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For example, hair color is usually thought of as a nominal variable, since it has no apparent ordering. [25] However, it is possible to order colors (including hair colors) in various ways, including by hue; this is known as colorimetry. Hue is an interval level variable.
A variable of this type is called a dummy variable. If the dependent variable is a dummy variable, then logistic regression or probit regression is commonly employed. In the case of regression analysis, a dummy variable can be used to represent subgroups of the sample in a study (e.g. the value 0 corresponding to a constituent of the control ...
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
The union of two intervals is an interval if and only if they have a non-empty intersection or an open end-point of one interval is a closed end-point of the other, for example (,) [,] = (,]. If R {\displaystyle \mathbb {R} } is viewed as a metric space , its open balls are the open bounded intervals ( c + r , c − r ) , and its closed balls ...
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical ...
Intermediate value theorem: Let be a continuous function defined on [,] and let be a number with () < < ().Then there exists some between and such that () =.. In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between () and () at some point within the interval.
To construct a histogram, the first step is to "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) are adjacent and are ...