Percentiles and quartiles divide an ordered dataset into standardised proportional segments based on rank position.
A percentile indicates the relative standing of an observation by reporting the percentage of values that fall below it.
For example, scoring at the seventieth percentile means an observation exceeds seventy percent of all recorded measurements.
The fiftieth percentile sits at the exact centre of the ordered distribution, which corresponds directly to the median.
Quartiles divide the ordered observations into four equal segments, each containing twenty-five percent of the data.
The first quartile, or Q1, marks the twenty-fifth percentile and separates the lowest quarter from the upper three quarters.
The second quartile, or Q2, marks the fiftieth percentile and represents the median of the entire dataset.
The third quartile, or Q3, marks the seventy-fifth percentile and separates the lower three quarters from the top quarter.
Together with the minimum and maximum values, the three quartiles establish the five-number summary of a dataset.
The five-number summary provides a comprehensive snapshot of central location, spread, and potential skewness.
Unlike standard deviations, percentiles do not assume any specific distributional shape, making them distribution-free.
They remain completely meaningful whether the underlying dataset is symmetric, multimodal, or heavily skewed.
For example, paediatric growth charts use percentiles to track child height and weight against national developmental baselines.
In cloud computing, service level agreements track the ninety-ninth percentile of response latency to guarantee performance under peak loads.
A frequent misconception is confusing percentiles with percentages: an eighty percent score on a test is not the eightieth percentile.