Describe the workflow you want to enable

Today, if a user wants to centre features by the median and scale them by the median absolute deviation (MAD) they must hand-roll code like:
mad = 1.4826 * np.median(np.abs(X - np.median(X, axis=0)), axis=0)
X_scaled = (X - np.median(X, axis=0)) / mad

A built-in MedianAbsoluteDeviationScaler (or a statistic="mad" option on RobustScaler) would let them write a single, self-documenting line:
from sklearn.preprocessing import MedianAbsoluteDeviationScaler
X_scaled = MedianAbsoluteDeviationScaler().fit_transform(X)

That makes robust MAD scaling first-class, composable in pipelines, and reversible via inverse_transform().

Describe your proposed solution

Add a new transformer:
class MedianAbsoluteDeviationScaler(BaseEstimator, TransformerMixin):
with_centering: bool = True
with_scaling: bool = True
copy: bool = True
unit_variance: bool = False

# learned in fit
center_: ndarray
scale_: ndarray

Fit logic

1. center_ = np.median(X, axis=0) (if with_centering)

2. mad = np.median(np.abs(X - center_), axis=0) * 1.4826

3. Guard against zeros with float_eps, store in scale_.

transform() and inverse_transform() reuse the pattern from RobustScaler.

Docs / tests

• Unit tests for shape preservation, inverse-transform round-trip, and robustness to outliers.

• A short subsection in preprocessing.rst and a gallery example comparing Standard, Robust (IQR) and MAD scalers.

• Changelog bullet in whats_new/v1.5.rst.

I am happy to implement this within ~2 weeks.

Describe alternatives you've considered, if relevant

• Keep user-land recipes – fragments the ecosystem and lacks inverse_transform().

• Extend RobustScaler with statistic={"iqr","mad"} (default "iqr"). This also works, but changes a long-standing API and may require a deprecation cycle.

Additional context

• MAD is a well-known σ-consistent robust scale estimator, more efficient than IQR for symmetric heavy-tailed or Laplace-like data.

• Estimated code diff ≈ 20 LOC plus tests/docs – labelled “good first issue” size.

/cc @jnothman @glemaitre for initial design feedback — thanks!