What defines an outlier in a data set?

An outlier in a data set is defined as a data point that differs significantly from the other observations. This means that when analyzing a dataset, some values may deviate greatly from the majority of data points, either being much higher or much lower. Identifying outliers is crucial because they can indicate variability in measurement, experimental errors, or a different population altogether.

Outliers can have a major impact on statistical analyses, such as influencing the mean and standard deviation, which is why they are carefully examined. For instance, in a set of exam scores, if most scores are between 70 and 90 but one score is 30, that score would be considered an outlier, as it does not fit the general pattern of the other scores.

In contrast, a data point that is repeated many times typically signifies regularity or frequency in that particular value rather than an anomaly. An average of the set represents a central tendency and is not indicative of a single outlier. Finally, a data point that falls within the interquartile range (IQR) is generally considered typical or expected, as the IQR represents the middle 50% of a dataset and excludes extremes or outliers. Hence, defining an outlier involves recognizing those values that