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What are statistics.
Statistics – the math and science of data collection, analysis, visualization, and interpretation. Typically paired with the study of probability, the study of likelihoods for a particular event, statistics can also be described as the study of events given a series of probabilities. A statistic on the other hand, is the result that is yielded after data is analysed. A statistic can be described as descriptive or inferential. Descriptive statistics provide general summaries such as the distribution, spread and centre of a dataset. Inferential statistics involves data analysis on just a sample of the population to make inferences on the larger population as a whole.
As suggested by Wells, Statistics math and probability math are both important topics you will likely encounter or require further on in life. At the very least, statistics are paramount in helping make major decisions that will have some effect on you. Governments are frequently tasked with collecting statistics from the population to inform them on the status of issues and how they can better serve the public. Academically speaking, be it in this course, an introduction to statistics course, probability and statistics or introduction to probability class, the purpose and study of statistics is to equip with you with strong mathematical induction and deduction skills when faced with data. Furthermore through exposure of the best practices in data collection, data analysis, data representation, and interpretation, the study of statistics aims to improve your analytical and problem-solving skills.
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Getting an A+ grade in Statistics homework (or assignments) is a challenging task for most students. It requires a massive amount of time, along with the focus and advanced knowledge of statistics topics. Many students don't have enough time to do their homework because they already have a hectic schedule for other subjects. Statistics also contains a variety of complex topics. That is why sometimes students wouldn't be able to do their statistics homework and have to seek the best statistics helper or statistics homework help provider.
Our experts provide online help with statistics homework. You can hire our professionals and upgrade your grades with the best solutions. Our experts have years of experience and always deliver you the best and finest statistics help. Don’t hesitate to contact us and hire our statistics expert. We always want students to never get confused, so they can chat with our experts first once they are satisfied then confirm their order. We provide the best help with statistics from the best statistics homework helper.
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We are accessible 24/7 -365/366 days to provide instant help in the hour of need. It is available at pocket-friendly prices. You can get our instant expert services without paying any extra charges
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We have a large team of qualified experts around the globe who are well experienced in their subject matter. Therefore, they always provide error-free and easy-to-understand solutions. Before delivery of a solution, our quality team checks the solution's quality.
Providing the Best Statistics Homework Help Since 2012
If you want to know why we are the best option for your statistics homework help, then there are multiple reasons to cover this statement. First of all, we have been providing statistics homework help since 2012. As a result, from 2012 till now we have successfully delivered more than 20,000 solved homework. Secondly, we have dedicated teams of experts and all have minimum experience of more than 2 to 3 years. Thirdly, those homework/assignments provided by us are 100% plagiarism/error free, which means that you can easily submit your homework without any doubt.
Moreover, our expert provides easy-to-read homework help. So, that you can easily read the homework provided by us. As a result, this will increase your grades as well as your knowledge.
What Is Statistics?
Statistics is a branch of applied mathematics Statistics is used in many different fields to help make decisions. Several statistical methods are used to get the conclusion for organized data (mainly numerical data) and make the best visualization of this data. The primary purpose of statistics is to make the raw or displayed data more useful for the statisticians.
Let's get some more details about statistics
Statistics are used in almost every scientific system, including the physical and social sciences, business, the humanities, government, and manufacturing. Statistics is an applied mathematics branch (students can take applied statistics assignment help from us) that evolved from calculus and linear algebra to probability theory. Statistics is the concept that we may learn about the features of large groups of objects or events (a population) by examining the characteristics of a smaller number of similar things or events (a sample). Because, in many circumstances, acquiring complete data about an entire population is too expensive, impractical, or impossible.
Example Of Statistics
Suppose that you want to calculate the average number of students who got below 50% in their final exams. You also have to calculate the difference between their marks with other students' marks. We can solve this complex problem with statistical reports. Our experts will provide you with various examples in statistics help service so that you can easily understand all the statistical concepts.
What are the Two Major Branches Of Statistics?
A short descriptive coefficient summarizes the data set, which can be either a team of the entire or a sample of the population. It is the measure of central tendencies and variable measures. Descriptive statistics are concerned primarily with the central tendency, variability, and distribution of sample data.
The estimate of the features, a specific aspect of a sample or population, is referred to as central tendency, and it comprises descriptive statistics such as mean, median, and mode.
