Mathematics (sometimes shortened to maths or math), is the study of numbers, shapes and patterns. Mathematicians are people who learn about and discover such things in mathematics. Mathematics is useful for solving problems that occur in the real world, so many people besides mathematicians study and use mathematics. Today, mathematics is needed in many jobs. Business, science, engineering, and construction need some knowledge of mathematics.
Mathematicians solveproblems by using logic. Mathematicians often use deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reason something is true is just as important as the fact that it is true. Using deduction is what makes mathematical thinking different from other kinds of thinking.
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Statistics is the science of data. It enables the collection, analysis, understanding, and presentation of data. It helps in the study of many other fields, such as medicine, economics, psychology, and marketing. Someone who works in statistics is called a statistician.
Statistics provides ways to get the data needed for a study without waste, such as surveys and controlled experiments. Once the data has been collected, there are two basic ways that data can be analysed:
First, statistics can help describe the data. This is known as descriptive statistics. Descriptive statistics is about finding meaningful ways to summarize the data, because it is easier to use the "summary" than having to use the whole set of data all the time. Summarizing the data also allows to find common patterns. In statistics, such patterns are called probability distributions. The basic idea is to look at the results of an experiment, and look at how the results are grouped.
Once the results have been summarized and described they can be used for prediction. This is called Inferential Statistics. As an example, the size of an animal is dependent on many factors. Some of these factors are controlled by the environment, but others are by inheritance. A biologist might therefore make a model that says that there's a high probability, the offspring will be small in size if the parents were small in size. This model probably allows to predict the size in better ways than by just guessing at random.