Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory.
People who do statistics are referred to as statisticians. They're particularly concerned with determining how to draw reliable conclusions about large groups and general events from the behavior and other observable characteristics of small samples. These small samples represent a portion of the large group or a limited number of instances of a general phenomenon.
Statistics are used in virtually all scientific disciplines, such as the physical and social sciences as well as in business, the humanities, government, and manufacturing. Statistics is fundamentally a branch of applied mathematics that developed from the application of mathematical tools, including calculus and linear algebra to probability theory.
In practice, statistics is the idea that we can learn about the properties of large sets of objects or events (a population) by studying the characteristics of a smaller number of similar objects or events (a sample). Gathering comprehensive data about an entire population is too costly, difficult, or impossible in many cases so statistics start with a sample that can be conveniently or affordably observed.