Types of descriptive statistics
- Central tendency measures
- Measures of Central Tendency include Mean, Median, and Mode. It is used to find the center point value of the numerical dataset.
- Variability measures
Inferential statistics is a set of assumptions that are made based on information found by Descriptive Statistics. This type of statistics takes a random sample of data taken from a population to describe and make deductions about that population. Inferential statistics are tools used by statisticians to draw inferences about the characteristics of a population-based on the features of a sample and determine how certain they may be about the reliability of those findings.
Statistics, which quantify the central tendency, variability, distribution, and correlations between attributes within a data sample, can provide an accurate picture of the corresponding parameters of the entire population from which the sample is drawn based on sample size and distribution.
Types of inferential statistics
- Regression analysis
- Analysis of variance (ANOVA)
- Analysis of covariance (ANCOVA)
- Statistical significance (t-test)
Difference Between Descriptive Statistics And Inferential Statistics
Descriptive statistics are used to characterize or summarize a sample's properties or data collection, such as the mean, standard deviation, or frequency of a variable. In contrast, inferential statistics uses various approaches to relate variables in a data set to one another, such as correlation or regression analysis. These can then be utilized to make predictions or infer causality.
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Students find statistics homework is always complex in nature and need help with statistics. Therefore, the students can have some concerns with their homework. To overcome their concern, they search on the internet to do my statistics homework help online. But having these kinds of services is always challenging for the students. The best way to find out the help is to search over the internet with the term like do my statistics homework for me. Whenever you search with this term, then you get plenty of results. We would recommend you to go with the top ones. And then cross-check the experts' credibility with reviews websites. In this way, you can find Statistics help as the solution to your problem, i.e., who can do my statistics homework easily.
Can I Pay Someone To Do My Statistics Homework?
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Statistics is a field of mathematics that students are disclosed to mostly in middle school. The subject teaches students how to create graphs and charts to express mathematical data statistically. It mostly works with numerical numbers and uses charts and graphs to concisely display a large amount of information. It also necessitates the memorization of formulas in order for students to solve arithmetic problems.
Despite the fact that statistics is a highly scientific topic, many students hate it and are unable to get the concepts and basics of this subject, which is heavily used by bankers and others in charge of keeping records. You just can't wish away statistics tasks given by your teacher at school. Thankfully, many statistics homework solvers offer help to students struggling with this topic. Therefore, it is also beneficial to consider our experts and get the best and easiest solutions to learn the concepts of statistics.
Get Statistics Homework Help Online From the Best Statistics Experts
Statistics can be a complex subject for students, especially if they do not have a background in mathematics. However, it is a critical subject that is essential in many fields, such as business, social sciences, and engineering. If you are struggling with statistics homework, it is essential to seek help from experts. Here are some reasons why you should get statistics homework help online from dedicated experts:
We have dedicated experts who are knowledgeable in the subject. They provide accurate solutions to problems, ensuring you receive the best grades possible.
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We offer qualitative statistics help for students over quantitative
Too much statistics homework may be hectic; this always leads to searching for the best statistics help for students. Yes, there are several resources that can help students with their statistics homework. You may go to a number of these websites and narrow down your choices based on customer comments and reviews. You can also compare our service with others, and finally find our statistics homework help is the best.
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List Of Statistics Projects That You Can Take From Our Statistics Experts
If you have any pending statistics projects, then don't worry. Here is a list of statistics projects that you can take from our statistic experts in order to achieve A+ grades in your statistics project:
College statistics homework help
It involves advanced statistics that require lots of skills to solve the questions. We know that the students don’t have enough time to sharpen their skills. Therefore the students are looking for the best college statistics help to submit their homework with the given deadline. If you are also looking for the same help, then you are in the right place.
Psychology statistics homework help
Psychology students are also required to do psychology statistics homework. But the psychology students are not ready to solve the complicated statistics homework. Therefore they search for the best Psychology statistics assignment help from the experts.
Business statistics assignment help
Business statistics homework involves intermediate-level statistics. Business statistics is one of the crucial parts of business studies. It is quite helpful to solve the majority of business problems. Therefore it is included in the business studies courses. Most business studies students don’t have time to solve the statistics homework. Thus they search for business statistics homework help.
