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Ideally, statisticians compile data about the entire population an operation called census. This may be organized by governmental statistical institutes.

Descriptive statistics can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data types like income , while frequency and percentage are more useful in terms of describing categorical data like race.

When a census is not feasible, a chosen subset of the population called a sample is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting.

Again, descriptive statistics can be used to summarize the sample data. However, the drawing of the sample has been subject to an element of randomness, hence the established numerical descriptors from the sample are also due to uncertainty.

To still draw meaningful conclusions about the entire population, inferential statistics is needed. It uses patterns in the sample data to draw inferences about the population represented, accounting for randomness.

These inferences may take the form of: Inference can extend to forecasting , prediction and estimation of unobserved values either in or associated with the population being studied; it can include extrapolation and interpolation of time series or spatial data , and can also include data mining.

When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples.

Statistics itself also provides tools for prediction and forecasting through statistical models. The idea of making inferences based on sampled data began around the mids in connection with estimating populations and developing precursors of life insurance.

To use a sample as a guide to an entire population, it is important that it truly represents the overall population.

Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole.

A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures.

There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.

Sampling theory is part of the mathematical discipline of probability theory. Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.

The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method.

The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples.

Statistical inference, however, moves in the opposite direction— inductively inferring from samples to the parameters of a larger or total population.

A common goal for a statistical research project is to investigate causality , and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables.

There are two major types of causal statistical studies: In both types of studies, the effect of differences of an independent variable or variables on the behavior of the dependent variable are observed.

The difference between the two types lies in how the study is actually conducted. Each can be very effective. Instead, data are gathered and correlations between predictors and response are investigated.

While the tools of data analysis work best on data from randomized studies , they are also applied to other kinds of data—like natural experiments and observational studies [15] —for which a statistician would use a modified, more structured estimation method e.

Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company.

The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line workers.

The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity.

It turned out that productivity indeed improved under the experimental conditions. However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness.

The Hawthorne effect refers to finding that an outcome in this case, worker productivity changed due to observation itself.

Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed. An example of an observational study is one that explores the association between smoking and lung cancer.

This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a cohort study , and then look for the number of cases of lung cancer in each group.

Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales.

Nominal measurements do not have meaningful rank order among values, and permit any one-to-one transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation.

Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary as in the case with longitude and temperature measurements in Celsius or Fahrenheit , and permit any linear transformation.

Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation.

Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables , whereas ratio and interval measurements are grouped together as quantitative variables , which can be either discrete or continuous , due to their numerical nature.

Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type , polytomous categorical variables with arbitrarily assigned integers in the integral data type , and continuous variables with the real data type involving floating point computation.

But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented.

Other categorizations have been proposed. For example, Mosteller and Tukey [18] distinguished grades, ranks, counted fractions, counts, amounts, and balances.

Nelder [19] described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman , [20] van den Berg The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions.

Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer" Hand, , p. Consider independent identically distributed IID random variables with a given probability distribution: A statistic is a random variable that is a function of the random sample, but not a function of unknown parameters.

The probability distribution of the statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: Commonly used estimators include sample mean , unbiased sample variance and sample covariance.

A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on the unknown parameter is called a pivotal quantity or pivot.

Widely used pivots include the z-score , the chi square statistic and Student's t-value. Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient.

Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the limit to the true value of such parameter.

Other desirable properties for estimators include: UMVUE estimators that have the lowest variance for all possible values of the parameter to be estimated this is usually an easier property to verify than efficiency and consistent estimators which converges in probability to the true value of such parameter.

This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: Interpretation of statistical information can often involve the development of a null hypothesis which is usually but not necessarily that no relationship exists among variables or that no change occurred over time.

The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H 0 , asserts that the defendant is innocent, whereas the alternative hypothesis, H 1 , asserts that the defendant is guilty.

The indictment comes because of suspicion of the guilt. The H 0 status quo stands in opposition to H 1 and is maintained unless H 1 is supported by evidence "beyond a reasonable doubt".

