Statistics · BEGINNER LESSON
Percentile
A percentile is a value in an ordered data set such that at most p×100 percent of the measurements are below it and at most 100×(1−p) percent are above it. The 50th percentile is the median.
What a percentile is
A percentile is a way to locate a value within ordered data. If a value is at the pth percentile, then at most p×100% of the measurements are less than that value and at most 100×(1−p)% are greater than it. In everyday terms, percentiles divide ordered data into hundredths, so the 70th percentile marks a value that about 70% of the data fall below. The 50th percentile is the median, the middle value of the ordered data.
[1] 7.2.6.2. Percentiles [3] 8.5 Percentiles - Contemporary Mathematics
How percentiles are used
Percentiles help compare a measurement with a reference group. In growth charts, for example, a percentile tells what percent of the reference population is below a child’s measurement. That makes percentiles useful for showing position within a population, not just the raw size of a measurement. Z-scores are related but different: a Z-score describes how far a measurement is from the population mean, while a percentile describes position in the ordered reference group.
[2] The Science of Growth Monitoring: Beyond the Basics - PMC
How percentiles are estimated
For real data, the desired percentile may fall between two observed values, so interpolation may be used. Interpolation means estimating between neighboring data points, often by averaging or by a formula built into software. There is no single universally accepted interpolation rule, so different software can give slightly different results, especially for small samples. Some methods use the nearest actual data value instead of interpolating.
[1] 7.2.6.2. Percentiles [3] 8.5 Percentiles - Contemporary Mathematics
Limitations and caution
Percentiles depend on the chosen definition and on the reference data used to compute them. Growth chart percentiles, for example, can differ between CDC and WHO charts because they are built from different populations and methods. Very low or very high percentiles may be less reliable when the source data are sparse or were trimmed during curve construction. For that reason, percentiles should be interpreted within the context of the specific reference set and calculation method.
[2] The Science of Growth Monitoring: Beyond the Basics - PMC [1] 7.2.6.2. Percentiles
SEE THE IDEA
How a percentile works
First arrange measurements from smallest to largest.
Pick a fraction such as the 70th percentile.
Find the value where about 70% of measurements are below it.
Interpret the cut point using the specific population and method.
Ordered data are searched to find a value that splits the data at a chosen percentage, then that value is interpreted relative to the reference group.
A percentile is a position in ordered data, not a physical unit by itself.
TRY IT YOURSELF
Test your understanding
Choose an answer, then check the explanation.
PUT IT TOGETHER
Match each concept to its meaning
Drag a label onto its description, or select a label and then select a description. This also works with a keyboard.
4 pairs to match
Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.