Elementary statistics homework help
For students, elementary statistics is a critical subject. Many students face difficulties while trying to complete their elementary statistics homework. So they want elementary statistics homework help from experienced experts. To learn the introduction of statistics and the advanced level of statistics, you may go through our best elementary statistics homework help. Get elementary statistics homework help here. Post your elementary statistics homework questions and get answers from qualified and experienced experts.
Probability assignment help
Sometimes, the students need to have the probability and statistics homework help. Advanced probability and advanced statistics are useful for business and computer science students.
AP statistics homework help
AP statistics stands for advanced placement statistics. It is useful for college-level students. Before the placement of the students, they need to submit the AP homework to the college. Therefore they need to have the best Help with AP statistics homework to get the best placement.
CPM statistics homework help
CPM statistics homework is for those students who want to learn everything about statistics. Most of the students who wish to become a statistician require to submit that statistics homework. We are helping those students with the help of our CPM statistics help.
Check The Sample Question Submitted By Our Experts For Statistics Homework
The following histogram displays the difference between the actual and “ideal” weights distribution for 119 female students.
What is the shape of the distribution (approx)?
- Nearly symmetric.
- Skewed to the right.
- Skewed to the left.
The median of the distribution is (approx):
- -10 pounds.
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Homework help and its kinds.
How to be successful in studying when there are other activities and duties that take your time and prevent you from finishing workload? The answer is simple! Get help of professionals who can solve all the tasks for you. Whether you need math homework help, or any other subject, there are plenty of online specialists ready to assist. It's not shameful for ask for help. Modern people fill their schedule with numerous tasks that sometimes can't even cope with them. Students can be working, might have kids or parents to look after, or just be tired of constant routine. College homework help was created for all these purposes, and for one main reason: to give student some free time. You can join help server and there will be plenty of people like you looking for assistance in foreign languages, science, statistics and other subjects. For that a special website was created. It's called homework help discord server, where you share ideas and conclusions online. After joining community you choose the subject you need and can start conversation with other people.
The major advantage of discord is possibility to find all answers you need. Homework help would not only boost your grades, but increase your knowledge of the subject. Sometimes you don't need someone to make task for you, it's just a little hint that would result successfully finished task. Joining discord server you can help other people as well.
Advantages of homework help online
Why not just hiring a private tutor to solve all problems? Well, it would require extra time and money to have a class with tutor. Besides, amount of complex subjects and tasks would be growing, and you would be spending your day only changing tutors. Asking for online homework help you will find an answer easily, and thus saving cash. After economics and maths soon your subjects would be even more complicated. Homework help servers have it all: there's always someone sharing ideas or starting discussion no matter how hard topic is. Looking for statistics homework help? You would find it. The second advantage is number of levels presented. Are you middle class student? Answers and help can be found here. Is your subject of university level? Welcome to discord servers, they have it all. Accounting homework help, technology and engineering: everything is in one place. Discord unites both students and tutors. Homework can be done easily and quickly if you use not books only, but also all the opportunities that website offers. Surfing online helps you to find the answer faster than tying to solve riddles yourself. Another great advantage is number of users. Even if you're studying in small school and it seems like there's no help at all, almighty Internet is always ready to assist in learning process.
How it's working?
If you think homework help is just website when you and other people are trying to do home task you are completely wrong. It would help you to find a necessary book online in the middle of night and don't wait until library is open. To proceed with studies you can hire a tutor to explain you some part or theories you don't understand. Finally, you can ask questions or open a discussion, and welcome everyone to join it. A simple principle of knowledge exchange is basis for each homework help website.
The downsides of free homework help..
How often do use assistance of the Internet in doing your homework? We bet, it's your daily routine to open a browser and start looking for solutions. Do you think the strangers on the other side of the screen will provide necessary information for your math homework help? Unlikely! After one successful task there might be a sad outcome. We want you to be cautious about the websites you look for assistance, that's why we have gathered the disadvantages of asking Google for free homework help.
First, and the main downside is the inability to check the result. People helping you with your task might not know the answers themselves. And what assistance would you get in this case? Wrong answers!
Second, it's the proficiency of the strangers on the other side of the screen. Who are they? College professors who came to provide homework help for free? Or just students like you who might not be able to cope with a simple task. They might not now anything about the subject, or might be way too self-confident and give you wrong answers.
