What parameters define a normal distribution?

A normal distribution is defined by its mean and standard deviation, which are the key parameters that describe its shape and spread. The mean indicates the center of the distribution, serving as the average value around which the data points are symmetrically distributed. The standard deviation measures the dispersion of the data points from the mean, indicating how much the values typically deviate from the average.

In a normal distribution, the mean, median, and mode are all equal, and the shape is symmetric about the mean. However, it is the mean and standard deviation that specifically characterize the distribution mathematically. As a result, knowing these two parameters allows one to fully understand the characteristics of the normal distribution, including its probability density function and the likelihood of finding values within certain ranges.

Other options may include parameters that describe aspects of data, but they do not define a normal distribution in the same fundamental way that the mean and standard deviation do. For example, variance is related but is derived from the standard deviation, and while skewness indicates asymmetry, a normal distribution is, by definition, symmetrical. The median and mode also do not provide complete characterization by themselves, as they can be the same in normal distributions but do not define its shape. The range and interquart