Quarttiiliväli

Quarttiiliväli, 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). The quartiles divide a dataset into four equal parts, with Q1 representing the 25th percentile, Q2 (the median) representing the 50th percentile, and Q3 representing the 75th percentile. Therefore, the quarttiiliväli represents the spread of the middle 50% of the data.

To calculate the quarttiiliväli, one first needs to find the median of the entire dataset. Then, the median of the lower half of the data (excluding the overall median if the dataset has an odd number of observations) is calculated to find Q1. Similarly, the median of the upper half of the data is calculated to find Q3. The quarttiiliväli is then computed as Q3 - Q1.

The quarttiiliväli is a robust measure of spread, meaning it is less affected by outliers than the range or standard deviation. This makes it particularly useful for describing the variability of skewed data or data with extreme values. It is often used in descriptive statistics and in constructing box plots, where the length of the box visually represents the quarttiiliväli. A larger quarttiiliväli indicates greater variability in the middle portion of the dataset, while a smaller quarttiiliväli suggests that the middle 50% of the data points are clustered more closely together.