real life problems that can be solved using statistics

7 Practical Solutions That Streamline Statistical Thinking

Thinking about statistics can be challenging for several reasons. Firstly, statistics involves abstract concepts and mathematical formulas that may be unfamiliar or difficult to grasp initially. The field requires logical thinking, problem-solving skills, and the ability to interpret and apply statistical methods correctly.

Additionally, statistics often deals with uncertainty and variability, making it necessary to understand concepts such as sampling error, probability, and hypothesis testing.

Lastly, statistical analysis often involves working with large datasets, complex software tools, and specialized techniques, which can add another layer of complexity. With practice, patience, and guidance, however, the difficulty of thinking about statistics can be gradually overcome, and a deeper understanding can be achieved.

This article gives practical suggestions to make students more comfortable when thinking about or applying statistical concepts and techniques. Beginners should keep these suggestions in mind as they start their journey in statistics and veteran statisticians should revisit them whenever they start to feel overwhelmed with a project. 

1. Understand the purpose of statistics

2. relate statistics to real-life examples ,  ask yourself…, 4. break down complex problems, 5. use visualizations, 6. seek clarity in terminology , different perspectives, peer learning, constructive feedback, reduced isolation, brainstorming and problem-solving, enhanced learning opportunities , quality control, skill development, confidence building, networking opportunities, bring it all together.

Statistics can be confusing if you lose sight of its purpose. Rather than viewing it as a collection of abstract concepts and formulas, approach statistics with a practical mindset. Understand that its purpose is to provide tools for organizing, summarizing, and analyzing data, and to answer questions or solve problems based on evidence.

By focusing on the practical application of statistics and its role in extracting meaningful insights from data, you can overcome the initial intimidation and appreciate its value as a powerful tool for making informed decisions in various fields of study and in everyday life.

When running your analyses, developing your study design, or understanding someone else’s research , be sure to focus on the purpose of the methods used. Are the analyses run meant to summarize the data, find evidence for a relationship, or test a hypothesis? Keep these questions in mind as you look at the results of statistical models. By focusing on the purpose of the analyses you can determine whether or not the statistician achieved their goals. This will prevent you from getting lost in the details, like exact measures, models, or thresholds of significance the researcher selected.

Once you feel comfortable determining if a study achieved its purpose, then you can look closer at the finer details of the statistics. This will help you become more comfortable engaging with reading statistical research, learning new methods or developing your own study design. 

Statistics is most meaningful when you can relate it to real-life situations. Look for examples or case studies that demonstrate how statistical analysis has been applied to solve problems or make decisions in various fields. Understanding the practical applications of statistics helps in contextualizing the concepts and makes them more relatable.

Exploring applications in areas such as healthcare, economics, social sciences, or environmental studies can provide insights into how statistics is used to address real-world challenges. This approach allows you to see the direct impact and relevance of statistical concepts and techniques in various contexts. Additionally, examining practical examples helps to reinforce your understanding by applying statistical principles to concrete situations. Actively seek out and explore case studies and examples that demonstrate the power and practicality of statistics, as it will enhance your comprehension and appreciation of the subject.

3. Emphasize conceptual understanding

Understanding the underlying concepts and principles of statistics is crucial for a strong foundation in the subject. Rather than simply memorizing formulas or procedures, focus on comprehending the logic and intuition behind statistical concepts. Here’s a checklist t

hat you can revisit when thinking about a statistical concept while learning, developing your own projects, or reading statistical research.

• How is this concept related to other concepts that I know?
• How is this concept different from other closely related concepts?
• What is the purpose of this concept? (i.e. what does it measure or test?)
• When should I use this concept in my own projects and when is it not appropriate? 

By doing so, you will develop a deeper understanding of how statistical techniques work and how they can be applied to solve problems in various contexts. 

