What Is a Statistical Outlier?
A statistical outlier is a data point that is significantly different from the other observations in a dataset. It is a value that lies an abnormal distance from other values in a random sample from a population, raising suspicions that it was generated by a different mechanism.
Section 2: How to Identify an Outlier
Outliers can be identified visually using charts like box plots or scatter plots, where they appear far from the main cluster of points. A common statistical method is the Interquartile Range (IQR) rule, which flags any data point that falls more than 1.5 times the IQR below the first quartile or above the third quartile.
Section 3: A Practical Example
Imagine recording the test scores for a class of students. If the scores are 85, 90, 88, 92, 89, and 21, the score of 21 is a clear outlier. It is substantially lower than all the other scores, which are tightly grouped in the high 80s and low 90s.
Section 4: Why Outliers Are Important
Outliers are important because they can heavily skew statistical measures like the mean (average) and standard deviation, potentially leading to misleading analysis and incorrect conclusions. Investigating outliers can reveal measurement errors, data entry mistakes, or genuinely rare and significant events that warrant further study.