What do percentiles tell us?
Percentiles tell us how a value of a dataset stands relative to the rest of the data.
One well-known example is for standardized test scores. Percentiles tell us how well someone performed relative to all other test scores. A score in the 95th percentile means that they performed better than 95 percent of test takers and 5 percent performed better.
Percentiles depend entirely on the dataset, so a set of scores from one school can have very different percentiles from the set of scores of another school. The measure used for the values will also affect the data, such as if the tests are out of 1600 or out of 100.
Further applications of percentiles that are important in data analysis are applications such as for determining the interquartile range (3rd - 1st percentile), which is used to know how spread a dataset is.