This approach allows you to adapt and apply statistical techniques to new and unfamiliar situations, as you will have a solid understanding of the underlying principles guiding their use. Moreover, understanding the concepts and principles helps in interpreting and critically evaluating statistical results, enabling you to make informed judgments about the validity and reliability of the analysis.

So, prioritize building a strong conceptual understanding of statistics, as it will serve as a solid foundation for your statistical knowledge and facilitate your ability to apply statistical techniques effectively.

Complex statistical problems can seem overwhelming at first glance. However, breaking them down into smaller, manageable parts can make the process more approachable. Start by identifying the key components and steps involved in solving the problem. This might include defining the research question, selecting appropriate statistical techniques, collecting and organizing data, conducting analyses, and interpreting the results.

By breaking the problem down into these individual components, you can focus on understanding and addressing each one separately, gradually building your understanding of the entire problem.

Once you have a clear understanding of each component, you can start connecting the pieces together to form a more comprehensive picture. This step-by-step approach allows you to manage the complexity of the problem and reduces the feeling of being overwhelmed. Additionally, it helps you identify any areas where you may need to further develop your understanding or seek additional resources or guidance.

Remember that learning statistics is a process, and it’s natural to encounter challenges along the way. By breaking down complex problems into smaller parts and taking them one step at a time, you can build your confidence and gradually develop the skills needed to tackle more intricate statistical problems.

A picture is worth a thousand words, even in statistics. Data visualization plays a vital role in understanding and communicating statistical information effectively. By utilizing graphs, charts, and visual representations, you can transform complex data sets into visual formats that are easier to interpret and comprehend. Visualizing data allows you to identify patterns, distributions, and relationships that may not be immediately apparent in raw data. It helps you to gain insights into trends, variations, and outliers, facilitating a deeper understanding of the underlying patterns and phenomena.

Furthermore, data visualization enhances communication by providing a clear and concise representation of information. Visuals can convey complex statistical concepts and findings in a more accessible and engaging manner, making it easier for others to grasp and interpret the information. Whether it’s presenting research findings, reporting trends in business data, or conveying important insights to a broader audience, data visualization ensures that information is effectively conveyed and understood.

When feeling stuck the best way to start to move forward is to employ a visualization. When designing a study, starting with scatter plots or bar graphs can help you start to think about how your variables relate. Or when reading statistical research, looking at the visualizations first can help you get an idea of the overall argument of the paper, especially when their writing becomes confusing. 

Statistics has its own terminology, and learning the jargon can initially be overwhelming. Take the time to familiarize yourself with statistical terms, definitions, and symbols. If you come across unfamiliar terms or symbols, don’t hesitate to seek clarification.

Reach out to instructors, knowledgeable individuals like statistics tutors , or online communities dedicated to statistics. Asking for explanations can provide valuable insights and help you grasp the meaning and context behind statistical jargon.

Learning statistics is like learning a new language . Beginners are happy just to be able to remember what a handful of words mean. Intermediate learners will have a larger vocabulary and will be able to organize them into words that are very similar and very different from each other. Advanced learners will have a very large vocabulary and have a deep understanding of how words relate and will be able to discuss complex nuances between words. 

Just like with learning a new language, immersion is the best way to learn statistics terminology. Practice with your own projects, talk about your projects with others, read the statistical research of others, and ask questions when something is new or confusing. Remember, learning any new field requires patience and persistence. By actively engaging with statistical terms and seeking clarity, you will gradually become more comfortable with the jargon, enabling you to communicate and understand statistical concepts with greater ease.

7. Collaborate and discuss

Engaging in discussions with peers, instructors, or online communities can greatly enhance your understanding of statistics. Here’s just some of the reasons collaboration makes statistical thinking easier:

When collaborating with others, you get exposed to diverse viewpoints and approaches. This exposure can broaden your understanding of statistical concepts, methods, and applications. Different perspectives can also challenge your assumptions and encourage critical thinking.

