Quantile

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quantile

[′kwän‚tīl]

(statistics)

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

Quantile

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 K_p 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 K_p < X < K′’_p is equal to p′ − p. The quantile K_½ is the median of the random quantity X. The quantiles K_¼ and K_¾ are called quartiles, and K_0.1, K_0.2, … E_0.9 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 K_0.1 = −1.28, K_0.2 = −0.84, K_0.3 = –0.52, K_0.4 = –0.25 K_0.5 = 0.25, K_0.7= 0.52, K_0.8 = 0.52, K_0.8 = 0.84, and K_0.9 =1.28. The quartiles of the normal distribution Φ(x) are K_¼ = − 0.67 and K = _0.67.

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