What does a normal distribution represent in statistics?

A normal distribution represents a key concept in statistics characterized by its bell-shaped curve, which indicates that data values are symmetrically distributed around a central mean. In a normal distribution, most of the observations cluster around the mean, with probabilities for values further away from the mean tapering off equally on both sides. This symmetry implies that about 68% of the data fall within one standard deviation from the mean, approximately 95% within two standard deviations, and about 99.7% within three standard deviations.

This characteristic makes the normal distribution particularly useful for statistical analysis, as many statistical tests and methods assume that the data follow this distribution. The regularity of a normal distribution allows for easier calculations of probabilities and facilitates the application of inferential statistics, such as hypothesis testing and confidence interval estimation. Hence, recognizing the properties of a normal distribution is fundamental in understanding data behavior and making informed inferences based on statistical analyses.