#### Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Preface
Basic Packages, Functions, and Concepts
Free Chapter
Mathematical Plotting with Matplotlib
Working with Randomness and Probability
Geometric Problems
Finding Optimal Solutions
Miscellaneous Topics
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One of the central problems in statistics is to make estimations—and quantify how good these estimations are—of the distribution of an entire population given only a small (random) sample. A classic example is to estimate the average height of all the people in a country when measuring the height of a randomly selected sample of people. These kinds of problems are particularly interesting when the true population distribution, by which we usually mean the mean of the whole population, cannot feasibly be measured. In this case, we must rely on our knowledge of statistics and a (usually much smaller) randomly selected sample to estimate the true population mean and standard deviation, and also quantify how good our estimations are. It is the latter that is the source of confusion, misunderstanding, and misrepresentation of statistics in the wider world.

In this recipe, we will see how to estimate the population mean...