How is an outlier defined in relation to the interquartile range?

In the context of statistical analysis, outliers are defined as observations that lie significantly outside the range of the majority of data points. When using the interquartile range (IQR) to detect outliers, the common rule is to identify any data point that falls below the lower quartile (Q1) by 1.5 times the IQR or above the upper quartile (Q3) by 1.5 times the IQR.

The interquartile range is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1), providing a measure of the middle 50% of the dataset. When determining whether an observation is an outlier, you calculate the lower bound as ( Q1 - 1.5 \times IQR ) and the upper bound as ( Q3 + 1.5 \times IQR ). Any data points outside these bounds are classified as outliers.

In this scenario, the answer correctly emphasizes that an outlier is identified based on exceeding or falling below the defined thresholds related to the IQR, specifically using the 1.5 times factor derived from the interquartile range. This standardized approach is widely employed in statistical analyses to ensure