Identify outliers by checking the data and its distribution first, then applying a rule suited to your analysis. The interquartile range (IQR) is a useful first-pass screen for a single variable; z-scores need stronger distributional assumptions. A flagged value is a candidate to investigate—not an automatic reason to delete it.
What counts as an outlier?
An outlier is an observation unusually distant from other values in a sample. What counts as unusual depends on the variable, the comparison group, and how the data was generated. A rare but valid event can be an outlier; a unit conversion or recording mistake can look like one. The label alone does not distinguish between them.
The National Institute of Standards and Technology (NIST) cautions that outliers may reflect random variation or something scientifically interesting. Treat detection as a prompt to investigate, not a verdict about data quality.
Check the data and its shape before applying a rule
Verify records and measurement context
- Confirm units and plausible value ranges; check whether a value was recorded in a different unit.
- Look for missing values encoded as numbers, duplicate records, and transcription or data-entry errors.
- Check whether observations are independent and whether they belong to the same population or process. A value may be unusual only because records from different groups were combined.
Choose a plot that fits the question
- Histogram or density plot: inspect the overall shape, skew, gaps, and tails of one variable.
- Box plot: see the median, quartiles, and values distant from the central spread.
- Scatter plot: examine paired variables, clusters, and whether an observation departs from a relationship.
For regression, a value that looks ordinary on its own may be unusual relative to the relationship between variables. A scatter plot can reveal observations that appear to come from a different generating process; NIST warns that including such a point in a linear regression can result in a model that fits poorly across much of the data.
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Use IQR fences for a robust first-pass screen
- Find Q1, the 25th percentile, and Q3, the 75th percentile.
- Calculate the interquartile range: IQR = Q3 − Q1.
- Calculate the inner fences: lower = Q1 − 1.5 × IQR and upper = Q3 + 1.5 × IQR.
- Flag observations below the lower fence or above the upper fence for investigation.
NIST calls these the inner fences. Its outer fences use 3 × IQR: values below Q1 − 3 × IQR or above Q3 + 3 × IQR lie beyond them. These are screening conventions, not proof that a value is wrong. Because quartiles are less influenced by extremes than the mean and standard deviation, IQR fences are a useful univariate starting point when skew or non-normality is plausible.
In a NIST example with 90 observations, the median is 559.5, Q1 is 429.75, Q3 is 742.25, and IQR is 312.5. The upper inner fence is 1211; the value 1441 exceeds it and is classified in the example as a mild outlier. These figures illustrate the rule, not universal cutoffs for other datasets.
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When to use z-scores or a modified z-score
Ordinary z-scores
An ordinary z-score measures a value’s distance from the mean in standard deviations: z = (x − mean) / sample standard deviation. It can be useful when the data are approximately normal, the mean and standard deviation are meaningful, and the sample is adequate for the intended analysis. A fixed z-score cutoff is not universal: small samples, non-normal distributions, and extreme values that distort the mean or standard deviation can make the result misleading.
Modified z-scores using MAD
When extremes may distort the mean and standard deviation, NIST describes a robust alternative based on the median and median absolute deviation (MAD): M = 0.6745 × (x − median) / MAD. NIST recommends labeling values with |M| > 3.5 as potential outliers. This is still a flag for review, not a deletion rule.
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How the main methods differ
| Method | Best suited to | Key limitation |
|---|---|---|
| IQR fences | First-pass screening of a single variable when skew or non-normality is plausible | Flags candidates by distance from quartiles; does not determine whether a value is erroneous. |
| Ordinary z-score | Approximately normal data where mean and standard deviation are appropriate summaries | Sensitive to extremes and can mislead in small samples or non-normal data. |
| Modified z-score (MAD) | Screening when contamination or skew may make mean and standard deviation unstable | A potential-outlier label still requires context and investigation. |
| Scatter plots and regression diagnostics | Questions about relationships, leverage, or observations that may come from another process | A single-variable rule cannot establish whether a point is unusual relative to a relationship. |
| Formal tests, such as Grubbs’ test | A defined testing question when assumptions and the number of suspected outliers are explicit | A formal test does not replace data-quality checks or contextual investigation. |
Look for masking and disagreement between methods
Several unusual observations can shift the mean and standard deviation toward themselves, so a test designed to find one outlier may fail to flag a group. Inspect plots and robust summaries before relying on a formal single-outlier test. If methods disagree, report the disagreement and examine the observations rather than choosing whichever result is most convenient. Consider whether the data are univariate or relational, how skewed they are, whether the sample supports the assumptions, and whether the goal is screening, formal identification, or robust estimation.
Investigate flagged values before changing the dataset
- Check the original record, units, coding, and collection process for measurement, transcription, or recording errors.
- Decide whether the value is valid but rare, and whether comparable values are expected in the process being studied.
- If an error is confirmed, correct it with an auditable record of the change. Do not silently overwrite or discard the observation.
- If the value is valid, retain it unless the analysis has a defensible reason to exclude it. Consider robust methods, a justified transformation, sensitivity analysis with and without the point, or a model that represents the data-generating process.
For regression, investigate the point in relation to the other variables and the fitted relationship; a marginal outlier rule alone cannot answer whether it is influential or belongs to another process.
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Make the analysis reproducible
Record the comparison group, missing-value policy, quartile convention, threshold, flagged rows, investigation result, and the effect of any decision on the final analysis. Different quartile conventions or missing-value handling can change results, so state the choices rather than reporting only that an outlier rule was applied.
For Python workflows, SciPy’s official scipy.stats.iqr documentation describes a function that computes the difference between the 75th and 25th percentiles. Its parameters include the axis, percentile range, scaling, and NaN policy (propagate, omit, or raise). Pin the SciPy version in reproducible work because API behavior and documentation can change.
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