Interacting with peers in collaborative settings provides an opportunity to learn from each other’s strengths and experiences. Discussing ideas, solving problems together, and sharing knowledge can accelerate learning and foster a supportive learning environment.

Collaboration enables you to receive constructive feedback on your statistical analyses or research. Feedback from others can help identify mistakes, suggest alternative approaches, and refine your understanding of statistical concepts.

Statistics can sometimes feel overwhelming when tackled alone. Collaboration provides a sense of camaraderie, reducing feelings of isolation, and providing a support system that boosts confidence in tackling complex statistical challenges.

Collaborative settings foster brainstorming sessions where participants collectively explore ideas and solutions. Group problem-solving can lead to innovative approaches and creative solutions to statistical challenges.

Collaborating on research projects, participating in workshops, or attending seminars with others allows you to take advantage of learning opportunities that may not be available otherwise.

In a collaborative setting, others can act as a “check and balance” system, ensuring that statistical analyses and interpretations are rigorously evaluated. This helps minimize errors and ensures the accuracy of results.

Collaborating with individuals who possess different skill sets can help you develop complementary skills. For example, collaborating with a data visualization expert can improve your ability to communicate statistical findings effectively.

Engaging in fruitful collaborations can boost your confidence in tackling complex statistical problems. As you contribute to collaborative projects, you’ll feel more assured in your statistical thinking abilities.

Collaborative endeavors often involve connecting with professionals in related fields. Building a network of colleagues with statistical expertise can lead to future collaborative projects and learning opportunities.

Whether you are learning new statistical methods, developing your own research project, or engaging with established statistical research, collaboration can help immensely. Talking with others forces you to clarify your thoughts and engage with new ways of thinking about statistics. Both will help ground your knowledge and make statistical thinking easier.

The suggestions provided in this article offer valuable insights to make statistical thinking easier and more approachable. Understanding the purpose of statistics and its practical applications helps contextualize concepts and appreciate their value in making informed decisions. Relating statistics to real-life examples enhances comprehension and reinforces the relevance of statistical methods across various fields.

Overall, statistical thinking becomes more manageable and rewarding through consistent practice, patience, and collaboration. As statisticians of all levels practice statistical thinking, embracing these practical suggestions will foster a deeper understanding of statistics and pave the way for successful application in diverse contexts.

So, whether you are a beginner or a seasoned statistician, keeping these suggestions in mind will empower you to navigate the complexities of statistical thinking with confidence and proficiency.

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Teach yourself statistics

Statistics Problems

One of the best ways to learn statistics is to solve practice problems. These problems test your understanding of statistics terminology and your ability to solve common statistics problems. Each problem includes a step-by-step explanation of the solution.

• Use the dropdown boxes to describe the type of problem you want to work on.
• click the Submit button to see problems and solutions.

Main topic:

Problem description:

In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second state, 47% of the voters are Republicans, and 53% are Democrats. Suppose a simple random sample of 100 voters are surveyed from each state.

What is the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state?

The correct answer is C. For this analysis, let P 1 = the proportion of Republican voters in the first state, P 2 = the proportion of Republican voters in the second state, p 1 = the proportion of Republican voters in the sample from the first state, and p 2 = the proportion of Republican voters in the sample from the second state. The number of voters sampled from the first state (n 1 ) = 100, and the number of voters sampled from the second state (n 2 ) = 100.

The solution involves four steps.

• Make sure the sample size is big enough to model differences with a normal population. Because n 1 P 1 = 100 * 0.52 = 52, n 1 (1 - P 1 ) = 100 * 0.48 = 48, n 2 P 2 = 100 * 0.47 = 47, and n 2 (1 - P 2 ) = 100 * 0.53 = 53 are each greater than 10, the sample size is large enough.
• Find the mean of the difference in sample proportions: E(p 1 - p 2 ) = P 1 - P 2 = 0.52 - 0.47 = 0.05.

