What shape describes a bell-shaped curve that is symmetrical on both sides?

The bell-shaped curve that is symmetrical on both sides is known as a normal distribution. This distribution plays a fundamental role in statistics due to its characteristics and the properties it exhibits. In a normal distribution, the mean, median, and mode are all located at the center of the distribution, and the probabilities of obtaining values further away from the mean decrease as you move away from this center point.

Normal distributions also follow the empirical rule, which states that approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and around 99.7% within three standard deviations. This property makes normal distributions particularly useful for inferential statistics, as many statistical tests assume that the underlying data follows a normal distribution.

The other choices, such as percentile ranks, variance, and standard deviation, are related to data analysis but do not specifically describe the shape of a distribution. Percentile ranks are used to understand the position of a particular score within a data set, variance measures the spread or dispersion of data points, and standard deviation indicates the average distance of data points from the mean. None of these concepts encapsulate the unique properties of the bell-shaped curve represented by a normal distribution.