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The field of statistics is the study of methods to collect, analyze, describe and present data. Statistics is a branch of mathematics. The field is concerned with questions like what does the data mean.
Machine learning can be well understood in a statistical framework where learning from training data is taken as a modelling of the structures and relationships in the data. As such, statistical modelling methods are adopted in machine learning but machine learning includes more than statistical modelling methods.
Artificial Intelligence
The field of artificial intelligence is the study and construction of computational systems that do things that humans can do or that do things that we think are intelligent. For example humans can move around an environment, understand what they see and understand language they read and hear, and we have corresponding subfields of robotics, computer vision and natural language processing. A grand master chess champion is considered intelligent, and so chess playing intelligent systems are created. Artificial Intelligence is a branch of computer science. The field is concerned with questions of what is intelligence and how to create intelligences.
Learning is a feature of an intelligent system. As such, Machine Learning is considered a branch of artificial intelligence concerned with the study and construction of systems that are capable of learning.