σ d = sqrt{ [ P1( 1 - P 1 ) / n 1 ] + [ P 2 (1 - P 2 ) / n 2 ] }

σ d = sqrt{ [ (0.52)(0.48) / 100 ] + [ (0.47)(0.53) / 100 ] }

σ d = sqrt (0.002496 + 0.002491) = sqrt(0.004987) = 0.0706

z p 1 - p 2 = (x - μ p 1 - p 2 ) / σ d = (0 - 0.05)/0.0706 = -0.7082

Using Stat Trek's Normal Distribution Calculator , we find that the probability of a z-score being -0.7082 or less is 0.24.

Therefore, the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state is 0.24.

See also: Difference Between Proportions

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Statistics - Maths of Real Life

This pilot collection of resources is designed to introduce key statistical ideas and help students to deepen their understanding.

Introduction

Statistical Shorts

Can you decide whether these short statistical statements are always, sometimes or never true?

A Population Survey

A geographical survey: answer the tiny questionnaire and then analyse all the collected responses...

Which Spinners?

Can you work out which spinners were used to generate the frequency charts?

Thousands of People

How many thousand people does each dot represent?

Counting Fish

I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?

Data Matching

Use your skill and judgement to match the sets of random data.

Where Are You Flying?

Where do people fly to from London? What is good and bad about these representations?

One Variable, Two Variable, Three Variable, More

Displaying one-variable and two-variable data can be straightforward; what about three or more?

Sleep: the Silent Killer

"Too much sleep is deadly" proclaimed the newspaper headline. Is this true?

Do You Brush Your Teeth Every Day?

How can we find out answers to questions like this if people often lie?

Stats Statements

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Hypothetical Shorts

Some short statements about hypothesis testing: are they true, false, or somewhere in between?

Robin's Hypothesis Testing

How many trials should we do in order to accept or reject our null hypothesis?

Powerful Hypothesis Testing

How effective are hypothesis tests at showing that our null hypothesis is wrong?

Can You Find ... Random Variable Edition

Can you create random variables satisfying certain conditions?

Binomial or Not?

Are these scenarios described by the binomial distribution?

Binomial Conditions

When is an experiment described by the binomial distribution? Why do we need both the condition about independence and the one about constant probability?

A Well-stirred Sample

Typical survey sample sizes are about 1000 people. Why is this?

Understanding Hypotheses

This article explores the process of making and testing hypotheses.

A Probability Conundrum

What do we mean by probability? This simple problem may challenge your ideas...

The Surveyor Who Came to Tea

This article discusses how a survey company carries out its surveys and some of the issues involved.

What Is a Random Variable, Really?

This article offers an advanced perspective on random variables for the interested reader.

What Is a Hypothesis Test?

This article explores the meaning of hypothesis tests, and also some of the major difficulties in interpreting them

Challenging Data Tasks: The Making of "Where Are You Flying?"

How was the data for this problem compiled? A guided tour through the process.

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Over-booking

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

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Statistics With R: Solving Problems Using Real-World Data

Student resources, welcome to the sage edge site for statistics with r, 1e.

Drawing on examples from across the social and behavioral sciences,  Statistics with R: Solving Problems Using Real-World Data  introduces foundational statistics concepts with beginner-friendly R programming in an exploration of the world’s tricky problems faced by the “R Team” characters. Inspired by the programming group “R Ladies,” the R Team works together to master the skills of statistical analysis and data visualization to untangle real-world, messy data using R. The storylines draw students into investigating contemporary issues such as marijuana legalization, voter registration, and the opioid epidemic, and lead them step-by-step through full-color illustrations of R statistics and interactive exercises.

This site features an array of free resources you can access anytime, anywhere.

Acknowledgments

We gratefully acknowledge Jenine K. Harris for writing an excellent text. Special thanks are also due to Adeline Yeh of Cornell University for developing the resources on this site.

For instructors

Access resources that are only available to Faculty and Administrative Staff.

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How To Solve Statistics Math Problems In The Real World?

