What is an outlier in statistics?

An outlier in statistics is defined as a data point that is significantly different from other observations in a data set. This typically means that the value lies far outside the range of the majority of the data, either being much larger or much smaller than the typical values. Outliers can arise from variability in the data, measurement errors, or they might indicate a novel phenomenon that warrants further investigation.

Identifying outliers is important because they can substantially affect the results of statistical analyses, such as the means or standard deviations, and can distort the overall understanding of the data set. For example, in a data set of test scores, if most scores range from 60 to 80, but one score is 30, this score would be considered an outlier because it is significantly lower than the rest.

The other options provide definitions that do not align with the concept of an outlier in statistics. The average or mean represents the central tendency of a data set, while the most common value indicates the mode. Values that lie within one standard deviation of the mean represent a portion of the data that is considered typical, rather than differing significantly. Therefore, option A is the most accurate depiction of what an outlier is in statistical terms.