A 正規分布, also known as a ガウス分布, is a continuous probability distribution characterized by its bell-shaped curve. It is defined by two parameters: the mean (average) and the standard deviation (which measures the spread of the distribution). The mean determines the center of the distribution, while the standard deviation indicates how spread out the values are around the mean.
正規分布では、データポイントの約68％が平均から1標準偏差以内に収まり、約95％が2標準偏差以内に収まり、約99.7％が3標準偏差以内に収まります。この性質はしばしば経験則または68-95-99.7ルールと呼ばれます。
正規分布は重要である statistics and is widely used in various fields such as psychology, finance, and natural sciences because many real-world phenomena tend to approximate a normal distribution. Examples include heights of individuals, test scores, and measurement 誤差。
グラフ的には、正規分布は左右対称であり、曲線の左側と右側は鏡像の関係にあります。この対称性は、分布の平均、中央値、最頻値がすべて等しく、分布の中心に位置していることを示しています。
これらの性質に加えて、正規分布は重要である 推論統計学において, as it is often assumed for various statistical tests and methods, allowing for the application of the Central Limit Theorem, which states that the means of samples of large enough size will be normally distributed, regardless of the shape of the population distribution.