Introduction to Math 444 Assignments

This sheet is about the regular individual assignments. there may be other written work stemming from group activity in class, etc., that is not covered by this description., what is the purpose of the written assignments.

As in most subjects, one masters math by doing. This means that all one's studying should involve drawing, working examples on paper, etc. But the written assignments provide the impetus to work out in polished form problems and constructions and proofs that develop understanding of geometry. They also provide a running assessment for student and instructor of what is going on in the class as to levels of understanding, areas of success, areas that need work, etc.

How often are assignments given?

In the beginning part of the course, shorter assignments will be due two or three times a week. This will gradually move to longer and less freqent assignments of about one per week. Students who don't like daily assignments are free to work ahead and treat assignments 1a, 1B, 1C, etc. as a single weekly assignment.

What kind of written assignments?

Assignment items to turn in will be of several forms.

  • Fairly routine exercises or constructions.
  • Problems to solve - some challenging and some less so. These can be construction problems, numerical or ratio problems, or existence of special geometrical relationships such as similarity, concurrence, etc.
  • Major or minor theorems to prove.
  • Physical models and drawings will sometines be assigned.
  • Investigations and open-ended problems. As the course moves on, such problems will appear on the assignments.

When are assignments due?

  • Assignments are due at the beginning of class on the due date .
  • No further writing is allowed once you walk into the room. Experience has shown that this leads to poor quality presentation, and sometimes to copying from other students.
  • Students may discuss problems outside of clas s, so long as each student writes up her/his work independently. However, "sharing" answers in the 10 minutes before class is too late for group reflection.
  • Late Assignments cause problem, so they may not be accepted. Often questions on an assignment will be answered during class. Also, the grading will sometimes be scheduled on the day the assignments are due. We do realize that nobody is perfect (least of all us) and that crises occur. If it happens that a student does not have an assignment on time once or even twice and asks to turn it in late, we will probably say OK, at least for partial credit. Once or twice also will not make or break one's grade. But don't make a habit of it.

Grading of Assignments will Follow several Strategies

We feel it is important that assignments be graded and feedback provided. However, some of the problems assigned in this course are not quickly graded. A bit of calculation will show that any problem that just takes 10 minutes per student will add up to about 5 or 6 hours of grading time. Thus the instructors will adopt a number of strategies to make grading possible. In some cases, students will self-report and then groups will discuss answers.

Quality of Presentation Counts

Since Math 444 is a course for students who intend to make a career explaining mathematics, the assignments turned in should be well-written as to language and thought. Answer in complete sentences. Use white space. Break up long explanations or proofs into paragraphs. Write neatly or word process. Presentation can definitely be part of the grade (plus or minus). Egregious examples of illegibility or bad writing will not be graded

What this means is that one should often write down a draft page for brainstorming and then write a completely new page to turn in.

Good and Bad News about Assignment Grades

This section gives two contradictory messages. The good news is that in Math 444 one does not have to get 100% to get a high grade. The problems are not routine, so perfection is not required, though a high standard is expected. The bad news (for some) is that skipping the homework and trying to get a high grade by being brilliant on the tests will not work because of the weight put on assignments. Only part of the course experience shows up on the tests, so high test grades alone do not ensure a high course grade in the absence of strong assignment grades.

  • Mastering the Art of Crafting an Engaging Introduction for Your Math Assignment

Math assignment, Introduction, Compelling, Strategies, Engaging

Dr. Mathew Johnson

Writing an introduction that captures the reader's attention while also setting the stage for the rest of the paper is one of the most difficult aspects of writing a mathematics assignment. Inviting readers into the world of numbers, formulas, and problem-solving, the introduction serves as a gateway. But the question still stands: How can you make sure that your introduction piques the reader's curiosity right away?

We will discuss efficient methods for crafting a strong introduction for your math assignment in this blog post. We will explore the art of involving your readers in mathematical ideas without boring them with technical language. You can write an introduction that compels your audience to read more by incorporating these techniques into your writing process.

A strong introduction achieves a number of goals. The topic is introduced, the assignment's context is given, and the main goals are spelled out in clear terms. Additionally, it establishes the topic's relevance and demonstrates your command of the subject. Additionally, a strong introduction should pique readers' interests and entice them to read on to learn the insights and defenses you will make in the sections that follow.

