Kvarttiiliväli

Kvarttiiliväli, also known as the interquartile range (IQR), is a measure of statistical dispersion in a dataset. It is defined as the difference between the third quartile (Q3) and the first quartile (Q1) of the data. The first quartile represents the 25th percentile, meaning 25% of the data falls below this value. The third quartile represents the 75th percentile, meaning 75% of the data falls below this value. Therefore, the quarttiiliväli encompasses the middle 50% of the data.

The quarttiiliväli is a robust statistic, meaning it is less affected by outliers compared to the range (the difference between the maximum and minimum values). This makes it a useful measure for describing the spread of data when extreme values might skew the results. For instance, in a dataset with a few very large or very small numbers, the range would be significantly influenced, while the quarttiiliväli would remain relatively stable.

To calculate the quarttiiliväli, one must first determine the median of the dataset. Then, the median of the lower half of the data (excluding the overall median if the dataset has an odd number of observations) gives Q1, and the median of the upper half of the data gives Q3. The quarttiiliväli is then Q3 - Q1. It is commonly used in box plots to visually represent the spread of the central part of the data and to identify potential outliers.