Detecting outliers with IQR and z-score

The problem, from first principles

02-imputing-missing-values assumed missing values are cleanly flagged as NaN, easy. Bad data is rarely that considerate: a sensor briefly malfunctions and reports a temperature of 9999, a data-entry error turns "$50,000" into "$50,000,000", nothing marks these as wrong, they're just numbers sitting in the dataset, quietly distorting every mean, variance, and gradient that touches them. Before you can trust a model built on real data, you need a systematic way to flag "this number looks implausible," not just eyeball a scatter plot and hope.

Two standard, complementary tools do this: the IQR method (based on percentiles, robust to extreme values) and the z-score method (based on standard deviations, but with a real weakness this question makes visible). Understanding both, and where each one fails, is a genuinely practical skill for any real dataset.

From theory to code

Theory gives both detection rules directly: IQR flags anything outside a fixed multiple of the interquartile range beyond Q1/Q3, z-score flags anything more than a fixed number of standard deviations from the mean.

Implement detect_outliers_iqr(x, k=1.5) and detect_outliers_zscore(x, threshold=3.0) against that reasoning. The signatures and docstrings are already in the editor.

Constraints

• Both functions return a boolean mask, same shape as x, True where a value is flagged.
• detect_outliers_iqr uses np.percentile for Q1 (25th) and Q3 (75th).
• detect_outliers_zscore uses the population std (np.std's default ddof=0).

Hints

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