Think twice before using the help from these people. In the next part of the article we describe the most popular sources of homework assistance and give our honest opinion about them.
The best websites for homework help.
When a student is looking for help he always (no exaggeration!) expects it to be free. Of course, being a college student always means being tight on budget and looking for the ways to save money even more. But it should be related to college homework help. Sadly, there are thousands of examples when a bad homework resulted in bad grades, and a poor student had to learn more to pass the exam. That's why we don't recommend to look for answers on the websites like Reddit or Chegg. Why? We explain below.
Chegg homework help is a paid service. You need to buy a monthly subscription to use it. Is it worth it? Depends on your professor. If the tasks you get are strictly from a textbook, then it might be good. To cope with a creative teachers this website has nothing to offer.
The same goes for Reddit homework help. It might be useful when you're looking for solutions on a standard task, the one that dozens of people are struggling with as well. There's nothing these services can offer if you're homework is unique and created by a teacher himself. What to do in this case? Read our recommendations below.
We recommend to try it!
There's an easy and cheap solution that will help you succeed in your studies. A personal assistance with homework created just for your tasks. No need to scroll pages looking for similar tasks and subjects, no need to copy from the screen and guess, if the results are correct. Professionals will perform the task for you! All you have to do is to provide it and enjoy a personalized approach and high quality service. After that you'll never come back to Reddit in search of answers!
Statistics Homework help services
Statistics homework help – our expert guidance from basic to complex, be open-minded give us a chance to serve you..
Seek for Expert Statistics Homework Help at Statistics Explained. The term ‘Statistics’ is not unheard of!
So, it wouldn’t be wrong to assume that it is ‘Statistics’ that attaches meaning to any data. We can extract meaningful information from databases with the help of statistics. The use of statistical tools to evaluate, analyze, and interpret the data, has been instrumental in supplementing our reasoning abilities, ultimately leading to the development of insightful findings.
It would be immaterial to think of the world without core ‘Statistics’ in the present day. The acquisition of statistical knowledge is the need of the hour. However, is acquiring and nurturing skills relating to a distinct field of study, such as statistics at all easy?
Well, we will leave that for you to answer!
We can begin by laying undiluted emphasis on the critical aspects of statistics, which might help you reach your ‘eye-opening moment.’
- Given the upsurging needs of Statistics in academics and all fields, Statistics must be well integrated with the school curriculum like any other basic subjects.
- Promoting critical thinking and reasoning abilities at a nascent stage is the first step to attaining statistical literacy.
- Concept clarity does not happen overnight. It is a stage-wise process, involving a systematic and strategic approach to teach the subject better.
An outpour of statistical information begins at tender academic levels, then why deprives ourselves of statistical knowledge?
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Business statistics homework help
The world of business is a booming world of information. Information up-gradation, in the dynamic world of business, leaves businesses on the lookout for the most relevant information. For businesses, the game is all about making the right decision. One wrong decision and your business are doomed. Decision making also involves the predictive analysis of upcoming events, market conditions, organizational structure, and employee dynamics. Business statistics is a vital determinant of organizational complexities and managerial inefficiencies. Here at StatisticsExplained , our galaxy of Statistics maestros enable you to take up heavy data work, but not the burden that comes along with it.
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College Statistics Homework Help
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We assure you flying grades with our assistance and not to worry about time constraints. Effective measures and well-crafted strategies keep us ahead of time and quality. College statistics homework help may entail any subject, psychology, economics, business studies, finance, etc. Not to worry! Our well-experienced professionals are equipped to cater to students from diverse streams, subjects. Basic to complex, our qualified homework helpers will shed light on the concept and solve the problems. Our easy teaching will erase doubts like they never existed, and fundamentals of the subject will be glued to your head and heart forever! Connect to us and bring out the best in yourself! Choose StatisticsExplained! Our elaborate explanation is sure to put you in the spotlight of “a statistician in the making.”
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11 Surprising Homework Statistics, Facts & Data
The age-old question of whether homework is good or bad for students is unanswerable because there are so many “ it depends ” factors.
For example, it depends on the age of the child, the type of homework being assigned, and even the child’s needs.
There are also many conflicting reports on whether homework is good or bad. This is a topic that largely relies on data interpretation for the researcher to come to their conclusions.