Statistics math problems are not only necessary to understand the math question in depth, but it also makes you familiar with real-time things more efficiently. Therefore, it is always important to understand what statistics are and how statistics relate to math. 

Don’t have any knowledge of it? No worries!! I will help you know what exactly statistics math problems are and how they are useful.

Table of Contents

Being a statistics subject student, it is necessary that you must have enough knowledge about statistics questions. Moreover, practice the problems as much as you can. It will help you to clear your doubts and strengthen your conceptual knowledge.

So, let’s check what exactly the statistics math problems are. 

What Are The Main Terminologies Used In Statistics?

Just as other subjects, statistics has its own terms and language. This language supports you to understand what actually the problem is, what result requires to come, and methods to describe and analyze the results in the right manner. 

Let’s Check Some Of The Main Terminologies Used In Statistics:

What are some problems with statistics.

There are some of the major problems that can occur when you deal with the statistics data. Therefore, it becomes necessary that you must understand these problems and keep in mind to ignore them.

1. Sometimes Extracting Meaning Can Make A Little Difference

When you look for the difference across subgroups and groups for findings, it explains if the percentage difference is large enough to make conclusions or not. 

Therefore, you need to be careful when you deal with the small difference as it can lead to no meaning for making conclusions.

2. Poor Survey Designs

The statistics quality directly depends on the survey quality. But sometimes, we design a survey with free tools and use the survey output for important decision-making. 

That is why you must take care of the survey design to help you make important decisions. It is beneficial if you assign this to an expert who knows how to perform surveys.

3. Representing Meaningless Details On A Graph

Sometimes, the graphs can misguide the readers. The graphs like bar graphs can show the bar of large value where the small value might look to be ignored. 

But actually, small values also play a significant role in the statistics data. Therefore, you must use a suitable graph to represent the data.

How To Solve Statistics Math Problems?

It has been seen that solving statistics questions needs some strategies. That is why below, I have mentioned important strategies or steps to solve these problems. Let’s find out.

Label Each Point Of The Problem Or Question Assigned To You

Suppose your statistics questions state that A is the normal distribution with a mean value of 5 and the standard deviation (SD) with 1. Then, circle all the numeric terms and write the respective symbols. Like circle 5 and write μ, and so on.

Write What The Question Demands To Find Out Statistically

Suppose you assign to calculate the probability of the more than 5 people who joined a competition. Then, write it as “Calculate P(X > 5).”

• What is dependent variable in math
• What is term in math
• A useful guide on what is constant in math

Recall the formula you studied to calculate a similar problem or question while practicing the problem. And connect it with the current statistics math problems.

Suppose your problem topics already have some terms like Standard deviation as 3, mean like 80, and so on. And you need to calculate the probability of x that is less than 80. 

You can see that the z-formula ( Z = ( X – μ )/ σ) can be relevant to solve this kind of problem. Put all the values in the formula. Now you can easily find out the value or the answer to your statistics math problems.

Let’s check a statistics math problem and solve it!!!

Two brothers, James and Caroline, are studying in the same class. The following is the table of their marks they got the whole year in their test.

Calculate in how many subjects Caroline scored better than the brother James. (The mark ranges from 1 to 5.)

As you can see that we need to calculate the statistical average or mean of each subject that looks like:

Caroline’s average marks:

mathematics: (1+2+3+1+1+5+2)/7 => 15/7 => 2.14 => 2 (approx)

physics : (3+3+1+1+1+2)/6 => 11/6 => 1.83 => 2 (approx)

chemistry : (1+1+1+3+4+1)/6 => 11/6 => 1.83 => 2 (approx)

geography : (2+2+3+1+5+4)/6 => 17/6 => 2.83 => 3 (approx)

James’ average marks:

mathematics: (4+4+1+2+2)/5 =>13/5 => 2.6 => 3 (approx)

physics: (2+2+2+2)/4 => 8/4 => 2

chemistry: (5+5+4+4+3+4+3+3)/8 => 31/8 => 3.88 => 4 (approx)

geography: (1+1+2+1+1+1+2+1)/8 => 10/8 => 1.25 => 1 (approx)

So, Caroline got better marks in one subject (that is geography) than James.

