An outlier in math, specifically in statistics, is a value in a data set that is significantly different from the other values. It is either much larger or much smaller than most of the other data points, lying outside the overall pattern of the data

. Outliers can affect statistical measures, especially the mean, more than the median or mode, because they skew the average if included

. For example, in a set of test scores, a very low or very high score compared to the rest would be considered an outlier

. Mathematically, outliers are often identified using the interquartile range (IQR). A common rule is that any value more than 1.5 times the IQR below the first quartile or above the third quartile is considered an outlier

. In summary:

• An outlier is an extreme data point much smaller or larger than the rest.
• It can distort statistical analyses, especially the mean.
• Outliers can be identified using statistical methods like the IQR rule.
• They may indicate measurement errors, variability, or novel phenomena in the data

This concept helps in understanding data distributions and deciding whether to include or exclude certain values in analysis.