What does a bell-shaped curve imply about data distribution?

A bell-shaped curve, commonly known as a normal distribution, indicates that the values in the data set are clustered around the mean. This means most of the data points are concentrated near the center or average value, creating a symmetrical and balanced appearance. As you move away from the mean in either direction, the frequency of data points decreases, leading to the characteristic tapering on both ends of the curve.

This clustering effect around the mean has significant implications for data analysis, particularly in statistics, as many statistical methods assume a normal distribution. The normal distribution also suggests that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and around 99.7% falls within three standard deviations. This property is crucial for making predictions and understanding the variability of the data.

In contrast, the other choices describe different characteristics that do not apply to a bell-shaped curve. Uniform distribution suggests that values are spread out evenly rather than clustered. A significant skew indicates an asymmetrical distribution, which would not resemble a bell shape. Finally, stating that data only has extreme low and high values implies an outlier-dominated distribution, which also departs from the normality suggested by a bell-shaped curve.