Interquartile range
Interquartile Range
The Interquartile Range (IQR), pronounced as /ˌɪntərˈkwɔːrtaɪl reɪndʒ/, is a statistical measure used to represent the dispersion or spread of a data set. It is derived from the quantiles of the data, specifically the first quartile (Q1) and the third quartile (Q3). The IQR is calculated by subtracting Q1 from Q3.
Etymology
The term "Interquartile Range" originates from the Latin words "inter" meaning "between" and "quartile" which is derived from "quartus" meaning "fourth". This is in reference to the range being between the first and third quartiles of a data set.
Calculation
The calculation of the Interquartile Range involves several steps:
- Arrange the data in ascending order.
- Find the median (Q2) of the data set.
- Find the first quartile (Q1), which is the median of the lower half of the data (not including Q2 if the data set count is odd).
- Find the third quartile (Q3), which is the median of the upper half of the data (not including Q2 if the data set count is odd).
- Subtract Q1 from Q3 to find the Interquartile Range.
Related Terms
Uses
The Interquartile Range is used in statistics to measure variability by dividing a data set into quartiles. It is particularly useful when dealing with data sets that may contain outliers, as it is not affected by extreme values. The IQR is often used in conjunction with other measures of central tendency, such as the mean or median, to provide a more complete picture of a data set's distribution.
External links
- Medical encyclopedia article on Interquartile range
- Wikipedia's article - Interquartile range
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