HSC Standard Math Practice Exam 2025 - Free Math Practice Questions and Study Guide

A fundamental characteristic of a normal distribution is that it is perfectly symmetrical, which means that the mean, median, and mode all occupy the same central point. This symmetry indicates that half of the data values lie below this central value and half lie above it, resulting in a bell-shaped curve.

In a normal distribution, the properties ensure that the averages used to describe the data—whether it's the mean, median, or mode—are the same, providing a consistent measure of central tendency. This equality is crucial for statistical analysis and the application of various mathematical techniques that rely on the assumptions of normality.

The other choices reflect characteristics that are not present in a normal distribution, such as skewness or the presence of multiple peaks, which suggest that the data distribution is not symmetrical or that it has a different shape entirely. Understanding this behavior is essential for recognizing how various distributions behave in statistics.