Mastering the Art of Crafting an Engaging Introduction for Your Math Assignment

Let's now examine a variety of efficient writing techniques that will enable you to create an introduction that not only demonstrates your subject knowledge and understanding but also enthralls your audience, causing them to want to learn more about your mathematical investigation.

Establish a Strong Hook First:

Every gripping story has a captivating introductory paragraph that grabs the reader's attention. It is comparable to the first spark that starts a wildfire. I should complete my math homework using the same logic. The introduction must be written so that it piques the reader's interest early on and keeps it throughout the entire assignment.

A strong hook doesn't necessarily need to be a lengthy tale or a challenging analogy. Simple hooks include provocative questions that pique readers' interest, unexpected facts about the subject at hand, and interesting anecdotes that resonate with the mathematical concept you're about to discuss. The idea is to catch the reader's interest, pique their curiosity, and encourage them to read more.

For instance, you might ask a question like, "Have you ever thought about how the ancient Greeks managed to determine the distances and heights without modern measuring tools?" before discussing the Pythagorean theorem. like "Did you know the Pythagorean theorem was discovered over 2000 years ago and is still being used in a variety of fields including construction, computer science, and even space travel?"

Give background and context information

Giving your readers some context is the second method for crafting a strong introduction for your math assignment. Here, your goal is to establish the scene by giving pertinent background information. Readers are better able to appreciate the assignment's content when they are familiar with the subject's underlying principles.

A brief history of the mathematical idea you're discussing, examples of it in real-world situations, or the importance of the issue you're trying to solve can all serve as examples of contextual information. You might, for instance, mention differential equations' crucial role in simulating natural phenomena like population dynamics, heat transfer, or the spread of diseases in a paper on differential equations.

Providing context also entails demonstrating the topic's relevance. Why should the reader be interested in this specific mathematical idea or issue? Why is it significant in the modern world? You should address questions like these in your introduction.

The purpose of the introduction is to direct the reader's attention as well as to draw them in. The subject of your assignment and your goals must be made clear from the outset.

This can be accomplished with a clear and succinct purpose statement or thesis statement. This is one or two sentences that briefly describe the main idea of your assignment. It gives a synopsis of the subject you're going to talk about or the issue you're going to try to solve. It keeps the reader interested and enables them to understand what to anticipate from your assignment.

A strong thesis statement is clear, concise, and debatable. Your thesis statement, for instance, might read, "This assignment aims to explore the properties of prime numbers and their crucial role in contemporary cryptographic systems," if the topic is prime numbers.

Give a brief description of your assignment:

Giving an overview of the assignment is one of the best ways to write a strong introduction for your math assignment. Here, you should lay out the assignment's overall structure and the expectations for each section for your reader.

Giving your readers a summary enables them to follow your thought process and comprehend the foundation of your argument or analysis. This keeps them interested and aids in their understanding of the logic behind your assignment.

An effective summary withholds certain details. Instead, it gives the reader a preview of what's to come, piquing their interest and encouraging them to read more of your assignment. For instance, you might write, "First, we'll look at the historical development of the idea of prime numbers, then we'll analyze them in great detail. Then, we'll look at how they're used in cryptography and talk about why those uses are important.

Stories have great power. They can help people understand and relate to difficult or abstract ideas. Making your mathematics assignment more interesting and memorable can be accomplished by incorporating a narrative into your introduction.

Mathematical storytelling need not always involve creating a make-believe story. It can be as easy as using a real-world situation to illustrate a mathematical concept, outlining the concept's development over time, or demonstrating how it has been applied in various fields.

For example, if you're writing about the Fibonacci sequence, you might begin with a narrative about how Leonardo of Pisa first learned about it through a problem involving the expansion of rabbit populations. You could then move on to talking about the sequence's mathematical properties and how it is frequently used in everything from computer algorithms to art and architecture.

Utilize Language Sensibly:

The way you write your introduction has a big impact on how interesting it is. Even though numbers, symbols, and equations make up the majority of mathematics, how you present these concepts in your writing can significantly affect your reader's interest and comprehension.

Your writing should be engaging, clear, and concise. Avoid using technical terms and jargon that your readers might not understand. Instead, describe mathematical ideas in straightforward, understandable language. Make your writing more dynamic and engaging by using the active voice and verb tenses.

Additionally, change up your sentence structure to add interest to your writing. Short, simple sentences can make your writing seem choppy and disjointed, while long, complex sentences can perplex your reader. You can make your writing more rhythmic and interesting by alternating between short and long sentences.

Review and Improve:

It's critical that the introduction is well-written and error-free because it's frequently the first thing your reader sees. Here's where editing and polishing are useful.

After you've finished writing your introduction, give it a thorough reading. Search for any spelling or grammar mistakes, awkward language use, or vague statements. Make sure your introduction establishes the tone for the remainder of your assignment and smoothly transitions from one idea to the next.

If necessary, make revisions to your introduction's clarity, coherence, and overall quality. This might entail rephrasing sentences, changing the order in which your ideas are presented, or even completely rewriting your introduction.

Your introduction needs to be improved over time. Throughout the writing process, you should repeat this action. You might discover that your introduction needs to be updated as your assignment changes.

Writing an engaging introduction for your math assignment entails using a strong hook to draw the reader in, giving context and background information, stating your assignment's purpose clearly, giving an overview of the assignment, using the storytelling technique, using language effectively, and revising and refining your introduction. Using these techniques, you can write an introduction that piques the interest of your reader and encourages them to read more of your assignment.

Conclusion:

The impact of your work can be greatly increased by developing a strong introduction for your math assignment. By using a variety of techniques, you can grab the attention of your audience right away and set the stage for an assignment that is successful.

This blog post has examined various methods for crafting an engaging introduction for your math assignment. We started out by highlighting how crucial it is to comprehend your audience and adjust your introduction to meet their needs and expectations. The importance of clearly stating your assignment's purpose and objectives was then covered in order to help readers understand its relevance and potential impact.

The effectiveness of storytelling and narrative devices in holding readers' attention was then discussed. You can make your introduction interesting and relatable by relating your mathematical ideas to historical events or current affairs.

As a result, crafting a strong introduction for your math assignment necessitates careful consideration, planning, and focus on the small print. By utilizing the techniques described in this blog post, you can write an introduction that not only demonstrates your knowledge and expertise but also enthralls your audience, creating the foundation for an assignment that is successful and significant.

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Mastering the art of crafting an engaging introduction for your math assignment submit your assignment, attached files.

Introduction to Algebra

Algebra is great fun - you get to solve puzzles!

What is the missing number?

OK, the answer is 6, right? Because 6 − 2 = 4 . Easy stuff.

Well, in Algebra we don't use blank boxes, we use a letter (usually an x or y, but any letter is fine). So we write:

It is really that simple. The letter (in this case an x) just means "we don't know this yet", and is often called the unknown or the variable .

And when we solve it we write:

Why Use a Letter?

  • it is easier to write "x" than drawing empty boxes (and easier to say "x" than "the empty box").
  • if there are several empty boxes (several "unknowns") we can use a different letter for each one.

So x is simply better than having an empty box. We aren't trying to make words with it!

And it doesn't have to be x , it could be y or w ... or any letter or symbol we like.

How to Solve

Algebra is just like a puzzle where we start with something like "x − 2 = 4" and we want to end up with something like "x = 6".

But instead of saying " obviously x=6", use this neat step-by-step approach:

  • Work out what to remove to get "x = ..."
  • Remove it by doing the opposite (adding is the opposite of subtracting)
  • Do that to both sides

Here is an example:

To remove it, do the opposite , in this case add 2

Do it to both sides

Which is ...

Why did we add 2 to both sides?

To "keep the balance"....

Just remember this:

See this in action at the Algebra Balance Animation .

Another Puzzle

What we want is an answer like "x = ...", but the +5 is in the way of that! We can cancel out the +5 with a −5 (because 5−5=0)

Have a Try Yourself

Now practice on this Simple Algebra Worksheet and then check your answers. Try to use the steps we have shown you here, rather than just guessing!

Try the questions below, then read Introduction to Algebra - Multiplication

Browse Course Material

Course info, instructors.

  • Dr. Jeremy Orloff
  • Dr. Jennifer French Kamrin

Departments

  • Mathematics

As Taught In

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  • Probability and Statistics

Learning Resource Types

Introduction to probability and statistics, exams with solutions.

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How Do You Write An Introduction to An Assignment? (With Examples of Assignment Introduction)

How Do You Write An Introduction to An Assignment? (With Examples of Assignment Introduction)

Whether you’re in school or college, you can’t avoid academic writing. It’s essential to write assignments to complete your course and graduate from it successfully. As a student, you must have discussed your assignments and academic writing projects with your friends, seniors, and mentors. Most assignments aim to gauge students’ knowledge about the subject and how well they express themselves while solving a problem or presenting their ideas and opinions. 

Writing an assignment introduction paves the way of how a reader or a teacher perceives an entire assignment and can be considered a face of an assignment. Our assignment help experts are here to offer you the best tips on how to write an assignment introduction.

How to introduce an assignment?

As they say – well begun is half done. Our assignment writers agree and believe in this adage. Countless times, you must have skipped a video because you didn’t find its first 5 seconds interesting or catchy enough to hold your attention. Or you must have chosen to watch a movie because you liked its trailer. Similarly, an introduction is a bait for your readers to read your assignment, report, essay, or dissertation with interest. It’s the first impression you will cast on your professors.

GoAssignmentHelp assignment assistance experts who handle hundreds of ‘ do my assignment ’ requests every month share that most students find it difficult to write an introductory paragraph that is clear and concise. Here, we will simplify the process of writing an introduction for the given assignment for you.

A good introduction to an assignment example is always one that gives a clear idea to the readers about what your assignment topic is or what are you going to talk about in the rest of the copy. An old trick is to talk about general ideas about the topic and narrow down your discussion to the specific problem or aspect of the topic you are going to discuss.

An introduction is a guide to your assignment. It should include:

  • Some background about the assignment topic, and
  • An outline of opinions and arguments you are going to present.

An assignment introduction example or two can perhaps give you a better idea of what needs to be done.

Contact our experts for a powerful introduction to your assignment!

Different Elements of the Introduction of an Assignment

Before we delve into introduction assignment examples, you must understand elements that constitute a good introduction to an assignment:

  • Importance of an assignment topic or the purpose of essay writing or dissertation writing,
  • Keywords from the essay topic or assignment question to show how well you have understood the writing task,
  • What is the proper definition of the assignment topic or the key terms it contains – and what can readers expect from the written piece,
  • Student’s reason for writing on the topic. You may get some hints on it from what your teacher mentions on the assignment list or what he/she shares in the class about it,
  • A quick bird-eye’s view of your approach on the assignment topic,
  • Key points of your discussion that you will elaborate in the body of the paper,
  • Quick discussion on previous studies, articles, news, or other works on the topic, and
  • What are some of the limitations of the topic?

You don’t have to include everything in an introduction – just enough to make your reader or teacher curious about the topic. The following example of introduction for assignment starts with a central issue, goes on to add some background, and then, presents the argument the assignment writer elaborated further in the essay. It ends with a smooth transition statement meant to transport the reader to the next part of the essay.

write introduction for an assignment- GoAssignmentHelp

How to write an introduction for a report?

When you are stuck with how to start a writing assignment, writing an introduction can solve most of your problems. Different types of assignments have different types of introductory paragraphs. The student introduction assignment example mentioned above is suitable for an essay. Now, we will see an example of an assignment introduction for a report.

write introduction for a report GoAssignmentHelp

Note that this kind of assignment introduction contains:

  • A Background: A quick mention of previous studies and articles on the topic gives your teachers a perspective on what is already known about the topic, key issues that need to be addressed, and what you are going to discuss in your report.
  • An Objective or a Thesis Statement: A hypothesis or a thesis statement is based on earlier findings and previous works on the topic. It provides a structure to your report. Check how the assignment writing service expert has mentioned the purpose of the study and a quick outline of the entailing discussion in one statement – right after the background.
  • Importance of the Study: If you’ve not already highlighted the importance of the study yet, you may include a few more lines to mention the gaps in the topic research and how your paper is going to bridge those gaps.

Consult our assignment writers for fresh ideas and introduction samples for any type of assignment!

How to write an introduction for a thesis or a dissertation?

Most students come across a dissertation or a thesis writing task in their Master’s or Ph.D. degree course. A few need to write a dissertation in their Bachelor’s degree programs. But since they are new to dissertation writing, they wonder how to write an introduction for an assignment that is much longer than a normal essay writing task they have encountered yet. The truth is that writing an introduction for a dissertation is not much different from writing an introduction for an essay or a report (depending on the nature of your dissertation topic).

You can use the points mentioned above to learn how to write a good assignment introduction longer than a paragraph. The ideal length for a dissertation introduction is 5-7% of the total length of your research paper. Most Master’s dissertations are around 15,000 to 50,000 words long – depending on the subject area. Hence, their introductions can have anywhere between 750 and 2,500 words.

We provide affordable writing services for students who find it difficult to paraphrase their ideas succinctly in an introduction. Besides the general introduction, we also help students write an introduction for each chapter, which will help you include more references throughout your research paper. It will also help research paper writers to remind their readers of the purpose of the dissertation again and to retain their interest.

You must also read :  Tips and Examples of The Conclusion Section of Assignments

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Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics. However, there are two important and basic ideas involved in statistics; they are  uncertainty and variation.  The uncertainty and variation in different fields can be determined only through statistical analysis. These uncertainties are basically determined by the probability that plays an important role in statistics. 

What is Statistics?

Statistics is simply defined as the study and manipulation of data. As we have already discussed in the introduction that statistics deals with the analysis and computation of numerical data. Let us see more definitions of statistics given by different authors here.

According to Merriam-Webster dictionary , statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.

According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.

Statistics – Download PDF

Statistics examples.

Some of the real-life examples of statistics are:

  • To find the mean of the marks obtained by each student in the class whose strength is 50. The average value here is the statistics of the marks obtained.
  • Suppose you need to find how many members are employed in a city. Since the city is populated with 15 lakh people, hence we will take a survey here for 1000 people (sample). Based on that, we will create the data, which is the statistic.

Basics of Statistics

The basics of statistics include the measure of central tendency and  the measure of dispersion. The central tendencies are  mean, median and mode  and dispersions comprise variance and standard deviation. 

Mean is the average of the observations. Median is the central value when observations are arranged in order. The mode determines the most frequent observations in a data set.

Variation is the measure of spread out of the collection of data. Standard deviation is the measure of the dispersion of data from the mean. The square of standard deviation is equal to the variance.

Mathematical Statistics

Mathematical statistics is the application of Mathematics to Statistics, which was initially conceived as the science of the state — the collection and analysis of facts about a country: its economy, and, military, population, and so forth.

Mathematical techniques used for different analytics include mathematical analysis, linear algebra, stochastic analysis, differential equation and measure-theoretic probability theory.

Types of Statistics

Basically, there are two types of statistics.

Descriptive Statistics

Inferential Statistics

In the case of descriptive statistics, the data or collection of data is described in summary. But in the case of inferential stats, it is used to explain the descriptive one. Both these types have been used on large scale.

The data is summarised and explained in descriptive statistics. The summarization is done from a population sample utilising several factors such as mean and standard deviation. Descriptive statistics is a way of organising, representing, and explaining a set of data using charts, graphs, and summary measures. Histograms, pie charts, bars, and scatter plots are common ways to summarise data and present it in tables or graphs. Descriptive statistics are just that: descriptive. They don’t need to be normalised beyond the data they collect.

We attempt to interpret the meaning of descriptive statistics using inferential statistics. We utilise inferential statistics to convey the meaning of the collected data after it has been collected, evaluated, and summarised. The probability principle is used in inferential statistics to determine if patterns found in a study sample may be extrapolated to the wider population from which the sample was drawn. Inferential statistics are used to test hypotheses and study correlations between variables, and they can also be used to predict population sizes. Inferential statistics are used to derive conclusions and inferences from samples, i.e. to create accurate generalisations.

Statistics Formulas

The formulas that are commonly used in statistical analysis are given in the table below.

Summary Statistics

In Statistics, summary statistics are a part of descriptive statistics (Which is one of the types of statistics), which gives the list of information about sample data. We know that statistics deals with the presentation of data visually and quantitatively. Thus, summary statistics deals with summarizing the statistical information. Summary statistics generally deal with condensing the data in a simpler form, so that the observer can understand the information at a glance.  Generally, statisticians try to describe the observations by finding:

  • The measure of central tendency or mean of the locations, such as arithmetic mean.
  • The measure of distribution shapes like skewness or kurtosis.
  • The measure of dispersion such as the standard mean absolute deviation.
  • The measure of statistical dependence such as correlation coefficient.

Summary Statistics Table

The summary statistics table is the visual representation of summarized statistical information about the data in tabular form.

For example, the blood group of 20 students in the class are O, A, B, AB, B, B, AB, O, A, B, B, AB, AB, O, O, B, A, AB, B, A.

Thus, the summary statistics table shows that 4 students in the class have O blood group, 4 students have A blood group, 7 students in the class have B blood group and 5 students in the class have AB blood group.  The summary statistics table is generally used to represent the big data related to population, unemployment, and the economy to be summarized systematically to interpret the accurate result.

Scope of Statistics

Statistics is used in many sectors such as psychology, geology, sociology, weather forecasting, probability and much more. The goal of statistics is to gain understanding from the data, it focuses on applications, and hence, it is distinctively considered as a mathematical science.

Methods in Statistics

The methods involve collecting, summarizing, analyzing, and interpreting variable numerical data. Here some of the methods are provided below.

  • Data collection
  • Data summarization
  • Statistical analysis

What is Data in Statistics?

Data is a collection of facts, such as numbers, words, measurements, observations etc.

Types of Data

  • Example- She can run fast, He is thin.
  • Example- An Octopus is an Eight legged creature.

Types of quantitative data

  • Discrete data- has a particular fixed value. It can be counted
  • Continuous data- is not fixed but has a range of data. It can be measured.

Representation of Data

There are different ways to represent data such as through graphs, charts or tables. The general representation of statistical data are:

  • Frequency Distribution

Measures of Central Tendency

In Mathematics, statistics are used to describe the central tendencies of the grouped and ungrouped data. The three measures of central tendency are:

All three measures of central tendency are used to find the central value of the set of data.

Measures of Dispersion

In statistics, the dispersion measures help interpret data variability, i.e. to understand how homogenous or heterogeneous the data is. In simple words, it indicates how squeezed or scattered the variable is. However, there are two types of dispersion measures, absolute and relative. They are tabulated as below:

Skewness in Statistics

Skewness, in statistics, is a measure of the asymmetry in a probability distribution. It measures the deviation of the curve of the normal distribution for a given set of data. 

The value of skewed distribution could be positive or negative or zero. Usually, the bell curve of normal distribution has zero skewness.

ANOVA Statistics

ANOVA Stands for Analysis of Variance. It is a collection of statistical models, used to measure the mean difference for the given set of data.

Degrees of freedom

In statistical analysis, the degree of freedom is used for the values that are free to change. The independent data or information that can be moved while estimating a parameter is the degree of freedom of information. 

Applications of Statistics

Statistics have huge applications across various fields in Mathematics as well as in real life. Some of the applications of statistics are given below:

  • Applied statistics, theoretical statistics and mathematical statistics
  • Machine learning and data mining
  • Statistics in society
  • Statistical computing
  • Statistics applied to the mathematics of the arts

Video Lesson

Grade 11 statistics.

maths assignment introduction

Statistics Related Articles

Hope this detailed discussion and formulas on statistics will help you to solve problems quickly and efficiently. Learn more Maths concepts at BYJU’S with the help of interactive videos.

Frequently Asked Questions on Statistics

What exactly is statistics.

Statistics is a branch that deals with the study of the collection, analysis, interpretation, organisation, and presentation of data. Mathematically, statistics is defined as the set of equations, which are used to analyse things.

What are the two types of statistics?

The two different types of statistics used for analyzing the data are:

  • Descriptive Statistics: It summarizes the data from the sample using indexes
  • Inferential Statistics: It concludes from the data which are subjected to the random variation

What is Summary Statistics?

How is statistics applicable in maths.

Statistics is a part of Applied Mathematics that uses probability theory to generalize the collected sample data. It helps to characterize the likelihood where the generalizations of data are accurate. This is known as statistical inference.

What is the purpose of statistics?

What is the importance of statistics in real life.

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