To cut through some of the fog, below I’ve outlined some great homework statistics that can help us understand the effects of homework on children.
Homework Statistics List
1. 45% of parents think homework is too easy for their children.
A study by the Center for American Progress found that parents are almost twice as likely to believe their children’s homework is too easy than to disagree with that statement.
Here are the figures for math homework:
- 46% of parents think their child’s math homework is too easy.
- 25% of parents think their child’s math homework is not too easy.
- 29% of parents offered no opinion.
Here are the figures for language arts homework:
- 44% of parents think their child’s language arts homework is too easy.
- 28% of parents think their child’s language arts homework is not too easy.
- 28% of parents offered no opinion.
These findings are based on online surveys of 372 parents of school-aged children conducted in 2018.
2. 93% of Fourth Grade Children Worldwide are Assigned Homework
The prestigious worldwide math assessment Trends in International Maths and Science Study (TIMSS) took a survey of worldwide homework trends in 2007. Their study concluded that 93% of fourth-grade children are regularly assigned homework, while just 7% never or rarely have homework assigned.
3. 17% of Teens Regularly Miss Homework due to Lack of High-Speed Internet Access
A 2018 Pew Research poll of 743 US teens found that 17%, or almost 2 in every 5 students, regularly struggled to complete homework because they didn’t have reliable access to the internet.
This figure rose to 25% of Black American teens and 24% of teens whose families have an income of less than $30,000 per year.
4. Parents Spend 6.7 Hours Per Week on their Children’s Homework
A 2018 study of 27,500 parents around the world found that the average amount of time parents spend on homework with their child is 6.7 hours per week. Furthermore, 25% of parents spend more than 7 hours per week on their child’s homework.
American parents spend slightly below average at 6.2 hours per week, while Indian parents spend 12 hours per week and Japanese parents spend 2.6 hours per week.
5. Students in High-Performing High Schools Spend on Average 3.1 Hours per night Doing Homework
A study by Galloway, Conner & Pope (2013) conducted a sample of 4,317 students from 10 high-performing high schools in upper-middle-class California.
Across these high-performing schools, students self-reported that they did 3.1 hours per night of homework.
Graduates from those schools also ended up going on to college 93% of the time.
6. One to Two Hours is the Optimal Duration for Homework
A 2012 peer-reviewed study in the High School Journal found that students who conducted between one and two hours achieved higher results in tests than any other group.
However, the authors were quick to highlight that this “t is an oversimplification of a much more complex problem.” I’m inclined to agree. The greater variable is likely the quality of the homework than time spent on it.
Nevertheless, one result was unequivocal: that some homework is better than none at all : “students who complete any amount of homework earn higher test scores than their peers who do not complete homework.”
7. 74% of Teens cite Homework as a Source of Stress
A study by the Better Sleep Council found that homework is a source of stress for 74% of students. Only school grades, at 75%, rated higher in the study.
That figure rises for girls, with 80% of girls citing homework as a source of stress.
Similarly, the study by Galloway, Conner & Pope (2013) found that 56% of students cite homework as a “primary stressor” in their lives.
8. US Teens Spend more than 15 Hours per Week on Homework
The same study by the Better Sleep Council also found that US teens spend over 2 hours per school night on homework, and overall this added up to over 15 hours per week.
Surprisingly, 4% of US teens say they do more than 6 hours of homework per night. That’s almost as much homework as there are hours in the school day.
The only activity that teens self-reported as doing more than homework was engaging in electronics, which included using phones, playing video games, and watching TV.
9. The 10-Minute Rule
The National Education Association (USA) endorses the concept of doing 10 minutes of homework per night per grade.
For example, if you are in 3rd grade, you should do 30 minutes of homework per night. If you are in 4th grade, you should do 40 minutes of homework per night.
However, this ‘rule’ appears not to be based in sound research. Nevertheless, it is true that homework benefits (no matter the quality of the homework) will likely wane after 2 hours (120 minutes) per night, which would be the NEA guidelines’ peak in grade 12.
10. 21.9% of Parents are Too Busy for their Children’s Homework
An online poll of nearly 300 parents found that 21.9% are too busy to review their children’s homework. On top of this, 31.6% of parents do not look at their children’s homework because their children do not want their help. For these parents, their children’s unwillingness to accept their support is a key source of frustration.
