Means and medians answer different versions of “where is the center?” Standard deviation and IQR describe different kinds of spread, while quantiles and graphs reveal skew, multiple modes, floor or ceiling effects, and outliers.

No single statistic is sufficient. Compare mean with median, inspect quartiles and impossible values, and display the full distribution. An outlier is a case to investigate—not an automatic deletion.

The purpose is the typical level, spread, position, shape, and quality of the observed data. Interpret means, medians, standard deviations, and IQRs alongside distribution plots and missingness, because a single summary can conceal skewness, subgroups, and impossible values.

Means and medians answer different versions of “where is the center?” Standard deviation and IQR describe different kinds of spread, while quantiles and graphs reveal skew, multiple modes, floor or ceiling effects, and outliers.

No single statistic is sufficient. Compare mean with median, inspect quartiles and impossible values, and display the full distribution. An outlier is a case to investigate—not an automatic deletion.

The purpose is the typical level, spread, position, shape, and quality of the observed data. Interpret means, medians, standard deviations, and IQRs alongside distribution plots and missingness, because a single summary can conceal skewness, subgroups, and impossible values.

Means and medians answer different versions of “where is the center?” Standard deviation and IQR describe different kinds of spread, while quantiles and graphs reveal skew, multiple modes, floor or ceiling effects, and outliers.

No single statistic is sufficient. Compare mean with median, inspect quartiles and impossible values, and display the full distribution. An outlier is a case to investigate—not an automatic deletion.

The purpose is the typical level, spread, position, shape, and quality of the observed data. Interpret means, medians, standard deviations, and IQRs alongside distribution plots and missingness, because a single summary can conceal skewness, subgroups, and impossible values.

If employee commute time has a mean of 36 minutes and a median of 30, the right tail may be pulling the mean upward. Report the median, IQR, range, and histogram before describing 36 minutes as typical.

Report sample size and missingness alongside the primary estimate, comparison standard, uncertainty, and visible pattern. A descriptive result becomes inferential or causal only when the design supports that claim.

Treat the worked number as the beginning of interpretation. Read means, medians, standard deviations, and IQRs alongside distribution plots and missingness; then state what the sample supports without turning a descriptive pattern into a population or causal claim.

A defensible workflow is Classify variables → Audit quality → Compute summaries → Plot distributions → Report in context. Record the variable definitions, exclusions, transformations, denominators, and decision rules. Reproducibility begins with these choices, not with the final number.

Begin by auditing type, unit, coding, missingness, and summaries and plots appropriate to the variable scale. Defaults are only starting points; document every denominator, exclusion, transformation, and decision rule needed to reproduce the result.

Common uses include survey response overviews, clinical baseline tables, sales and operations audits, pre-model data checks. Before operational use, define how the same quantity will be recomputed for new data, how subgroup differences will be monitored, and what action the result is meant to support.

The purpose is the typical level, spread, position, shape, and quality of the observed data. Interpret means, medians, standard deviations, and IQRs alongside distribution plots and missingness, because a single summary can conceal skewness, subgroups, and impossible values.

Compare mean with median, inspect quartiles and impossible values, and display the full distribution. An outlier is a case to investigate—not an automatic deletion.

Strengths include Summarizes scale and shape quickly; Guides transformations and downstream model choice; Produces results in units stakeholders understand. Important limitations are Summaries can conceal subgroups and individual cases; Does not establish association, causation, or prediction; Accurate sample summaries do not fix selection bias.

Diagnostics are part of the result because a single summary can conceal skewness, subgroups, and impossible values. Compare reasonable alternatives and inspect the observations that drive the summary before treating one output as stable.

A useful descriptive summary answers where values cluster, how widely they vary, what shape they form, and what is missing. Recommended sequence: Classify variables → Audit quality → Compute summaries → Plot distributions → Report in context.

A complete report links the question, analysis population, summaries and plots appropriate to the variable scale, the primary result, and the diagnostic evidence. A reader should be able to reconstruct the same quantity from those decisions.