# Range (statistics)

**rangerangingsample rangemoving rangeranged order**

In statistics, the range of a set of data is the difference between the largest and smallest values.wikipedia

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### Statistical dispersion

**dispersionvariabilityspread**

The range is the size of the smallest interval (statistics) which contains all the data and provides an indication of statistical dispersion.

Range

### Descriptive statistics

**descriptivedescriptive statisticstatistics**

However, in descriptive statistics, this concept of range has a more complex meaning.

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).

### Order statistic

**order statisticsorderedth-smallest of items**

The range is a simple function of the sample maximum and minimum and these are specific examples of order statistics.

The sample range is the difference between the maximum and minimum.

### Sample maximum and minimum

**sample maximumsample minimumMaximum**

The range is a simple function of the sample maximum and minimum and these are specific examples of order statistics.

In addition to being a component of every statistic that uses all elements of the sample, the sample extrema are important parts of the range, a measure of dispersion, and mid-range, a measure of location.

### L-estimator

**L-estimation**

In particular, the range is a linear function of order statistics, which brings it into the scope of L-estimation.

A more detailed list of examples includes: with a single point, the maximum, the minimum, or any single order statistic or quantile; with one or two points, the median; with two points, the mid-range, the range, the midsummary (trimmed mid-range, including the midhinge), and the trimmed range (including the interquartile range and interdecile range); with three points, the trimean; with a fixed fraction of the points, the trimmed mean (including interquartile mean) and the Winsorized mean; with all points, the mean.

### Interquartile range

**inter-quartile rangebelowinterquartile**

Interquartile range

It is a trimmed estimator, defined as the 25% trimmed range, and is a commonly used robust measure of scale.

### Statistics

**statisticalstatistical analysisstatistician**

In statistics, the range of a set of data is the difference between the largest and smallest values.

### Interval estimation

**interval estimateintervalinterval (statistics)**

The range is the size of the smallest interval (statistics) which contains all the data and provides an indication of statistical dispersion.

### Independent and identically distributed random variables

**independent and identically distributedi.i.d.iid**

For n independent and identically distributed continuous random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability density function g(x). Let T denote the range of a sample of size n from a population with distribution function G(x).

### Cumulative distribution function

**distribution functionCDFcumulative probability distribution function**

For n independent and identically distributed continuous random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability density function g(x). Let T denote the range of a sample of size n from a population with distribution function G(x). For n independent and identically distributed discrete random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability mass function g(x) the range of the X i is the range of a sample of size n from a population with distribution function G(x). We can assume without loss of generality that the support of each X i is {1,2,3,...,N} where N is a positive integer or infinity.

### Probability density function

**probability densitydensity functiondensity**

For n independent and identically distributed continuous random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability density function g(x). Let T denote the range of a sample of size n from a population with distribution function G(x).

### Emil Julius Gumbel

**GumbelGumbel, Emil JuliusE[mil] J. Gumbel**

Gumbel notes that the "beauty of this formula is completely marred by the facts that, in general, we cannot express G(x + t) by G(x), and that the numerical integration is lengthy and tiresome."

### Bessel function

**modified Bessel functionspherical Bessel functionBessel**

For more general distributions the asymptotic distribution can be expressed as a Bessel function.

### Normal distribution

**normally distributednormalGaussian**

In the case where each of the X i has a standard normal distribution, the mean range is given by

### Probability mass function

**mass functionprobability massmass**

For n independent and identically distributed discrete random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability mass function g(x) the range of the X i is the range of a sample of size n from a population with distribution function G(x). We can assume without loss of generality that the support of each X i is {1,2,3,...,N} where N is a positive integer or infinity.

### Without loss of generality

**WLOGloss of generalityw.l.o.g.**

For n independent and identically distributed discrete random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability mass function g(x) the range of the X i is the range of a sample of size n from a population with distribution function G(x). We can assume without loss of generality that the support of each X i is {1,2,3,...,N} where N is a positive integer or infinity.

### Support (mathematics)

**supportcompact supportcompactly supported**

For n independent and identically distributed discrete random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability mass function g(x) the range of the X i is the range of a sample of size n from a population with distribution function G(x). We can assume without loss of generality that the support of each X i is {1,2,3,...,N} where N is a positive integer or infinity.

### Discrete uniform distribution

**uniform distributionuniformly distributeduniformly at random**

If we suppose that g(x) = 1/N, the discrete uniform distribution for all x, then we find

### Studentized range

**studentized range statistics**

Studentized range

### Reference range

**reference valuesreference rangescut-off**

In health-related fields, a reference range or reference interval is the range of values that is deemed normal for a physiologic measurement in healthy persons (for example, the amount of creatinine in the blood, or the partial pressure of oxygen).

### Qualitative variation

**M2Margalef index**

Several are standard statistics that are used elsewhere - range, standard deviation, variance, mean deviation, coefficient of variation, median absolute deviation, interquartile range and quartile deviation.

### Tetraplasandra

**ohe mauka**

The range of variation in Tetraplasandra is unusually large for a genus in Araliaceae Most of the species were originally described in other genera which were later merged with Tetraplasandra.

### Rescaled range

**R/S analysis**

The rescaled range is calculated from dividing the range of the values exhibited in a portion of the time series by the standard deviation of the values over the same portion of the time series.

### HSL and HSV

**HSVHSLHSV color wheel**

Because these definitions of saturation—in which very dark (in both models) or very light (in HSL) near-neutral colors are considered fully saturated (for instance, from the bottom right in the sliced HSL cylinder or from the top right)—conflict with the intuitive notion of color purity, often a conic or biconic solid is drawn instead, with what this article calls chroma as its radial dimension (equal to the range of the RGB values), instead of saturation (where the saturation is equal to the chroma over the maximum chroma in that slice of the (bi)cone).

### Mid-range

**midsummarymidrangehalf-range**

The mid-range is the midpoint of the range; as such, it is a measure of central tendency.