Quartiles, deciles, and percentiles divide a frequency distribution into a number of parts containing equal frequencies. The items are first put into order of increasing magnitude. Quartiles divide the range of values into four parts, each containing one quarter of the values. Again, if an item comes exactly on a dividing line, half of it is counted in the group above and half is counted below. Similarly, deciles divide into ten parts, each containing one tenth of the total frequency, and percentiles divide into a hundred parts, each containing one hundredth of the total frequency. If we think again about the median, it is the second or middle quartile, the fifth decile, and the fiftieth percentile. If a quartile, decile, or percentile falls between two items in order of size, for our purposes the value halfway between the two items will be used. Other conventions are also common, but the effect of different choices is usually not important. Remember that we are dealing with a quantity which varies randomly, so another sample would likely show a different quartile or decile or percentile.
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