kvartiilivälillä

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

The IQR is a robust measure of spread, meaning it is less affected by extreme values or outliers compared to the standard deviation or range. This makes it particularly useful for datasets that are skewed or contain unusual data points. Calculating the IQR involves first sorting the data in ascending order. Then, the median of the entire dataset is found. If the number of data points is odd, the median is excluded when finding the medians of the lower and upper halves. If the number of data points is even, the dataset is split exactly in half. The median of the lower half is Q1, and the median of the upper half is Q3. The IQR is then calculated as Q3 - Q1.

The IQR is commonly used in descriptive statistics and exploratory data analysis. It is often presented alongside the median to describe the central tendency and spread of a dataset. For instance, in box plots, the IQR is visually represented by the length of the box itself, with the lines extending from the box indicating the whiskers. A larger IQR suggests greater variability in the middle portion of the data, while a smaller IQR indicates that the middle 50% of the data points are clustered more closely together.