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A value which divides a set of data into equal proportions; examples are quartile and decile.



one of the numerical characteristics of random quantities used in mathematical statistics. If a distribution function of a random quantity X is continuous, then the quantile Kp of order p is defined as that number for which the probability of the inequality X < K<p is equal to p. From the definition of quantile it follows that the probability of the inequality Kp < X < K′’p is equal to p′p. The quantile K½ is the median of the random quantity X. The quantiles K¼ and K¾ are called quartiles, and K0.1, K0.2, … E0.9 are called deciles. Knowledge of the quantiles for suitably selected values of p makes it possible to visualize the distribution function.

Figure 1

For example, for the normal distribution (see Figure 1)

the graph of the function Φ (x) may be plotted by means of the deciles K0.1 = −1.28, K0.2 = −0.84, K0.3 = –0.52, K0.4 = –0.25 K0.5 = 0.25, K0.7= 0.52, K0.8 = 0.52, K0.8 = 0.84, and K0.9 =1.28. The quartiles of the normal distribution Φ(x) are K¼ = − 0.67 and K = 0.67.

References in periodicals archive ?
The second set of constraints imposed on the SCF adjustment involves shifting the top fractile cutoffs to be on a tax unit instead of a household basis.
The upper fractile of the [chi square] distribution is set to [alpha] = 0.
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k], is defined by the 5% lower-tail fractile, and is commonly calculated with the following equation.
He has just painted the geneticist Sir John Solston, and next comes Lord May, the president of the Royal Society who is known for his work on fractile geometries and chaos theory.
Whether readers will tolerate a fractile history of theory, or whether they may prefer the more traditional type of anthology Rajan and O'Driscoll have published, time will tell.
The solution requires selecting capacity so that the fractile of customers serviced equates the expected costs of over- and under-capacity.
The conclusion from all of the above may be that setting requirements for imprecision from within-subject biological variation data is as arbitrary as setting these requirements from a fractile of participating laboratories in external quality assessment schemes (daily inter-laboratory quality-control programs), that is to say, from the state of the art.
Kielpinsky and Nelson[2] considered the design of Type I censored ALTs which minimize the asymptotic variance of maximum likelihood estimator of fractile p at design condition, and obtained the optimum design and sample allocation.