Analysing Statistical Data

01Analysing Statistical Data

Outliers

Identify unusually extreme observations using the rule specified in a question.

Flag unusual values before deciding what to do with them

An outlier is an observation unusually far from the general pattern of the data. It may be a genuine extreme event or a recording error; identifying it does not establish its cause.

Use the definition in the question. A common rule flags values below Q1−k IQRQ_1-k\,\mathrm{IQR} or above Q3+k IQRQ_3+k\,\mathrm{IQR}, where IQR=Q3−Q1\mathrm{IQR}=Q_3-Q_1 and often k=1.5k=1.5. Another rule uses values outside xˉ±kσ\bar x\pm k\sigma, often with k=2k=2.

On a box plot, mark outliers separately, usually with crosses. When the observations are available, whiskers end at the most extreme non-outliers. If those values are unavailable, use the stated plotting convention; a question may use the outlier boundaries.

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