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'Study Sea Storm' 2017 Spring (People's Education Edition) Eighth Grade Mathematics Book Preparation Materials Fun Math - Statistics Development History Download 'School Storm' 2017 Spring (People's Education Edition) Eighth grade mathematics book preparation materials interesting mathematics - statistical development history statistical overview [Edit this paragraph] Statistics is a branch of applied mathematics, mainly through the use of probability theory to establish mathematical models, collecting data of the observed system, Quantitative analysis, summarization, and further inference and prediction, to provide basis and reference for relevant decisions. It is widely used in various disciplines, from physical and social sciences to humanities, and even to business and government and government intelligence decisions. ?? Statistics are mainly divided into descriptive statistics and inferential statistics. Given a set of data, statistics can summarize and describe this data, which is called descriptive statistics.

In addition, the observer constructs a mathematical model to explain its randomness and uncertainty in the form of data, in order to infer the steps and maternal in the study. This usage is called inferential statistics.

Both of these usages can be referred to as applied statistics.

An additional discipline called mathematical statistics is devoted to discussing the theoretical foundation behind this subject.

The development of statistics [Edit this paragraph]? Statistical English statistics were originally derived from the modern Latin statisticumcollegium (Congress) and the Italian statista (national or politician).

Devin Statisik, first used by Gottfried Achenwall (1749), represents the study of national data, that is, 'the study of national science.'

In the nineteenth century, statistics explored its significance in a wide range of data and materials, and was introduced to the English-speaking world by John Sinclair.

?? Statistics is a very old science. It is generally believed that its academic research began in the Aristotle era of ancient Greece and has a history of more than 2,300 years.

It originated from the study of socio-economic problems. In the course of more than two thousand years of development, statistics have experienced at least three stages of development: “city-state politics”, “political calculations” and “statistical analysis science”.

The so-called 'mathematical statistics' is not a new discipline independent of statistics. Rather, it is a comprehensive term for all new methods of collecting and analyzing data formed by statistics in the third stage of development.

Probability theory is the theoretical basis of mathematical statistics methods, but it does not belong to the category of statistics, but belongs to the category of mathematics.

?? Three stages of the development of statistics? The first stage is called the 'Mattersofstate' stage? The 'City State Political Situation' stage begins with Aristotle in ancient Greece to write 'City State Politics' 'or 'City State Minutes.'

He has written a total of 150 kinds of records, including the comparison, analysis and social science characteristics of the history, administration, science, art, population, resources and wealth of various city-states.

The statistical study of the 'city-state politics' continued for a thousand or two years until the mid-17th century, when it was gradually replaced by the term 'political arithmetic' and quickly evolved into 'statistics'.

Statistics still retains the root of the state.

?? The second stage is called the “Politcalarthmetic” stage. There is no obvious demarcation point between the “City State Politics” stage and the essential difference.

?? 'Political arithmetic' is characterized by the combination of statistical methods and mathematical calculations and reasoning methods.

The way to analyze socioeconomic issues is more focused on using quantitative analysis methods.

?? In 1690, the British William Pedi Publishing (Political Arithmetic) book was the starting point of this stage.?? William's method of using the figures, weights and scales to quantify socio-economic phenomena is modern statistics. An important feature of learning.

So, William? The younger brother's (political arithmetic) was later evaluated by scholars as the source of modern statistics, William? The younger brother was also evaluated as the father of modern statistics.

?? There are three types of numbers used by the younger brother in the book: ?? The first category is the number of statistical surveys and empirical observations of socioeconomic phenomena. Because of historical conditions, the book passed a rigorous statistical survey. The data obtained is small, and the number based on experience is large; the second type is the number calculated by some mathematical method.

The method of calculation can be divided into three types: ?? '(1) Based on known or known quantities, the method of estimating according to a specific relationship; ?? (2) by applying the theory of numbers Sexual reasoning to calculate the method; (3) the method based on the average number of calculations;;? The third type is the exemplary number used for theoretical reasoning. The reasoning with symbols is called 'algebraic algorithm'.

From the method of using data by the younger brother, the statistics of the 'political arithmetic' stage have more clearly reflected the characteristics of 'collecting and analyzing the science and art of data', and the statistical empirical methods and theoretical analysis methods are integrated. The method is still inherited even by modern statistics.

?? The third stage is called the “Science of Statistical Analysis” stage. The combination of statistics and mathematics that appeared in the “political arithmetic” stage gradually developed into “statistical analysis science”.

?? At the end of the 19th century, the names of courses such as 'national conditions' or 'political calculations' opened by European universities gradually disappeared, and the 'Statistical Analysis Science' course was replaced by the 'Statistical Analysis Science' course. The content is still an analysis of socioeconomic issues.

