The interquartile range (IQR) is a measure of statistical dispersion, representing the spread of the middle 50% of a dataset. Its calculation involves several steps. First, the data must be ordered from least to greatest. Subsequently, the first quartile (Q1), which represents the 25th percentile, and the third quartile (Q3), representing the 75th percentile, must be identified. The IQR is then calculated by subtracting Q1 from Q3 (IQR = Q3 – Q1). For instance, if Q1 is 20 and Q3 is 50, the IQR would be 30.
The importance of this range stems from its resistance to outliers. Unlike the overall range (maximum value minus minimum value), the IQR focuses on the central portion of the data, mitigating the impact of extreme values. This makes it a robust measure of spread, particularly useful when dealing with datasets that may contain errors or unusual observations. The concept of quartiles and interquartile ranges emerged as part of early efforts to quantify data distribution, contributing to the development of more sophisticated statistical methods.