However, "failure to reject H 0 " in this case does not imply innocence, but merely that the evidence was insufficient to convict.

So the jury does not necessarily accept H 0 but fails to reject H 0. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test , which tests for type II errors.

What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis. Working from a null hypothesis , two basic forms of error are recognized:.

Standard deviation refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean.

A statistical error is the amount by which an observation differs from its expected value , a residual is the amount an observation differs from the value the estimator of the expected value assumes on a given sample also called prediction.

Mean squared error is used for obtaining efficient estimators , a widely used class of estimators. Root mean square error is simply the square root of mean squared error.

Many statistical methods seek to minimize the residual sum of squares , and these are called " methods of least squares " in contrast to Least absolute deviations.

The latter gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also differentiable , which provides a handy property for doing regression.

Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares.

Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise.

The Schalker Kreisel literally: Schalke won all three matches played in the years — The two teams did not meet again until the creation of the Gauliga in With the creation of the Gauliga in , Dortmund developed its intense rivalry with Schalke.

Schalke was the most successful German club of the era, six of the club's to date seven German Championships and one Cup victory date back to the years of to Schalke dominated the early meetings, winning 14 matches, and losing only once, with one match played to a draw.

August Lenz's goal on 14 November secured Dortmund's first ever victory against Schalke. Dortmund win the Westphalia championship final 3—2 over Schalke, ending Schalke's domination in the region.

The years —63 continued to be a reversal of fortune for Dortmund, winning 9 of the first 13 Revierderbies during this era, and losing only 7 of 32 overall.

Dortmund also won three Oberliga championships in these years. The creation of the Bundesliga in began with Dortmund continuing their winning ways, by taking 8 of the first 10 meetings.

Schalke's 1—0 victory on 20 April , saw the return of Schalke's fortune and the fall of Dortmund.

After Dortmund's 0—3 defeat on 4 March , and subsequent relegation from the league, the teams did not play each other again until

## Revierderby statistik -

Schalke 04 empfängt am Sonntag Borussia Dortmund zum Revierderby Als Revierderby bezeichnet man im weiteren Sinne das Aufeinandertreffen zweier Sportvereine aus dem Ruhrgebiet. Das erste Bundesliga-Duell am 7. Doch in Erinnerung bleiben nicht Statistiken, sondern Geschichten. Fakten zum Revierderby Schalke - Borussia Dortmund. Dann aber bricht Dortmund ein, Schalke trifft vor Lutz Wagner sitzt in der Schiedsrichterkabine.### statistik revierderby -

Ligarekord sind die zwölf Dortmunder Treffer in der Viertelstunde nach dem Wechsel. Rausgehen, gefühlt bei Null anfangen und wenigstens die zweite Halbzeit gewinnen, lautete die Vorgabe. Und machte seinem Team dann ganz ruhig eine simple Ansage: Doch er bricht nach dem ersten Gegentor in der Die Antwort ist ernüchternd: Gerd Henning hatte eine Taktik. Bereits die erste Partie nach Kriegsende konnte Borussia Dortmund für sich entscheiden und wurde durch einen 3: Und als Nuri Sahin erklärte, es sei "fatal, dass wir einem Gegner noch ein Stück vom Kuchen geben, der schon am Boden lag", da sprach der traurig-leere Blick Bände.To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case: The concept of correlation is particularly noteworthy for the potential confusion it can cause.

Statistical analysis of a data set often reveals that two variables properties of the population under consideration tend to vary together, as if they were connected.

For example, a study of annual income that also looks at age of death might find that poor people tend to have shorter lives than affluent people. The two variables are said to be correlated; however, they may or may not be the cause of one another.

The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable.

For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. See Correlation does not imply causation.

Some scholars pinpoint the origin of statistics to , with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.

The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general.

Today, statistics is widely employed in government, business, and natural and social sciences. Its mathematical foundations were laid in the 17th century with the development of the probability theory by Gerolamo Cardano , Blaise Pascal and Pierre de Fermat.

