Gain insights into connecting discrete mathematics with programming. Explore variables, expressions, data structures, and algorithm design to enhance your problem-solving and implementation skills.

Discrete Mathematical Algorithms and Data Structures-02-02.png

momoexp4.tar.gz

java and C++

OnlyPython

OnlyJava

OnlyCplusplus

OnlyC

JavaLang3

Discrete mathematics is the basis of several popular algorithms. This course shows the discreteness of data structures and algorithms. It can benefit programmers with a non-CS background looking to strengthen their foundations by connecting theoretical concepts with practical programming scenarios.

The course starts with discussing relating discrete mathematics with algorithms and data structures. You will have examples demonstrating variables, conditional expressions, and arrays as basic building blocks of programming. Then, you will use classes and objects to define and implement linear data structures. You will also learn about the binary tree traversals and templates and the topics of time complexity, set difference, and rearranging the values in a string.

By the end of the course, you will have a strong grasp of algorithm design, data structure implementation, and overall problem-solving.

Programming Discrete Math Concepts for Beginners

# Mean, skewed mean, and median

**Skewness**, in general, is the measure of the asymmetry of a distribution. The skewed mean portrays biased behavior and is not a good sign. Let’s look at how the national income per capita of a country can be manipulated. We can easily skew it because it’s calculated based on the mean of a set of income inputs. Keeping that fact in mind, we always think the median is more trustworthy.



In one sense, this is true. In another, it's false.

Let's say we have a natural algorithm where we take the income of a nation of 10 people and make a set out of it. Eight of those 10 people have an income of less than $5. But the other two earn more than $150. The definition of a mean of a set tells us that calculating the average of those 10 inputs gives us an idea of the national income per capita.

As a result, the average income of those 10 people becomes nearly $45, and we know that the truth has been discarded. When 80% of people earn less than $5, it can't be true that the average income could be nearly $45.

Theoretically, choosing the median is more trustworthy because the median value comes to around $4, closer to the actual value.

Our question is, how trustworthy is the median? Can it not be skewed or manipulated at all? This section will sift through the myths to find the absolute truth.

> **Note:** Usually, in a set of positive integers where the numbers are increasing in ascending order, the mean and the median stay close.


# Mean and median for an odd number of values

Consider a set of unique and distinct positive integers. In the set of values in the example below, the mean and median are almost the same. We can check that by running the Java program below:

Learn about mean, skewed mean, and the role of the median.

Course Introduction

Programming Language and Boolean Algebra

Logical Expressions and Algorithms

Arrays and Discrete Mathematics

Classes, Objects, and Methods

Linear Data Structures

Tree, Algorithms, and Templates

Time Complexity

Propositional Logic

Combinatorics

Wrapping Up

Central Tendency of an Array

Mean, skewed mean, and median

Mean and median for an odd number of values