Where does range collide?

In statistics the range is the simplest measure of how spread out a dataset is: the difference between its largest and its smallest value. Tippett's 1925 study On the Extreme Individuals and the Range of Samples Taken from a Normal Population worked out how this quantity behaves as a random variable and how it grows with the size of the sample, which made it a workable summary of dispersion. A related figure, the interquartile range, throws away the extremes and reports the spread of the middle half instead. Here the range is a single number describing scatter in data, not the outputs of a function, the territory of a species, or the pitches a voice can sing.[1]

Unit

One number: largest value minus smallest value, in the data's own units

Recovery means

Not applicable

Measured by

Computed as maximum minus minimum, or as the interquartile range from the first and third quartiles

In mathematics the range of a function is the collection of all values it actually produces as its input runs over the domain, also called its image. Halmos's 1974 Naive Set Theory sets out functions as a special kind of relation and defines the range as the set of second coordinates, the outputs the map really attains. It must be kept apart from the codomain, the larger set the outputs are declared to live in, which may hold values the function never reaches. This range is a set of outputs of a map, not the scatter of a dataset, the area a species occupies, or the span of a singer's voice.[2]

Unit

A set: every output value the function attains

Recovery means

Not applicable

Measured by

Determined by finding the image of the domain under the function

In ecology and biogeography a species' geographic range is the area of the Earth over which that species is found, described by its size, its shape, and its boundaries. Brown, Stevens, and Kaufman's 1996 review The Geographic Range set out how these areas vary in extent and internal structure across species, and Gaston's 1996 work charted the distribution of range sizes. Ranges are not fixed: Parmesan and Yohe's 2003 study documented many of them shifting toward the poles and up mountainsides as the climate warms. This range is a patch of territory on a map, not a number summarising data, the outputs of a function, or the reach of a musical instrument.[3][4][5]

Unit

An area on the map where a species occurs, in square kilometres

Recovery means

A contracted range can expand again where suitable habitat returns and dispersal allows recolonisation

Measured by

Delimited from occurrence records as extent of occurrence or as area of occupancy

In music and voice science the range is the span between the lowest and the highest pitch a voice or instrument can produce, the reason a soprano, a tenor, and a piano are each described by where their range begins and ends. Coleman, Mabis, and Hinson's 1977 study Fundamental Frequency-Sound Pressure Level Profiles of Adult Male and Female Voices charted the voice range profile, plotting the lowest to highest frequencies a voice can sustain at each level of loudness. Here the range is a span of pitch measured in frequency, not the spread of a dataset, the outputs of a function, or the ground a species covers.[6]

Unit

A span of pitch from lowest to highest note, in hertz or in musical intervals

Recovery means

Not applicable

Measured by

Charted as a voice range profile of fundamental frequency against loudness, or read off as the interval between the lowest and highest playable notes