Mathematical probability theory arose from the study of games of chance, although the concept of probability was already examined in medieval law and by philosophers such as Juan Caramuel.

The modern field of statistics emerged in the late 19th and early 20th century in three stages. Galton's contributions included introducing the concepts of standard deviation , correlation , regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight, eyelash length among others.

Ronald Fisher coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation".

The second wave of the s and 20s was initiated by William Gosset , and reached its culmination in the insights of Ronald Fisher , who wrote the textbooks that were to define the academic discipline in universities around the world.

Fisher's most important publications were his seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance , which was the first to use the statistical term, variance , his classic work Statistical Methods for Research Workers and his The Design of Experiments , [44] [45] [46] [47] where he developed rigorous design of experiments models.

He originated the concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information.

Edwards has remarked that it is "probably the most celebrated argument in evolutionary biology ". The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the s.

They introduced the concepts of " Type II " error, power of a test and confidence intervals. Jerzy Neyman in showed that stratified random sampling was in general a better method of estimation than purposive quota sampling.

Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology.

The use of modern computers has expedited large-scale statistical computations, and has also made possible new methods that are impractical to perform manually.

Statistics continues to be an area of active research, for example on the problem of how to analyze Big data. Applied statistics comprises descriptive statistics and the application of inferential statistics.

Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.

There are two applications for machine learning and data mining: Statistics tools are necessary for the data analysis.

Statistics is applicable to a wide variety of academic disciplines , including natural and social sciences , government, and business. Statistical consultants can help organizations and companies that don't have in-house expertise relevant to their particular questions.

The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science.

Early statistical models were almost always from the class of linear models , but powerful computers, coupled with suitable numerical algorithms , caused an increased interest in nonlinear models such as neural networks as well as the creation of new types, such as generalized linear models and multilevel models.

Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling , such as permutation tests and the bootstrap , while techniques such as Gibbs sampling have made use of Bayesian models more feasible.

The computer revolution has implications for the future of statistics with new emphasis on "experimental" and "empirical" statistics.

A large number of both general and special purpose statistical software are now available. Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences.

What was once considered a dry subject, taken in many fields as a degree-requirement, is now viewed enthusiastically.

Statistical techniques are used in a wide range of types of scientific and social research, including: Some fields of inquiry use applied statistics so extensively that they have specialized terminology.

In addition, there are particular types of statistical analysis that have also developed their own specialised terminology and methodology:. Statistics form a key basis tool in business and manufacturing as well.

It is used to understand measurement systems variability, control processes as in statistical process control or SPC , for summarizing data, and to make data-driven decisions.

In these roles, it is a key tool, and perhaps the only reliable tool. From Wikipedia, the free encyclopedia. For other uses, see Statistics disambiguation.

Statistical data type and Levels of measurement. History of statistics and Founders of statistics. List of fields of application of statistics.

Actuarial science assesses risk in the insurance and finance industries Applied information economics Astrostatistics statistical evaluation of astronomical data Biostatistics Business statistics Chemometrics for analysis of data from chemistry Data mining applying statistics and pattern recognition to discover knowledge from data Data science Demography statistical study of populations Econometrics statistical analysis of economic data Energy statistics Engineering statistics Epidemiology statistical analysis of disease Geography and geographic information systems , specifically in spatial analysis Image processing Medical statistics Political science Psychological statistics Reliability engineering Social statistics Statistical mechanics.

Abundance estimation Data science Glossary of probability and statistics List of academic statistical associations List of important publications in statistics List of national and international statistical services List of statistical packages software List of statistics articles List of university statistical consulting centers Notation in probability and statistics.

Foundations of statistics List of statisticians Official statistics Multivariate analysis of variance. Stanford Encyclopedia of Philosophy.

Meaning and Definition of Statistics". Statistics for the Twenty-First Century. The Mathematical Association of America. Handbook of stochastic analysis and applications.

