Interkvartiilvahe

Interkvartiilvahe, often abbreviated as IQR, is a measure of statistical dispersion, representing the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The first quartile, Q1, is the value below which 25% of the data falls, and the third quartile, Q3, is the value below which 75% of the data falls.

The IQR is a robust statistic, meaning it is less sensitive to extreme values or outliers than measures like the range. This makes it a valuable tool when analyzing datasets that may contain unusual data points. For example, if a dataset includes very high or very low values, the range could be significantly distorted, while the IQR would provide a more representative measure of the typical spread of the data.

To calculate the IQR, one must first determine the quartiles of the dataset. This typically involves ordering the data from smallest to largest and then finding the median of the entire dataset. Q1 is the median of the lower half of the data (excluding the overall median if the dataset has an odd number of points), and Q3 is the median of the upper half of the data (again, excluding the overall median for odd-sized datasets). The IQR is then simply Q3 - Q1.

The IQR is frequently used in exploratory data analysis, particularly in the creation of box plots, where it defines the length of the box that visually represents the interquartile range. It is also employed in identifying potential outliers, often defined as data points that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR.