05 Jul How Maths Helps to Do Statistics Homework Easily?
Over the years, a very common question that arises in the teaching and learning industry is whether or not mathematics and statistics are related. Well, that ought to be discussed in details under the next subhead. As of now, this information will be revolving around how a student could use his or her mathematical concepts in the field of statistics. Yes, indeed a lot of mathematics is required in the field of statistics and individuals in the field of statistics certainly, cannot go about their work if they don’t have any sort of idea regarding mathematics.
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Are mathematics and statistics related?
As you go for higher studies, mathematics and statistics are classified as two different subjects. However, in lower classes, statistics is considered to be a part of mathematics. Whether or not statistics is a part of mathematics, is quite arguably a topic. However, the fact cannot be ignored that both the subjects are interlinked in various ways.
If you compare both subjects, you ought to find out that concepts and theorems of both these subjects are interrelated, and theorems of one subject are essentially needed in another. For example, simple arithmetic operations such as additions, subtraction, division, multiplication, average, percentage, etc. are an integral part of mathematics. These simple arithmetic operations find a wide range of applications as far as statistics is concerned.
Statistics is defined as the mathematical modelling of a certain observable and measurable phenomenon. Statistics mainly makes use of stochastic models in order to understand a phenomenon thoroughly and in turn analyzed the data that is collected from this model. Well, it doesn’t end here.
After the data has been collected, the various parameters of the model are estimated, and the hypotheses are tested. These steps are crucial as numerous critical real time projects are based on the analysis that the team of statistical experts provide.
There are various theoretical and practical properties that must be analyzed with the help of standard notations. For this, it is extremely important for an individual to have a firm background in mathematics as most of these analysis require a lot of calculations.
The act of applying mathematical ideas, concepts and theories in the field of statistics is often referred to as mathematical statistics. This field is an ever emerging one with new ideas and concepts being introduced every day. This is because the different students create on a certain measurable phenomenon are quite different from one another as the view point of different individuals are different.
Hence, the most efficient and optimum model is selected among these. The major mathematical techniques that are used in the field of statistics are listed below:
- Mathematical analysis:
Mathematical analysis is defined as the branch of mathematics that deals with various limits, limiting values and the theories that are related to these limiting values. This includes differentiation, measure, integration, analytic functions and infinite series. Most of these theories are based on real as well as complex functions and numbers.
These techniques have mostly evolved from the field of calculus, which forms a major portion of the mathematics syllabus in the higher standards. Without the help of these theorems in calculus, it is not possible to carry out the statistical analysis of data properly. These theorems can be applied to any space-time variations.
- Linear Algebra:
Linear algebra as you must know forms a major portion of mathematics. The mathematics of the 5th to the 8th standard under most boards consists of a major portion of linear algebra. This branch predominantly deals with vector space and the linear mapping between such vector space. This field is a vast one, and several operations in statistics cannot be carried out without the help of linear algebra.
It is majorly concerned about properties that are related to the various vector spaces. It also includes the study of sub spaces, lines and planes. If a set of points with coordinates exists such that it satisfies a linear equation, then the collection of these points ought to form a hyper plane. This hyper plane is mostly considered in space which has n dimensions.
- Stochastic Analysis:
Stochastic analysis often referred to as stochastic calculus is the branch of mathematics that details with the various stochastic processes that go on around us. It makes away of various theories of integration to be defined for a set of finite integrals for various stochastic processes.
This form of analysis is used mostly for the modelling of system with a random behavior, i.e. for systems that do not follow any regular course as far as the variations of its parameters are concerned. Under such circumstances, stochastic analysis is perhaps the best possible solution. For example, one of the most common stochastic processes on which calculus is applied is the Wiener process. This process is mostly used for the modelling of Brownian motion.
- Differential Equation:
Differential equations form a major portion of the mathematics as one goes for higher studies. It is the mathematical equations that form the relationship of a particular function with derivatives. At the time of application, the functions mostly represent physical quantities whereas the derivatives represent the rate at which a small change is brought about.
A differential equation is one which defines the relationship between the two. These are extremely common in the fields of engineering, physics, economics, etc. In pure mathematics, differential equation mostly deals with a set of functions that satisfy the given equation.
To be very precise, the simplest differential equation is solvable for a finite set of values. Most of the equations produce a set of conditions that are satisfied by the roots of the equation. If a formula is not available for the solution, then various online applications can be used in order to find an approximate solution. For reasons, you can take online academic help to complete your assignments on time.
- Theoretic Probability Theory:
Mathematics describes probability of a certain outcome to occur while considering a specific event as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability has a wide range of applications as far as mathematics is concerned and an even wider range of applications in the field of statistics.
The probability distribution curve is an integral part of any proper statistical analysis. Without it, a statistical analysis cannot be considered to be a standard one.