interquantile

Interquantile refers to the range between two quantiles of a dataset. Quantiles are points that divide a dataset into equal-sized groups. For example, the median is the second quartile, which divides the dataset into two equal halves. Interquantile ranges are often used to describe the spread of a dataset and to identify outliers.

The most commonly used interquantile range is the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). The IQR is calculated as Q3 minus Q1. It is a measure of the spread of the middle 50% of the data, making it less sensitive to outliers than the range or standard deviation.

Interquantile ranges can also be used to compare the spread of different datasets or to identify the spread of different parts of a dataset. For example, the interdecile range is the range between the first and ninth deciles, which divide the dataset into ten equal parts.

Interquantile ranges are widely used in statistics, data analysis, and quality control. They provide a simple and intuitive way to describe the spread of a dataset and to identify outliers. However, they are not without limitations. For example, they do not take into account the shape of the distribution or the presence of multiple modes. Therefore, they should be used in conjunction with other measures of spread and central tendency.