A percentile is a statistical measure that indicates the value below which a certain percentage of data falls. For instance, the 70th percentile is the value below which 70% of the observations can be found. Percentiles are particularly useful in understanding the distribution of data, as they help identify significant values within a dataset.

Quantiles, on the other hand, are specific types of percentiles that divide a dataset into equal parts. The most common quantiles are quartiles, which split the data into four equal parts, corresponding to the 25th, 50th (median), and 75th percentiles. Other quantiles include deciles (dividing the data into ten parts) and percentiles (dividing the data into one hundred parts).

In R, you can calculate percentiles and quantiles using the quantile() function. For example, to find the 25th, 50th, and 75th percentiles of a dataset, you would use quantile(data, c(0.25, 0.5, 0.75)) ¹².