Tiles is a measurement of relative standing of a particular entry in a [[Math/Probability and Statistics/Dataset|dataset]]. Within a distribution, the $k^{th}$ $\frac{1}{m}$-tile is a value such that $\frac{k}{m}$ of the data fall **at or below** that data. ### Percentiles For the case of percentiles, for $1 \le k \le 99$, the k-th percentile, $P_k$ of a distribution is a value such that $k$% of the data fall **at or below** the data. To determine the value of $P_k$: Let $L = \frac{k}{100}n$, if $L$ is not an integer, round it up, otherwise $P_k$ is the average of the $L$-th and $(L+1)$-th values. In a [[Frequency|frequency]] table for discrete quantitative data, the $k$-th percentile is the value whose cumulative relative frequency is the first to exceed or equal $k$%. ### Quartiles Quartiles are special cases of percentiles, where the 25th, 50th, 75th, and 100th percentiles are referred to as the 1st, 2nd ([[Median|median]]), 3rd, and 4th quartiles, denoted as $Q_1$, $Q_2$, $Q_3$, and $Q_4$.