Variance

In probability theory and statistics, variance measures how far a set of numbers are spread out. A variance of zero indicates that all the values are identical. Variance is always non-negative: a small variance indicates that the data points tend to be very close to the mean (expected value) and hence to each other, while a high variance indicates that the data points are very spread out around the mean and from each other.

An equivalent measure is the square root of the variance, called the standard deviation. The standard deviation has the same dimension as the data, and hence is comparable to deviations from the mean.

There are two distinct concepts that are both called "variance". One variance is a characteristic of a set of observations. The other is part of a theoretical probability distribution and is defined by an equation. When variance is calculated from observations, those observations are typically measured from a real world system. If all possible observations of the system are present then the calculated variance is called the population variance. Normally, however, only a subset is available, and the variance calculated from this is called the sample variance. The variance calculated from a sample is considered an estimate of the full population variance. There are multiple ways to calculate an estimate of the population variance, as discussed in the section below.

Covariance and contravariance (computer science)

The type system of many programming languages support subtyping. For instance, if Cat is subtype of Animal, then an expression of type Cat can be used whenever an expression of type Animal could. Variance refers to how subtyping between more complex types (list of Cats versus list of Animals, function returning Cat versus function returning Animal, ...) relates to subtyping between their components. Depending on the variance of the type constructor, the subtyping relation may be either preserved, reversed, or ignored. For example, in C#:

The variance of a C# interface is determined by in/out annotations on its type parameters; the above interfaces are declared as IEnumerable<out T>, Action<in T>, and IList<T>. Types with more than one type parameter may specify different variances on each type parameter. For example, the delegate type Func<in T, out TResult> represents a function with a contravariant input parameter of type T and a covariant return value of type TResult.

Variance (land use)

A variance is a deviation from the set of rules a municipality applies to land use and land development, typically a zoning ordinance, building code or municipal code. The manner in which variances are employed can differ greatly depending on the municipality. A variance may also be known as a standards variance, referring to the development standards contained in code.

Description

A variance is an administrative exception to land use regulations. The use and application of variances can differ considerably throughout the great number of municipalities worldwide that regulate land use on this model. The issuance of variances may be very common, or nearly unheard-of in a given municipality. This can depend on a municipality's regulations, built environment and development pattern, and even political climate. One city may view variances as a routine matter, while another city may see variances as highly unusual exceptions to the norm. Community attitudes and political climates can change within a city as well, affecting the manner in which variances are granted even when no changes are made to the regulations governing variances.