Theory of statistics Corr. A New Kind of Science. Theory and Practice , Cambridge University Press.

Modern Epidemiology 3rd ed. Data analysis and regression. The knowledge needed to computerise the analysis and interpretation of statistical information.

In Expert systems and artificial intelligence: Library Association Report, London, March, 23— Cartography and Geographic Information Science.

Choosing an analysis method. Measurement theory and practice: The world through quantification. The Cambridge Dictionary of Statistics.

Cambridge, UK New York: In Pearsall, Deborah M. Journal of the American Statistical Association. How to Lie with Statistics.

The dependability of a sample can be destroyed by [bias] Review of the International Statistical Institute 5 4: Franklin, The Science of Conjecture: Studies in the history of statistical method.

Archived from the original on Fisher, The Design of Experiments ii. American Educational Research Journal. Fisher and the Design of Experiments, —".

Eugenics Review 7 Anecdotal, Historial and Critical Commentaries on Genetics. The Genetics Society of America Trends, Ecology and Evolution 21 Comptes Rendus Biologies The method of stratified sampling and the method of purposive selection".

On 24 August , in front of over 70, fans, former Dortmund midfielder Ingo Anderbrügge scored in the 2nd minute to put Schalke ahead 1—0.

However, Dortmund equalized in the 36th and the 1st half finished with the scored tied 1—1. In the 2nd half, Schalke exploded, stunning Dortmund 5—2.

Dortmund's overall success that season eclipsed the defeat, winning the next Revierderby 2—0, and finishing the league in second place that year, tied in points, but losing out to VfB Stuttgart on goal differential.

The following years saw Schalke holding a slim advantage since , winning 11, drawing 14, and losing 8 of the matches.

Despite Schalke's recent Revierderby success, including losing only five derbies since until April , Dortmund holds the advantage in overall success during this era, winning five Bundesliga championships —95, —96, —02, —11 and —12 , one German Cup , one UEFA Champions League competition , and one Intercontinental Cup since , while Schalke won the UEFA Cup once and the German Cup three times , and One of these, in , ended a nearly seven-year undefeated streak for Schalke in the derby, while the other, in May , took on almost traumatic proportions, as Schalke lost the derby and the league lead, which they had held for three months, on the penultimate day of the season in Dortmund.

After each of these victories, Borussia Dortmund took the unprecedented step of selling specially-decorated replica shirts to commemorate the occasion.

In , Dortmund fan groups celebrated Schalke's fifty years without a league title. From Wikipedia, the free encyclopedia.

Revierderby Map of the Ruhr area including Gelsenkirchen and Dortmund. Deutsches Aussprachewörterbuch in German.

With an October deadline looming and an unpopular proposal in hand, time is running out for Theresa May to secure a deal with the European Union.

This topic highlights some the main issues standing in the way of a deal and explores how the British public have reacted to the ongoing political drama.

Revenue might still pale in comparison to other sports, but the recent growth of electronic sports, or eSports, has been immense.

This dossier analyzes the popularity of video games and digital games in the Netherlands and the attitude shown towards the trend of online gaming.

As consumers become aware of the potentially harmful ingredients used in conventional beauty products, many are seeking green alternatives which pose a lesser risk to the skin and the environment.

This topic page provides an overview of natural and organic cosmetic sales and UK consumer attitudes. The first football study that compares the 5 big European leagues from a fan's perspective.

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Zwei der drei Partien verlor Schalke Beste Spielothek in Gotzweis finden. Nachher spricht er von "persönlicher Wahrnehmung", was niemanden wirklich zufriedenstellt. Die Treffer gegen Dortmund sind die zweitbeste "königsblaue" Ausbeute in der Liga. Ihr Kommentar zum Thema. Doch in Erinnerung bleiben nicht Statistiken, sondern Geschichten. Auf der anderen Seite fiel es den Borussen schwer, die Sprache überhaupt wiederzufinden.### Revierderby Statistik Video

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