what is an outlier

In statistics, an outlier is a data point that differs significantly from other observations. Outliers can be due to a variability in the measurement, an indication of novel data, or the result of experimental error. They can occur by chance in any distribution, but they can also indicate novel behavior or structures in the dataset, measurement error, or that the population has a heavy-tailed distribution. Outliers can have many anomalous causes, such as a physical apparatus for taking measurements that may have suffered a transient malfunction, an error in data transmission or transcription, changes in system behavior, fraudulent behavior, human error, instrument error, or simply through natural deviations in populations. There is no rigid mathematical definition of what constitutes an outlier, and determining whether or not an observation is an outlier is ultimately a subjective exercise. However, there are various methods of outlier detection, some of which are treated as synonymous with novelty detection, such as graphical methods like normal probability plots, and model-based methods like box plots. Outliers should be investigated carefully because they can contain valuable information about the process under investigation or the data gathering and recording process.