kvartiiliväliä

Kvartiiliväliä, often translated as interquartile range (IQR), is a measure of statistical dispersion representing the difference between the 75th percentile (third quartile, Q3) and the 25th percentile (first quartile, Q1) of a dataset. It quantifies the spread of the middle 50% of the data. The formula for calculating the interquartile range is IQR = Q3 - Q1.

The interquartile range is a robust statistic, meaning it is less affected by outliers than the standard deviation. This makes it a valuable tool when dealing with datasets that may contain extreme values. To find Q1 and Q3, the data must first be ordered from least to greatest. Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data. If the dataset has an odd number of observations, the median is not included in either half when calculating Q1 and Q3.

The IQR is often used in conjunction with the median to describe the distribution of a dataset. A smaller IQR indicates that the middle 50% of the data are clustered closely together, suggesting less variability. Conversely, a larger IQR suggests greater variability in the central portion of the data. The IQR is also a key component in constructing box plots, which visually represent the distribution of data, including quartiles and potential outliers.