Percentile Rank Midrank Guide
Percentile rank answers how a target sits relative to a data set. Because tie handling varies, Lynara uses an explicit midrank convention instead of hiding the rule.
Method
- Count observations below the target.
- Count observations equal to the target.
- Add half of the equal count to the below count.
- Divide by the total number of observations and multiply by 100.
Worked example
For 10, 20, 20, 30 and target 20: one value is below and two are equal, so the midrank percentile is 50%.
Notes
- Other software may use different percentile-rank formulas.
- The target does not need to appear in the data.
- Percentile rank is not the same operation as finding a percentile cutoff value.
- Tie handling is the main reason percentile-rank answers can differ across calculators. When reporting a result, state the midrank convention if the audience needs reproducibility, and use the exact convention required by your course, test provider or software package.
Ties change the answer even when no observation changes
Take the sorted scores 60, 70, 70, 70 and 90, and ask for the percentile rank of 70. One score is strictly below it and three are equal. Under the stated midrank convention, (1 + 0.5 × 3) ÷ 5 × 100 = 50%. The strict-below convention would report 20%, while the at-or-below convention would report 80%.
This is not a rounding error; it is a choice about how tied values are counted. Reporting 50% without naming the convention could mislead a reader comparing the result with a different website or a school's rank policy.
Use midrank for the empirical dataset entered into this tool. For a probability based on a theoretical normal distribution, use the separate z-score percentile calculator and check the normal-model assumption instead.
Percentile rank conventions differ most when there are ties
A midrank-style percentile counts observations below the target plus half of the observations tied with it, then divides by the total. Other systems may use less-than-or-equal rules or different rank conventions. The same dataset can therefore produce slightly different percentile values without an arithmetic error.
State the convention when the result matters for comparison with another report or software package.
Do not confuse percentile rank with percent correct
A percentile rank describes relative position within a reference dataset. A score at the 80th percentile does not mean 80% of questions were answered correctly; it means the score is positioned above a defined proportion of the comparison distribution under the chosen convention.
The result is only as meaningful as the reference group. Changing the population or sample used for comparison can change percentile rank even when the raw score stays the same.
Editorial review and limitations
Continue with the related tools
Use the linked tools for your own inputs and scenarios.
- Five Number Summary & Outlier Calculator — Calculate min, Q1, median, Q3, max, IQR, 1.5×IQR fences, box-plot whiskers and flagged outliers from numeric data.
- Mean Median Mode Calculator — Calculate mean, median, mode, minimum and maximum from a list of numeric values.
- Z-Score & Normal Percentile Calculator — Calculate a z-score from value, mean and standard deviation, plus normal-model percentile and right-tail probability.