Start with position, not percentage
A percentile describes a value’s position within a distribution. If a test score is at the 75th percentile, it is at or above roughly 75% of the scores in the group used for comparison. It does not mean the student answered 75% of the questions correctly. A score of 18 out of 20 could be at a low percentile if nearly everyone scored higher, or a high percentile if most people scored lower.
Always ask what group forms the comparison. A reading score’s percentile among students in one class may differ from its percentile among students in an entire grade. The percentile makes sense only alongside that reference group and the measure being ranked.
See how quartiles divide ordered data
Quartiles are three cut points that divide ordered data into four parts. The first quartile, Q1, marks approximately the 25th percentile. The second quartile, Q2, is the median, or approximately the 50th percentile. The third quartile, Q3, marks approximately the 75th percentile. About one quarter of the observations fall in each part, though ties and calculation methods can make the boundaries less exact.
Consider eight response times, in minutes, arranged from smallest to largest: 40, 48, 52, 58, 62, 70, 76, 94. Because there are eight values, the median is halfway between the fourth and fifth: (58 + 62) ÷ 2 = 60. Using the method of taking the median of each half, Q1 is (48 + 52) ÷ 2 = 50, and Q3 is (70 + 76) ÷ 2 = 73.
Quartile calculations are not identical in every spreadsheet, statistics package, or textbook. Some methods use different rules for values between observed data points. When comparing published quartiles or reproducing a calculation, check which method was used rather than assuming a small difference is an error.
Read the spread between the quartiles
The interquartile range, or IQR, is Q3 minus Q1. In the response-time example, it is 73 − 50 = 23 minutes. This describes the span of the middle half of the data. It is often useful when an unusually high or low value makes the full range less representative of typical observations. Here, the full range is 94 − 40 = 54 minutes, but the middle half occupies a narrower interval.
Quartiles also reveal uneven spacing. If the gap from the median to Q3 is much wider than the gap from Q1 to the median, the upper portion of the middle half is more spread out. That observation describes the distribution; it does not explain why the values differ. A chart or the original data may be needed to investigate further.
Avoid treating ranks as distances
A move from the 50th to the 60th percentile is a change in rank, not a fixed increase in the measured value. In a tightly clustered part of a distribution, a small change in score might shift a person past many others. Where scores are far apart, a larger change might barely affect rank. Likewise, two people at the same percentile in different groups need not have the same raw score.
A percentile is not a probability about what will happen next. Being at the 90th percentile for past response times, for example, does not mean there is a 90% chance that a future response will take less time. That would require a separate prediction supported by assumptions about how future responses compare with the observed ones.
Use them as a starting point
Before interpreting a percentile or quartile, check the sample size, the comparison group, the units, and whether higher values are desirable. In a very small dataset, a single added observation can noticeably shift a reported percentile. Many equal values can also produce ties, making an exact-sounding rank less informative than it appears.
When presenting findings, pair ranks with raw values where possible: “The median response time was 60 minutes, and the middle half ran from 50 to 73 minutes” is more informative than “Q1 was 50 and Q3 was 73” alone. Percentiles and quartiles are compact summaries of position and spread. They are most useful when readers can also see what was measured and which observations were included.
