Detecting and counting missing values in a dataset

The problem, from first principles

Real datasets are never as clean as the small, hand-picked arrays this curriculum's Math & Statistics tracks used, a survey respondent skips a question, a sensor drops a reading, a merge between two tables leaves some rows without a match. Before anything else, 03-mse-gradient, PCA, a Gaussian's MLE, all assume every entry of the data actually holds a real number, a single missing value silently poisons a mean, a covariance, a gradient, everywhere it touches.

The very first, unglamorous step of any real ML pipeline is knowing exactly where the gaps are, before deciding what to do about them (02-imputing-missing-values, the next question, is that "what to do about them" step). This question is purely about detection: finding missing entries reliably, a surprisingly easy thing to get subtly wrong.

From theory to code

Theory names the standard representation for a missing numeric value (np.nan) and flags the single most common bug in detecting it (== np.nan never works, by design). Implement a boolean mask using the correct tool, then column-wise counts and fractions built directly from that mask.

Implement missing_mask(x), missing_count_per_column(x) and missing_fraction_per_column(x) against that reasoning. The signatures and docstrings are already in the editor.

Constraints

• x is a 2D float array, (num_rows, num_columns), missing values represented as np.nan.
• Use np.isnan, never == np.nan (Theory explains exactly why the latter silently fails).
• missing_fraction_per_column returns fractions in [0.0, 1.0], one per column.

Hints

Open one at a time. Each gives away a little more than the last.