11. 46.5% of Parents find Homework too Hard
The same online poll of parents of children from grades 1 to 12 also found that many parents struggle to help their children with homework because parents find it confusing themselves. Unfortunately, the study did not ask the age of the students so more data is required here to get a full picture of the issue.
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Interpreting the Data
Unfortunately, homework is one of those topics that can be interpreted by different people pursuing differing agendas. All studies of homework have a wide range of variables, such as:
- What age were the children in the study?
- What was the homework they were assigned?
- What tools were available to them?
- What were the cultural attitudes to homework and how did they impact the study?
- Is the study replicable?
The more questions we ask about the data, the more we realize that it’s hard to come to firm conclusions about the pros and cons of homework .
Furthermore, questions about the opportunity cost of homework remain. Even if homework is good for children’s test scores, is it worthwhile if the children consequently do less exercise or experience more stress?
Thus, this ends up becoming a largely qualitative exercise. If parents and teachers zoom in on an individual child’s needs, they’ll be able to more effectively understand how much homework a child needs as well as the type of homework they should be assigned.
Related: Funny Homework Excuses
The debate over whether homework should be banned will not be resolved with these homework statistics. But, these facts and figures can help you to pursue a position in a school debate on the topic – and with that, I hope your debate goes well and you develop some great debating skills!
Chris Drew (PhD)
Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]
- Chris Drew (PhD) https://helpfulprofessor.com/author/admin/ 31 Instinct Examples (In Humans and Animals)
- Chris Drew (PhD) https://helpfulprofessor.com/author/admin/ Montessori vs Reggio Emilia vs Steiner-Waldorf vs Froebel
- Chris Drew (PhD) https://helpfulprofessor.com/author/admin/ 15 Meritocracy Examples
- Chris Drew (PhD) https://helpfulprofessor.com/author/admin/ 21 Types of Teaching Styles
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News and insight from the office for national statistics, health data: preparing for the next global pandemic.
- Statistically Speaking
- November 20, 2023
The ONS led the way informing the UK response to the Coronavirus pandemic, but looking beyond our shores, how well equipped is the world to spot and monitor emerging infections?
In the latest episode of Statistically Speaking we explore how pandemic preparedness has been the driving force behind two important pieces of work.
Joining podcast host Miles Fletcher are Josie Golding of the Wellcome Trust, who’ll share how even weather events like El Niño could affect the spread of viruses, and ONS colleague Joy Preece to tell us all about the ‘pandemic preparedness toolkit’, a five-year project backed by Wellcome to create and develop resources that will help countries with health surveillance in the event of future pandemics.
Closer to home, a new UK winter surveillance study to gather vital data on COVID-19 is now well underway. Jo Evans, its head of operations, explains:
“ We know that the NHS really suffers through the winter with increased pressures , and this is all about understanding what’s happening in the community, and the impact that is having on our healthcare services.”
Around 145,000 people will take part, and remarkably we got halfway to that target within the first 48 hours, that’s how keen people are to take part in this study and help us to get on the front foot of potential future outbreaks.”
Click here to listen to the full episode now or find it on your podcast app of choice.
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Amazon Redshift announces integration with AWS Glue column-level statistics
Posted On: Nov 20, 2023
Amazon Redshift can now leverage the column-level statistics stored in AWS Glue Data Catalog to improve data lake query performance by generating optimized query plans.
AWS Glue supports column-level statistics in the AWS Glue Data Catalog, which allows customers to store statistical information such as minimum and maximum values and number of distinct values for each column. Amazon Redshift now automatically retrieves this information from AWS Glue, then optimize query plans using statistics and provide performance improvements for your data lake queries. With the recently introduced AWS Glue capability of generating column-level statistics, you can automatically collect statistical information from your data lake tables and update the column-level statistics instead of populating this information manually.
To get started, you can use AWS Glue Console or AWS Glue APIs to generate column statistics for your data lake tables, and then you can run queries on these tables in Redshift using auto-mounted Glue catalog or external schemas.
Amazon Redshift data lake query plan optimizations using AWS Glue column-level statistics is generally available in all AWS Regions where Amazon Redshift Spectrum or Amazon Redshift Serverless are available. To learn more visit the Amazon Redshift Database Developer Guide and AWS Glue documentation .