Descriptive Statistics › Choosing Appropriate Descriptive Statistics
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Which descriptive statistics to report depends on the data's characteristics and your analysis goals. Consider these guidelines:
- For roughly symmetric, unimodal distributions without influential extremes: Mean and standard deviation are often useful summaries. Their adequacy still depends on the analytical question and the distribution's tails.
- For skewed distributions or data with influential extremes: Median and IQR are useful resistant summaries. Retain the mean when the target is an expectation, total, or cost, and consider reporting both conventional and resistant summaries.
- For nominal categorical data: Report frequencies or proportions and, when useful, the mode. For discrete counts, the mean, median, quantiles, frequencies, or modes may be appropriate depending on the question. When a plot has several stable peaks, report and investigate them rather than compressing the distribution into one center.
Reporting several compatible statistics usually gives a more useful picture than relying on one measure. A difference between mean and median can suggest asymmetry, while a large difference between standard deviation and IQR can prompt investigation of tails or outliers; neither comparison proves the cause. Skewness and kurtosis add compact shape information, but plots and context are still needed to avoid misleading simplifications.