Quartile

quartileslower quartilelower and upper quartilesQ2 (statistics)upper quartile
A quartile is a type of quantile.wikipedia
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Quantile

quantilestertilequintile
A quartile is a type of quantile.
Thus quartiles are the three cut points that will divide a dataset into four equal-sized groups.

Median

averagesample medianmedian-unbiased estimator
The first quartile (Q 1 ) is defined as the middle number between the smallest number and the median of the data set.
The median is the 2nd quartile, 5th decile, and 50th percentile.

Percentile

percentiles50th percentile85th percentile speed
The 25th percentile is also known as the first quartile (Q 1 ), the 50th percentile as the median or second quartile (Q 2 ), and the 75th percentile as the third quartile (Q 3 ).

Midhinge

In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location.

Interquartile range

inter-quartile rangebelowinterquartile
In the case of quartiles, the Interquartile Range (IQR) may be used to characterize the data when there may be extremities that skew the data; the interquartile range is a relatively robust statistic (also sometimes called "resistance") compared to the range and standard deviation.
In descriptive statistics, the interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q 3 − Q 1.

Box plot

boxplotbox and whisker plotadjusted boxplots
In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles.

Outlier

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There are methods by which to check for outliers in the discipline of statistics and statistical analysis. As is the basic idea of descriptive statistics, when encountering an outlier, we have to explain this value by further analysis of the cause or origin of the outlier.
For example, if Q_1 and Q_3 are the lower and upper quartiles respectively, then one could define an outlier to be any observation outside the range:

Descriptive statistics

descriptivedescriptive statisticstatistics
As is the basic idea of descriptive statistics, when encountering an outlier, we have to explain this value by further analysis of the cause or origin of the outlier.
Univariate analysis involves describing the distribution of a single variable, including its central tendency (including the mean, median, and mode) and dispersion (including the range and quartiles of the data-set, and measures of spread such as the variance and standard deviation).

Statistics

statisticalstatistical analysisstatistician
There are methods by which to check for outliers in the discipline of statistics and statistical analysis.

Robust statistics

robustbreakdown pointrobustness
In the case of quartiles, the Interquartile Range (IQR) may be used to characterize the data when there may be extremities that skew the data; the interquartile range is a relatively robust statistic (also sometimes called "resistance") compared to the range and standard deviation.

Range (statistics)

rangerangingsample range
In the case of quartiles, the Interquartile Range (IQR) may be used to characterize the data when there may be extremities that skew the data; the interquartile range is a relatively robust statistic (also sometimes called "resistance") compared to the range and standard deviation.

Standard deviation

standard deviationssample standard deviationSD
In the case of quartiles, the Interquartile Range (IQR) may be used to characterize the data when there may be extremities that skew the data; the interquartile range is a relatively robust statistic (also sometimes called "resistance") compared to the range and standard deviation.

Digital divide in Canada

Findings show that 97.7% of households that reside within the highest income quartile have high speed internet access, while only 58% of households that reside within the lowest income quartile possess access to the internet at home.

Exploratory data analysis

explorative data analysisexploratorydata analysis
Tukey promoted the use of five number summary of numerical data—the two extremes (maximum and minimum), the median, and the quartiles—because these median and quartiles, being functions of the empirical distribution are defined for all distributions, unlike the mean and standard deviation; moreover, the quartiles and median are more robust to skewed or heavy-tailed distributions than traditional summaries (the mean and standard deviation).

Quantile function

quantileinverse distribution functionnormal quantile function
The quartiles are therefore:

Exponential distribution

exponentialexponentially distributedexponentially
The quartiles are therefore:

Trimean

In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles: