Algorithmic decision-making systems are increasingly deployed in consequential domains such as employment screening, credit allocation, law enforcement risk assessment, and healthcare triage. While these systems promise efficiency and objectivity, mounting empirical evidence demonstrates that they can perpetuate — and in certain cases amplify — historical patterns of discrimination against protected groups, raising fundamental human rights concerns. This paper presents a systematic empirical investigation of algorithmic bias using the UCI Adult Income dataset (n = 48,842), a benchmark widely used in the fairness literature because it encodes real-world socioeconomic inequalities. We train and evaluate four machine learning classifiers — Logistic Regression, Decision Tree, Random Forest, and Gradient Boosting — and rigorously quantify bias across gender and race using three complementary fairness metrics: Demographic Parity Difference (DPD), Equalized Odds Difference (EOD), and Demographic Parity Ratio (DPR). Three bias mitigation techniques are then applied and compared: two post-processing ThresholdOptimizer variants targeting Demographic Parity and Equalized Odds constraints respectively, and an in-processing Exponentiated Gradient reduction with a Demographic Parity constraint. Results reveal that all baseline classifiers exhibit severe gender-based selection disparities, with Demographic Parity Ratios ranging from 0.18 to 0.38 — far below the 0.8 adverse impact threshold — despite achieving strong predictive accuracy between 82.4% and 87.7%. Post-processing mitigation achieves a 94.4% DPD reduction (from 0.1473 to 0.0083) for the Demographic Parity-constrained ThresholdOptimizer, pushing the DPR to 0.977, at an accuracy cost of 7.4 percentage points. In-processing via Exponentiated Gradient yields a 92.0% DPD reduction against its logistic regression baseline (from 0.1707 to 0.0136) with a substantially smaller accuracy cost of only 1.9 percentage points, though with a different fairness profile. These findings indicate that substantial fairness improvement is technically feasible on this benchmark. All disparity and mitigation estimates are accompanied by bootstrap 95% confidence intervals and five-fold cross-validation, both of which confirm that the baseline disparities and their reduction under mitigation are statistically robust rather than artefacts of a particular data partition. We interpret the observed statistical disparities in the light of human rights and regulatory debates while emphasising that establishing discrimination in a legal sense would require contextual evidence beyond the scope of a technical audit.