Quartile

quartileslower quartilelower and upper quartilesupper quartile
A quartile is a type of quantile.wikipedia
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Quantile

quantilesquintiletertile
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

The values found by this method are also known as "Tukey's hinges"; see also 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 . In other words, the IQR is the first quartile subtracted from the third quartile; these quartiles can be clearly seen on a box plot on the data.

Box plot

boxplotbox and whisker plotadjusted boxplots
This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions.
In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles.

Outlier

outliersconservative estimateirregularities
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:

Five-number summary

five-number summaries
Five-number summary
2) the lower quartile or first quartile

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).

Epidemiology

epidemiologistepidemiologicalepidemiologists
In applications of statistics such as epidemiology, sociology and finance, the quartiles of a ranked set of data values are the four subsets whose boundaries are the three quartile points.

Sociology

sociologistsociologicalsociologists
In applications of statistics such as epidemiology, sociology and finance, the quartiles of a ranked set of data values are the four subsets whose boundaries are the three quartile points.

Finance

financialfinancesfiscal
In applications of statistics such as epidemiology, sociology and finance, the quartiles of a ranked set of data values are the four subsets whose boundaries are the three quartile points.

TI-83 series

TI-83TI-83 PlusTI-83+ series
This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions.

John Tukey

TukeyTukey, JohnJohn W. Tukey
The values found by this method are also known as "Tukey's hinges"; see also midhinge.

Arithmetic mean

meanaveragearithmetic
This always gives the arithmetic mean of Methods 1 and 2; it ensures that the median value is given its correct weight, and thus quartile values change as smoothly as possible as additional data points are added.

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 deviationsigma
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.

Summary statistics

summary statisticSummarizationdata summarization
Summary statistics

Q1

first quartile in descriptive statistics

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.

Q2

Q2 (statistics), the second quartile in descriptive statistics (i.e. the median)

Q3

The third quartile, in descriptive statistics