Centiles in Biostatistics Data
The basic idea of the median (that half of your numbers are less than the median) can be extended to other fractions besides 1/2. A centile is a value that a certain percentage of the values are less than. For example, 1/4 of the values are less than the 25th centile (and 3/4 of the values are greater). The median is just the 50th centile.
Some centiles have common nicknames:
The 25th, 50th, and 75th centiles are called the first, second, and third quartiles, respectively.
The 20th, 40th, 60th, and 80th centiles are called quintiles.
The 10th, 20th, 30th, and so on, up to the 90th centile, are called deciles.
Other Latin-based nicknames include tertiles, sextiles, and so forth.
If the sorted sequence has no middle value, you have to calculate the median as the average of the two middle numbers. The same situation comes up in calculating other centiles, but it's not as simple as just averaging the two closest numbers; there are at least eight different formulas for estimating centiles.
Your statistical software may pick one of the formulas (and may not tell you which one it picked), or it may let you choose the formula you prefer. Fortunately, the different formulas usually give nearly the same result.
The inter-quartile range (or IQR) is the difference between the 25th and 75th centiles (the first and third quartiles). The middle one-half of your data falls within the IQR; the remaining one-half is evenly split above and below the IQR. When summarizing data from strangely shaped distributions, the median and IQR are often used instead of the mean and SD.