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In mathematics, a modal is a value that represents the most common or frequent observation in a given set of data. More specifically, the mode is the value that occurs most frequently in a dataset.

For example, consider the following set of data: 1, 2, 3, 3, 4, 5, 5, 5, 6. In this dataset, the value 5 occurs most frequently, three times, so the mode of this dataset is 5.

The mode is just one of several measures of central tendency used in statistics. Other measures of central tendency include the mean, which is the sum of all the values divided by the total number of values, and the median, which is the value that lies in the middle of the dataset when the values are arranged in order.

The mode is particularly useful when dealing with categorical data, such as the favorite color of a group of people or the type of car they drive.

Certainly! Here are a few highly-regarded math exercise books that are known for their challenging content:

"The Art of Problem Solving, Volume 1: The Basics" by Richard Rusczyk and Sandor Lehoczky. This book is designed to challenge and develop the problem-solving skills of students preparing for mathematical competitions. It covers topics such as algebra, counting and probability, number theory, and geometry.

"Putnam and Beyond" by Titu Andreescu and Razvan Gelca. This book contains a collection of challenging problems from the prestigious William Lowell Putnam Mathematical Competition, along with detailed solutions and explanations.

"Problem-Solving Strategies" by Arthur Engel. This book covers a wide range of mathematical topics, with a focus on problem-solving strategies and techniques. It includes hundreds of challenging problems, along with detailed solutions and commentary.

"The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics" by D. O. Shklarsky, N. N. Chentzov, and I. M. Yaglom. Originally written for Soviet high school students preparing for math competitions, this book contains a wide range of challenging problems in algebra, geometry, and number theory.

"Challenging Problems in Algebra" by Alfred S. Posamentier and Charles T. Salkind. This book contains over 200 challenging problems in algebra, along with detailed solutions and commentary. It covers topics such as equations and inequalities, polynomials, and functions.

I hope this helps, and happy studying!

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