Jyoti Luhaniwal

 Statistics helps us understand data and make informed decisions. However, collecting data is not enough. We often need to determine whether the information we observe provides sufficient evidence to support a particular claim. This is where hypothesis testing becomes useful. Hypothesis testing is a statistical method used to examine claims about a population using information obtained from a sample. It is widely applied in education, healthcare, business, economics, and scientific research. What Is Hypothesis Testing? Hypothesis testing is a procedure that helps us decide whether a claim about a population should be rejected based on sample data. For example, suppose a university claims that the average marks of its students in a mathematics examination are 70. We can select a sample of students, calculate their average marks, and examine whether the sample provides sufficient evidence to question the university's claim. The main purpose is not to prove a claim with comp...

Ever wondered why so many things in statistics end up looking like a bell curve? Well, the answer is in the Central Limit Theorem (CLT), which is referred to as the most important theorem in statistics, and it’s really amazing how it works. What Does the CLT Say? In simple terms: Whenever we have many random samples from a certain population and find out the average of each of the samples, the distribution of the averages obtained will become normally distributed in spite of the form of the original distribution, as long as the size of the samples is large enough. This means that regardless of how weird the original distribution looks like, the average of many samples will form a bell shape.. The Formal Version Let's say that we have a population whose average and spread are known. In this case, when taking samples of a certain size at random from such a population, we can assume that the sampling distribution of the average will be normal and has the following prop...

 Statistics helps us understand patterns hidden inside data. One of the most important and widely used patterns in statistics is the Normal Distribution . It appears in many areas, including education, healthcare, business, science, engineering, and computer science. Understanding the normal distribution helps us describe data, compare observations, and make useful predictions. What is a Normal Distribution? A normal distribution is a type of distribution that has a characteristic bell shape curve. Many data values lie near the center, whereas few data values lie farther from the center. Take an instance where we consider the height of the students in the whole population; many of them will have heights equal to the average, whereas few of them will have either very small or very large heights. In such a scenario, when the heights are plotted on a graph, they will form a bell shape. This is an example of normally distributed data. The mean (μ) denotes the average of the val...

 Machine Learning (ML) is one of the main components of the current technological environment. ML is used in various applications such as recommendation systems, fraud detection, speech recognition, diagnostic systems, autonomous vehicles, and others. Machine learning is commonly perceived as a combination of programming, algorithms, and big data. Yet, one of the fundamental elements that enable machine learning is statistics. Statistics allows machine learning models to comprehend the nature of the data, discover patterns in it, cope with uncertainty, and make predictions. In other words, machine learning learns data, whereas statistics is helpful to interpret what machine learning learned. Understanding Data Machine learning models are as good as the data that is used in them. In the real world, data is usually incomplete, noisy, has variability, and even includes outliers. To use the machine learning algorithm for processing, it is important to know the nature of the data ...

For many students, linear algebra feels like one of those subjects that lives only inside textbooks—full of matrices, vectors, and abstract operations that seem far removed from real life. Questions like “Where will I ever use this?” are common in classrooms. But the reality is quite the opposite. Linear algebra is not just a theoretical subject—it is one of the most widely used mathematical tools in modern careers , often working quietly behind the scenes in technologies we use every day. More Than Just Numbers and Symbols At its core, linear algebra is about understanding relationships and transformations . Vectors represent quantities with direction and magnitude, while matrices help us organize and manipulate data efficiently. Although these ideas may seem abstract, they form the foundation of many real-world systems. Once you move beyond the classroom, you begin to see that linear algebra is less about solving equations and more about modeling and interpreting complex p...

In many mathematical problems, especially in engineering and applied sciences, we often come across equations that are not easy to solve directly. These equations may be nonlinear, complicated, or simply too difficult to rearrange into a clean, exact solution. In such cases, instead of trying to find a perfect answer, we rely on numerical methods that help us get very close to the correct value. One of the most important and widely used techniques for this purpose is the Newton–Raphson method . It is known for its speed, accuracy, and practical usefulness in solving real-world problems. Why Do We Need This Method? In basic mathematics, we are used to solving equations like quadratic or linear expressions where formulas are available. However, real-life problems are rarely that simple. For example, equations involving trigonometric functions, exponential terms, or complex system behavior cannot always be solved analytically. This creates a need for methods that can approximate s...