Question bank — Handling missing values (deletion, imputation strategies)

True on bias, but you still pay a price — deletion under MCAR loses statistical power (fewer rows = wider confidence intervals), it just doesn't tilt the estimates in any direction.

True — that's exactly why it feels safe. But it silently shrinks the variance, because every filled value sits at the center with zero spread.

False — "at random" is a misleading name. Under MAR the missingness is predictable from observed variables (e.g. younger people skip income), so ignoring it biases results unless you condition on those variables.

True — with all points as neighbours and uniform weights, the imputed value is just the average of every observed value in that feature, i.e. the global mean.

False — its main gift is honesty about uncertainty. Single imputation pretends the guess is a fact; multiple imputation spreads answers so downstream standard errors reflect that we were guessing.

False — forward fill carries the last past value into a gap, backward fill pulls the next future value backward. They agree only if the values bracketing the gap happen to be equal.

True — listwise deletion discards all the observed values in that row too, which is why it can waste enormous amounts of data when missingness is scattered.

False — imputing 60% means most of the column is invented, so it can inject a fake, low-variance signal. Often dropping the column (or adding only a missingness indicator) is the safer call.

The no-bias claim is fine, but if many features each have a little missingness, listwise deletion can compound into huge data loss (independent 5% gaps across 10 features drops ~40% of rows), hurting power badly.

The tight intervals are an artifact. Mean imputation pins values at the center and shrinks variance, so the model becomes overconfident — the reported precision is fake.

That leaks test information into training — the imputation statistic saw test rows. See 5.2.03-Data-leakage-prevention; the mean must be computed on the training set only and then applied to validation/test.

Categories have no meaningful mean — 1.7 isn't a color. Use the mode (most frequent category) or a dedicated "Missing" category instead.

Distance is dominated by the large-scale feature (Income), so neighbours are chosen almost entirely by income. Features must be scaled first (2.2.01-Feature-scaling-and-normalization) so each contributes fairly.

This is MNAR — missingness depends on the hidden income value itself. No observed-data method (KNN, MICE) can recover it, because the very people who'd anchor the high end are systematically absent.

Forward fill assumes values change slowly and carries the last pre-gap price flat for 30 days, badly underestimating during a strong trend. It only works for short gaps with high autocorrelation.

Variance measures spread around the mean, and every imputed point is placed exactly at the mean — contributing zero to the spread while inflating the count, so the average squared deviation can only shrink.

The median minimizes the sum of absolute deviations, so a few extreme values barely move it; the mean minimizes squared deviations, so outliers drag it strongly toward the tail.

Each pairwise correlation is computed on a different subset of rows (whichever pairs are both present), so the entries aren't mutually consistent, and the assembled matrix can violate the geometric constraints a real covariance structure must satisfy.

The first pass uses crude initial guesses (mean-fill), so the regression models are trained on partly-fake data. Each cycle re-trains using the improved values, letting the estimates and the feature relationships they rely on refine together until they stabilize.

The fact that a value was missing can itself be predictive (e.g. skipping a question signals something). The indicator lets the model separate "real value X" from "we guessed X", so imputation error doesn't silently corrupt the signal.

Mean imputation fills every blank with one constant, erasing any link to other features. Conditional methods predict the blank from the other features, so a correlation like Age–Income survives instead of being flattened.

Nothing meaningful — with no observed values there's no distribution and no neighbours to borrow from. Drop the column; only its (constant) missingness indicator carries any information.

There's no earlier observation to carry forward, so forward fill leaves it blank — you need backward fill (or another rule) to seed the leading gap.

There's nothing to average, so the neighbourhood must be expanded or those rows excluded; naively you'd get an undefined (division-by-zero-style) result with no valid values to weight.

Technically unbiased, practically useless — such tiny samples give estimates with enormous variance, so "no bias" is cold comfort. Prefer imputation to retain data. Relevant to a sane 3.1.02-Training-validation-test-split.

Don't impute the label — imputing the target manufactures the answer you're supposed to learn. Drop those rows from training or treat them as a semi-supervised problem instead.

Yes: aggressive low-variance imputation (mean fill) adds bias and false confidence, while flexible imputation (MICE) can lower bias but add variance/leakage risk — the same tension studied in 4.3.01-Bias-variance-tradeoff.