Home Statistical Dictionary Mean Imputation
Mean Imputation
A simple imputation method that replaces every missing value of a variable with that variable's observed sample mean, easy to implement but known to distort the variable's variance, covariances, and distributional shape.
In Plain English
Mean imputation is the simplest possible way to fill in a missing value: just plug in the average of whatever values you did observe for that variable. It's trivially easy to implement and guarantees the variable's overall mean stays unchanged, but it comes with a well-known and serious downside, artificially piling up a bunch of identical values (the mean) at the center of the distribution shrinks the variable's apparent variance below its true value, distorts its relationship (correlation) with other variables, and can make an otherwise normally shaped distribution look artificially spiked. Because of these distortions, mean imputation is now generally considered a poor default choice and mainly persists as a cautionary example of what not to do, or occasionally as a genuinely acceptable quick fix when only a tiny fraction of values are missing.
Definition
Mean imputation replaces every missing value of a variable with the sample mean computed from the variable's observed (non-missing) values, for every missing observation . While trivially simple and preserving the variable's overall observed mean exactly, mean imputation systematically underestimates the variable's true variance (every imputed value contributes zero deviation from the mean, artificially shrinking the sample variance below what it would be with genuinely observed data) and attenuates the variable's estimated correlation or covariance with every other variable in the dataset toward zero, since the imputed constant values contribute no genuine covariation; these well-documented distortions have made mean imputation a widely discouraged default in modern statistical practice, superseded by regression imputation (which at least preserves some relationship with other variables) or, preferably, multiple imputation (which additionally propagates the correct level of uncertainty into subsequent analyses).
Formula
Properties
- Mean imputation's variance-shrinking effect is mechanical and unavoidable, every imputed value equals exactly the mean, contributing zero to the sum of squared deviations, so the more values that are imputed, the more the variable's apparent variance is artificially compressed relative to its true value.
- Mean imputation attenuates estimated correlations and regression coefficients involving the imputed variable toward zero, because the imputed constant values carry no genuine relationship with other variables, a serious problem for any analysis that studies associations between variables, not just univariate summaries.
- Mean imputation is occasionally still considered an acceptable, low-cost shortcut when the proportion of missing data is very small and the analysis goal is limited to simple univariate summaries, but it is not recommended for any analysis involving variance estimates, correlations, or regression models, where its distortions can meaningfully bias results.
At a Glance