?? The emergence of the 'Statistical Analysis Science' course is the beginning of the stage of modern statistical development. In 1908, 'Student' (WilliamSleeyGosset's pen name Student) published a paper on t distribution, which is a development in statistics An epoch-making article in history.

It created a small sample instead of a large sample, creating a new era of statistics.

?? The representative of modern statistics is the first to promote the Belgian statistician AdolpheQuelet, who applies statistical analysis science widely in the social sciences, natural sciences and engineering technology sciences because he believes that statistics can be The general research method used to study any science. The theoretical basis of modern statistics The probability theory begins with the study of the opportunity of gambling, which began around 1477.

The mathematicians conducted long-term research to explain the general rules governing opportunities, and gradually formed a theoretical framework of probability theory.

Based on the further development of probability theory, by the beginning of the 19th century, mathematicians gradually established the theory of observation error, the theory of normal distribution and the method of least squares.

Therefore, modern statistical methods have a solid theoretical foundation.

Statistical concepts [Edit this paragraph] In order to apply statistics to scientific, industrial and social issues, we start with the research matrix.

This could be the people of a country, the crystals in the stone, or the goods produced in a particular factory.

A parent may even consist of many identical observations; the mother of this data collection is called a time series.

?? For practical reasons, we chose to study a subset of the maternal instead of studying each of the maternal data. This subset is called a sample.

The sample collected by an experimental design experiment is called data.

Information is the subject of statistical analysis and is used for two related purposes: description and inference.

?? Describe the statistical processing of the narrative question: Can the material be validly abstracted, whether mathematical or graphical, to represent the nature of the parent? The basic mathematical description includes the mean and standard deviation.

The abstract of the image contains a variety of tables and diagrams.

?? Inferential statistics are used to model the data in the data, calculate its probability, and make inferences about the parent.

This inference may be presented as an answer to a yes/wrong question (hypothetical test), an estimate of the amount of digital features (estimation), a prediction of future observations, a prediction of relevance (correlation), or a relational model (regression).

Other modeling techniques include analysis of variance (ANOVA), time series, and data mining.

?? Relevant concepts are particularly worthy of being discussed.

A statistical analysis of a collection of data may show that two variables (two properties in the parent) tend to change together as if they were connected.

For example, research journals on human income and age of death may find that the poor tend to have shorter lives on average than the rich.

These two variables are called related.

But actually, we can't directly infer the causal relationship between these two variables; see the correlation inference causality (logical fallacy).

?? If the sample is sufficient to represent the mother, the inferences and conclusions made by the sample can be extended to the entire parent.

The biggest problem is to decide if the sample is enough to represent the entire parent.

Statistics provides a number of methods to estimate and correct the randomness (error) in the sample and data collection process, as described above through empirically designed experiments.

See experimental design.

?? To understand randomness or probability, you must have basic mathematical concepts.

Mathematical statistics (often also called statistical theory) is a branch of applied mathematics that uses probability theory to analyze and validate the theoretical basis of statistics.

?? Any statistical method is valid only if the system or the parent in question satisfies the basic assumptions of the methodology.

Misuse of statistics can lead to serious errors in description or inference, which can affect the reliability of social policies, medical practices, and the structure of bridges or nuclear power generation plans.

?? Even if statistics are applied correctly, the results may be difficult for people who are not experts to make statements.

For example, significant changes in statistics may be caused by random variables in the sample, but this significance may be contrary to public intuition.

People need some statistical skills (or doubts) to face the information they get through daily citing statistics in their daily lives.

Statistical methods [Edit this paragraph] 1) The scale of measurement?? Statistics There are four measurement scales or four measurement methods.

These four measurements (name, order, equidistance, equal ratio) have unequal applicability in the statistical process.

Ratiomeasurements have a zero value and the distance between the data is equal. The distance between the data of the Intervalmeasures is equal, but its zero value is not absolute. Defined (such as intelligence or temperature measurements).

(Ordinalmeasurements) The meaning of the order scale is not expressed in its value but above its order.

The measured values ??of Nominalmeasurements are not meaningful.

?? 2) Statistical Techniques? Here are some well-known statistical verification methods and procedures for validating experimental data? Fisher'sLeastSignificantDifferencetest? Student's t-test (Student' -test)?? Mann-WhitneyU?? Regression analysis (regressionanalysis)? Correlation? Pearson product-moment correlation coefficient (? Pearsonproduct-momentcorrelationcoefficient)?? Correlation coefficient (Spearman 'srankcorrelationcoefficient'?? Chi-square.

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