What does it mean when data follows a normal distribution?

When data follows a normal distribution, it means that the scores are concentrated around the mean. In a normal distribution, the majority of observations cluster near the central value (the mean), which results in a symmetry about that mean. This creates a bell-shaped curve, where most values are close to the average, and fewer values are found as one moves away from the mean towards the extremes.

The key characteristics of a normal distribution include the mean, median, and mode all being equal and located at the center of the distribution. As you move away from the mean in either direction, the frequency of scores decreases, creating the characteristic tapering effect of the curve. This concentration of scores around the mean is important in statistics and psychology because it allows for predictions about the behavior of data and the application of various statistical methods.

In contrast to this, uniform distribution suggests that all scores occur with equal frequency, distinct scores indicate variability without clustering around a mean, and clustering at extremes describes a skewed distribution, which does not represent a normal distribution.