This is how you can understand and solve the statistics math problems in an easy manner.

Applications Of Statistics In The Real World In 2023

Here are some applications of statistics in the real world in 2023:

1. Business and Finance

Statistics plays a vital role in business decision-making and financial analysis. It is used for market research, forecasting sales trends, risk assessment, portfolio management, and evaluating investment opportunities.

2. Healthcare and Medicine

Statistics is used in medical research to analyze clinical trials, study disease patterns, evaluate treatment effectiveness, and assess public health trends. It helps make informed decisions about patient care, drug development, and healthcare resource allocation.

3. Sports Analytics

Statistics is widely employed in sports to analyze player performance, evaluate team strategies, and make data-driven decisions. It helps in player scouting, game strategy planning, performance tracking, and predicting outcomes.

4. Social Sciences

Statistics is extensively used in social sciences like sociology, psychology, and economics. It helps researchers analyze survey data, conduct experiments, study population trends, and draw meaningful conclusions about human behavior and societal patterns.

5. Environmental Analysis

Statistics is used in environmental studies to analyze climate data, monitor pollution levels, assess ecological impacts, and model environmental phenomena. It helps in understanding climate change, making policy decisions, and implementing sustainable practices.

6. Market Research and Consumer Behavior

Statistics is used in market research to analyze consumer behavior, conduct surveys, and gather data on preferences and buying patterns. It helps businesses understand customer needs, develop targeted marketing strategies, and optimize product offerings.

7. Quality Control and Manufacturing

Statistics is employed in quality control processes to monitor product quality, detect defects, and ensure consistent manufacturing standards. It helps in statistical process control, reliability analysis, and optimizing production efficiency.

Tips For Improving Your Statistics Math Skills

Here are 5 tips for improving your statistics math skills, each in 2 lines:

1. Practice Regularly

Make it a habit to practice solving statistics problems regularly. The more you practice, the better you apply statistical concepts and techniques.

2. Understand The Concepts

Instead of just memorizing formulas and procedures, try to understand the basic ideas behind statistical calculations. This will help you grasp the reasoning and logic behind statistical analyses.

3. Use Real-Life Examples

Apply statistics to real-world situations to develop a practical understanding of how statistical concepts are used. Analyze data from everyday scenarios like surveys, sports, or social media trends.

4. Seek Help When Needed

Do not hesitate to ask for help if you are stuck on a concept or problem. Consult your instructor, classmates, or online resources to get guidance and clarification.

5. Review And Reflect

After solving problems, take the time to review your work and reflect on your approach. Understand any mistakes you made and learn from them to improve your problem-solving skills.

Statistics math problems can be useful to make a better understanding of how to use statistics concepts. Therefore, it is always necessary that you must know the method to solve these problems.

I have detailed the necessary steps along with other useful information. Bookmark this website and understand the concepts of statistics.

Still have any doubt, then let me know through your comments. I will help you to understand statistical concepts. If you still have some doubts then get best math homework help to clear then in real time.

“Be a great statistician with enough knowledge about statistics with our useful blogs.”

Frequently Asked Questions

What is statistics math with examples.

Statistics consider as the number that shows or describes the sample’s properties. For example, suppose you consider a math class as the sample of all math classes. The mean value of the marks scored in the particular math class in the final exam is the statistics example.

What type of math is used in statistics?

The particular math techniques used in the statistics are as follows:

linear algebra, differential equation, mathematical analysis, stochastic analysis, measure theory.

Why do we rely on statistics?

With the help of statistical knowledge, you can collect helpful data, develop valuable insights by analyzing the data, and develop useful decisions. Moreover, statistics play an essential role in various scientific discoveries, data-based decisions, and making predictions.

