where do they appear?
The five-number summary lists the minimum, Q1, median, Q3, and maximum. These five values draw a box plot directly.
What mistake is common?
Thinking quartiles split the range into four equal widths. They split the count of data points, not the distance between the smallest and largest values.
Where to learn it
- Measuring Center and Variability in Data – lesson
- Asking Statistical Questions and Showing Data – lesson