bellshaped

Bellshaped (also written bell-shaped) is an adjective describing something that resembles the form of a bell or a bell-shaped curve. The term is used in geometry, statistics, and biology to indicate a rounded, symmetrical profile with a peak that tapers toward both ends.

In statistics, the bell-shaped curve most often refers to the normal distribution, or Gaussian distribution. It is symmetric, unimodal, and characterized by mean μ and standard deviation σ. Its probability density function is f(x) = (1/(σ√(2π))) exp(- (x-μ)^2/(2σ^2)). Real-world data approximate this shape under the central limit theorem, and rules of thumb describe data around the mean within 1, 2, or 3 standard deviations.

In biology and botany, bell-shaped describes flowers with a cup-like corolla that flares at the mouth, as in many Campanula species, and other genera. The term helps distinguish from tubular, urceolate, or star-shaped forms. Outside biology, objects such as bells, certain instrument bells, or lighting fixtures may be described as bell-shaped due to their silhouette.

Other uses include descriptions of distributions or signals that appear symmetric and unimodal, though not perfectly normal. In applied settings, bell-shaped models are used for measurement errors, residuals, and score distributions, providing a convenient shorthand for a familiar, gradual rise and fall around a central value.