In a normal distribution, what measures are equal?

In a normal distribution, the mean, median, and mode are all equal due to the symmetric nature of the distribution. A normal distribution is characterized by its bell-shaped curve, which is centered around the mean. This central point is where the majority of the data points cluster, and because of the symmetry, both the median (the middle value when data is ordered) and the mode (the most frequently occurring value) align with that central point.

This equality among these three measures is a fundamental property of normal distributions, distinguishing them from other types of distributions that may be skewed or have varying shapes, where these measures will not necessarily coincide. In non-normal distributions, the mean can be pulled in the direction of skewness, leading to differences among these measures. However, in a perfectly normal distribution, the balance of data above and below the mean ensures that all three measures remain equal at the center of the distribution.