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Is a precise answer always better than a slightly less detailed one? Not necessarily. Some problems could take forever to compute and tie up vast IT capacity. Where solutions are needed urgently, e.g. in business or manufacturing, near-enough can be more than enough. ERC-funded research has produced a library of fast, powerful approximation algorithms.

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When you want to tackle a problem that would require a disproportionate amount of time and effort to solve exactly, you can use an approximation algorithm, says Piotr Sankowski of the University of Warsaw. The result may not be as precise as the outcome of an exact calculation, but it will be very close — and, depending on what you need it for, there may be little point in getting bogged down in details. Sankowski has benefited from an ERC Starting Grant for the PAAL project, which produced a library of such algorithms. Together with his team, he designed these approximation programmes to be generic: they don’t just work for individual examples of particular types of problems, but can be adapted to address other questions of a similar nature. “Our library is easy to install, to use and to modify,” Sankowski notes. “It is based on templates that you can adapt for different use cases.”

Adaptable algorithms As an example of a conundrum best addressed through approximation, Sankowski points to the notorious Travelling Salesman Problem — the challenge of working out the shortest possible route for a sales rep who wants to visit several cities and then return home. Doable with paper, pen and patience if there are very few cities to consider, no doubt, but as the list grows longer, so does the number of possible permutations, and thus the difficulty of the task. Of course, using a computer, it is possible to work out the optimal sequence even for large numbers of cities. In theory, it would also be possible to cover additional criteria, such as preferences for different types of transport. But by the time a programme written for this purpose would deliver a conclusive answer, the salesman’s travelling days may well be over. Does it matter? In fact, it does. This type of problem arises in areas as varied as transport and manufacturing, e.g., with regard to routing vehicles or drilling holes into circuit boards. Timely, efficient solutions can help businesses to save time and money, and approximation algorithms can help to produce them.

A fresh approach to approximation Sankowski intends to tap this potential in a new enterprising venture following the imminent end of PAAL. The follow-on project, named PAAL-POC, will develop e-commerce support services based on this library, with the eventual aim of setting up a spin-off company. “Approximation algorithms can be used to model trade or customer behaviour. We will work on this aspect with a number of companies involved in e-commerce,” Sankowski explains. “The aim is to predict how the market is likely to react when a company introduces changes — in its business strategy, for example.” Prospective clients of the future spin-off will benefit from another specificity of the algorithms developed in PAAL: their ability to factor in both random and regular structures. Social networks, for example, grow partly along existing lines of interaction and partly through spontaneous new connections, Sankowski explains. Such interplay between average case and worst-case scenarios is relevant to many mechanisms at play in e-business, he notes.   PAAL was backed by an ERC Starting Grant, a type of funding which the European Research Council awards to outstanding research proposals submitted by young researchers with a promising scientific track record. PAAL-POC also benefits from ERC support, attributed in this case through the Proof of Concept scheme. This programme encourages beneficiaries of earlier ERC grants to explore the commercial or innovation potential of their findings. The grants have advanced Sankowski’s career in a number of ways, he reports. They have helped to establish him as an independent team leader within his university, he notes, and they have also raised his visibility at international level. The establishment of a spin-off should give his career a further boost. Once this is new venture is up and running, he intends to return to his research. Clearly, algorithms and approximation hold endless fascination.

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Solved Statistics Problems – Practice Problems to prepare for your exams

In this section we present a collection of solved statistics problem, with fairly complete solutions. Ideally you can use these problems to practice any statistics subject that you are in need of, for any practicing purpose, such as stats homework or tests.

The collection contains solved statistic problems of various different areas in statistics, such as Descriptive Statistics, Confidence Intervals, Calculation of Normal Probabilities, Hypothesis Testing, Correlation and Regression, and Analysis of Variance (For a list of 30,00+ step-by-step solved math problems, click here )