Quantiles, in statistics, refer to values that divide a dataset into equal-sized groups or intervals. They are a vital measure in understanding the distribution and variability of data. Quantiles provide important information about the spread and location of observations within a dataset.
To calculate quantiles, the dataset is first ordered in ascending order. The n-th quantile can then be determined as the value which divides the dataset into n equal parts. In particular, the quartiles are often used, which divide the data into four equal parts. The first quartile, or the lower quartile, denoted Q1, is the value below which 25% of the data falls. The second quartile, or the median (Q2), divides the data into two equal parts. Finally, the third quartile, or the upper quartile (Q3), is the value below which 75% of the data falls.
Quantiles can also be calculated more generally, such as deciles (values dividing the dataset into 10 equal parts) or percentiles (values dividing the dataset into 100 equal parts). For instance, the 90th percentile represents the value below which 90% of the data falls.
Quantiles are particularly useful when dealing with skewed datasets or data with outliers. They provide a robust alternative to measures like the mean or the standard deviation by summarizing the spread of data in a more resistant manner.
In summary, quantiles are statistical measures that divide a dataset into equal-sized parts, typically quartiles, deciles, or percentiles. They are crucial in understanding the distribution, variability, and important characteristics of data.
