Professional Guide
Descriptive Statistics and Outlier Detection
How to describe data with mean, median, mode, standard deviation, coefficient of variation and percentile ranks — and how to find and handle outliers honestly.
Before any model, test or chart, you have to know what the data look like. Descriptive statistics summarise central tendency and spread; outlier detection finds the values that do not belong. Both are quick to compute and frequently done carelessly.
This guide covers the standard descriptive measures, when each is the right choice, and how to detect outliers without throwing away real signal.
Central tendency and spread
The mean is the arithmetic average, the median is the middle value, and the mode is the most frequent value. For skewed data (salaries, response times), the median is usually the more honest centre than the mean. The mean/median/mode calculator returns all three from a set of values.
Spread matters as much as the centre. The standard deviation summarises the typical distance from the mean; the coefficient of variation (σ ÷ mean) expresses spread relative to the mean, which lets you compare variability across data sets with different scales. Percentile ranks tell you where a value sits in the distribution.
Detecting outliers
The two standard approaches are the interquartile-range rule and statistical tests. The IQR rule flags values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. For roughly normal data, Grubbs' test flags the single most extreme value as a statistical outlier at a chosen significance level. The IQR-outlier-boundary and outlier-test calculators implement both.
Outliers are not automatically errors: they may be genuine extremes or the most interesting values in the data. Investigate before excluding.
Handling outliers honestly
Decide on a rule before you look at the data, state it in your methods, and report both the analysis with and without excluded values. Removing outliers to improve a result is a form of p-hacking — the rule must be principled and pre-registered in spirit.
For analysis downstream, the confidence-interval and correlation/regression calculators assume your data are clean; clean them with a stated rule first.
Key takeaways
- Use the median for skewed data; report spread (σ, CV) alongside the centre.
- IQR rule: flag values outside Q1−1.5·IQR to Q3+1.5·IQR; Grubbs' test for the extreme value.
- Outliers can be signal — investigate before excluding.
- State your outlier rule before analysis and report results with and without exclusions.
Tools used in this guide
Related guides
References
References are provided for further reading; PanelRoster is not affiliated with the linked resources.