Quartile in the context of "Percentile"

In descriptive statistics, a decile is any of the nine values that divide the sorted data into ten equal parts, so that each part represents 1/10 of the sample or population. A decile is one possible form of a quantile; others include the quartile and percentile. A decile rank arranges the data in order from lowest to highest and is done on a scale of one to ten where each successive number corresponds to an increase of 10 percentage points.

In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created. Common quantiles have special names, such as quartiles (four groups), deciles (ten groups), and percentiles (100 groups). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.

q-quantiles are values that partition a finite set of values into q subsets of (nearly) equal sizes. There are q − 1 partitions of the q-quantiles, one for each integer k satisfying 0 < k < q. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables (see percentile rank). When the cumulative distribution function of a random variable is known, the q-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values {1/q, 2/q, …, (q − 1)/q}.

In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data. To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q₁ (also called the lower quartile), Q₂ (the median), and Q₃ (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q₃ −  Q_1.

The IQR is an example of a trimmed estimator, defined as the 25% trimmed range, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. It is also used as a robust measure of scale It can be clearly visualized by the box on a box plot.

In descriptive statistics, a box plot or boxplot is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their quartiles.

In addition to the box on a box plot, there can be lines (which are called whiskers) extending from the box indicating variability outside the upper and lower quartiles, thus, the plot is also called the box-and-whisker plot and the box-and-whisker diagram. Outliers that differ significantly from the rest of the dataset may be plotted as individual points beyond the whiskers on the box-plot. Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length).

A growth chart is used by pediatricians and other health care providers to follow a child's growth with age. Growth charts have been constructed by observing the growth of large numbers of healthy children over time. The height, weight, and head circumference of a child can be compared to the expected parameters of children of the same age and sex to determine whether the child is growing appropriately. For each parameter, a set of growth curves are graphed for the median value (the "middle" value, at 50 percentile), lower and upper quartiles (bottom and top 25%), as well the lower and upper deciles (bottom and top 10%).

Growth charts can also be used to predict the expected adult height and weight of a child because, in general, children maintain a fairly constant growth curve. When a child deviates from his or her previously established growth curve, investigation into the cause is generally warranted. Parameters used to analyze growth charts include weight velocity (defined as rate of change in weight over time), height velocity (defined as rate of change in stature over time), and whether someone's growth chart crosses percentiles. For instance, endocrine disorders can be associated with a decrease in height velocity and preserved weight velocity while normal growth variants are associated with a decrease in height and weight velocity that are proportional to each other. It's important to note that other parameters are more commonly used such as waist circumference for assessing obesity and skin fold difference for assessing malnutrition. Growth charts can also be compiled with a portion of the population deemed to have been raised in more or less ideal environments, such as nutrition that conforms to pediatric guidelines, and no maternal smoking. Charts from these sources end up with slightly taller but thinner averages.