How are outliers defined in data analysis?

Outliers in data analysis are defined as data points that significantly differ from others. This definition captures the essence of what an outlier is: an observation that deviates markedly from the pattern established by the rest of the dataset. Identifying these outliers is crucial as they can influence statistical outcomes, such as the mean or standard deviation, and may indicate variability in measurements, errors, or novel insights worth investigating further.

In contrast, the other definitions fail to capture the essence of outliers. Data points that conform closely to the majority are actually representative of common trends, not outliers. Data points that replicate common trends reflect the bulk of the data and thus are not deemed outliers, as they fall within the expected range. Lastly, data points with no variance would suggest uniformity rather than deviation, which does not align with the fundamental concept of outliers being distinct from the majority of data. Therefore, the correct identification of outliers enhances the understanding and reliability of data analysis.