Quantitative Data Cleaning (QDC) is the use of statistical and other analytical techniques to detect, quantify, and correct data quality problems (or glitches). Current QDC approaches focus on addressing each category of data glitch individually. However, in real-world data, different types of data glitches co-occur in complex patterns. These patterns and interactions between glitches offer valuable clues for developing effective domain-specific quantitative cleaning strategies. In this paper, we address the shortcomings of the extant QDC methods by proposing a novel framework, the DEC (Detect-Explore-Clean) framework. It is a comprehensive approach for the definition, detection and cleaning of complex, multi-type data glitches. We exploit the distributions and interactions of different types of glitches to develop data-driven cleaning strategies that may offer significant advantages over blind strategies. The DEC framework is a statistically rigorous methodology for evaluating and scoring glitches and selecting the quantitative cleaning strategies that result in cleaned data sets that are statistically proximal to user specifications. We demonstrate the efficacy and scalability of the DEC framework on very large real-world and synthetic data sets.