Key Concepts

• The value that corresponds to the kth percentile of a data set is the value where k percent of the data set is less than the value.
• When a data set is ordered, it can be divided into quarters or quartiles. A quartile is also a percentile.
• The median is the middle value of a set of ordered data.
• The first quartile and the third quartile are the medians of the lower half and upper half of an ordered data set.
• The interquartile range (IQR) describes the range of the middle 50 percent of the data values and can be used to help identify outliers.

Glossary

first quartile: the value that is the median of the of the lower half of the ordered data set

interquartile range (IQR): the range of the middle 50% of the data values. The IQR is found by subtracting the first quartile from the third quartile.

median: a number that separates ordered data into halves; half the values are the same number or smaller than the median and half the values are the same number or larger than the median. The median may or may not be part of the data.

outlier: an observation that does not fit the rest of the data. Values more than Q3 plus 1.5 times the IQR or less than Q1 minus 1.5 times the IQR are considered outliers.

percentile: a number that divides ordered data into hundredths; percentiles may or may not be part of the data. The median of the data is the second quartile and the 50th percentile. The first and third quartiles are the 25th and the 75th percentiles, respectively.

quartiles: the numbers that separate the data into quarters; quartiles may or may not be part of the data. The second quartile is the median of the data.