What characterizes a normal distribution?

A normal distribution is characterized by a bell-shaped curve, which represents how values are distributed around a central mean. In a normal distribution, the majority of the data points cluster around the mean, creating that distinctive peak in the center of the graph, with symmetrically decreasing frequencies as you move away from the center in both directions. This shape signifies that most values are close to the average, while fewer values exist at the extremes, thus illustrating the concept of standard deviations and how they relate to the spread of the data.

The bell-shaped curve is significant in statistics as it allows for the application of various statistical methods and theories, including hypothesis testing and confidence intervals, all of which assume that the data follows this normal distribution pattern. The properties of the mean, median, and mode coincide at the peak, which is another characteristic feature of a normal distribution. This contrasts with the other descriptions; a random scatter of values suggests no specific distribution pattern, a U-shaped curve implies a different kind of distribution, often indicative of a bimodal or non-normal trend, and a skewed representation of data indicates that the data does not follow the symmetry of a normal distribution and might be biased to one side.