Final answer:
Data that form a normal distribution sample are typically symmetric, with the mean, median, and mode coinciding at the same point on a bell-shaped curve.
Step-by-step explanation:
Often data that form a normal distribution sample is symmetric. This means that a normal distribution, which is also known as a bell-shaped distribution, has its data evenly distributed around the mean, creating a symmetrical shape when graphed. This distribution is characterized by the mean, median, and mode being located at the same point and the data falls off evenly on both sides of the center, creating a mirror-like image about the central value. It is distinct from distributions that are skewed, bimodal, or exponential in nature.
The bell-shaped curve of a normal distribution follows the Empirical Rule, which states that approximately 68% of the data is within one standard deviation of the mean, about 95% is within two standard deviations, and more than 99% is within three standard deviations. Unlike skewed distributions where the mean, median, and mode lie at different points, in a symmetrical distribution they coincide. The question of skewness introduces concepts like right (positive) skew or left (negative) skew where the bulk of the data values lie to the right or left of the center, respectively. A bimodal distribution would have two peaks (modes), and an exponential distribution decreases rapidly and then levels off, which is not symmetrical.