what is statistics?
statistics is a branch of applied mathematics that involves the collection, description, analysis, and interference of conclusion from quantitative data. The mathematicl theroies behind statistics rely heavily on diffrential and integral calculus,linear algebra, and probabillity theory. Statisticans, people who do statistics , are particularly concerned with determining how to draw reliable conclusions about large groups and genrel events from the behavior and other observable characteristics of small samples. These small samples represent a portion of the large group or a limited number of in stances of agenrel phenomenon.
The two major areas of statistics are known ad descriptive statistics, which describe the properties of sample and population data, and inferential, which use those properties to test hypotheses and draw con clusions.
some common statistic tool and procedures include the following:
Descriptive
Mean(average)
variance
skewness
inferential
linear regression analysis
Analysis of variance (ANOVA)
Logit/probit models
Null hypothesis testing
KEY TAKEAWAYS
Statistics is the study and manipulation of data, including ways to gather, review,analyze, and draw conclusions from data.
The two major areas of statistics are descrptive and inferential statistics.
statustics can be used to make better informed business and investing decision.
UNDERSTANDING STATISTICS
Statistics are used virtually all scientific deciplines such as the physical and social science, as well as in business, the humanties, government, and munufacturing. Statistics is fundamentally a branch of applied mathematics that develiped from the application of mathematical tools including calculas and linear algebra to probability theory.
In practice, statistics is the idea we can learn about the properties of large sets of objects or events by studying the characteristics of a smaller number of similer objects or events. Becuse in many cases gathering comprehensive data about an etire population is too costly, costly, difficult, or flat out impossible, statistics start with a sample that can conventiently or affordably be observed.
Two types of statistics methods are used in analyzing dat: descriptive statistics and inferential statistics. Statistics measure and gather data about the individulas or elements of sample, then analyz this data to generate descriptive statistics. They can the use these observed characteristivs o the sample data , which are properly called "statistics" to make inferences or educated, guesses about the unmeasured characteristics of the broader population, known as the parameters.
Descriptive statistics
Descriptive statistics mostly focus on the central tendecy, variable, and distrubution of sample data. Central tedency means the estimate of the characteristic, a typical element of a sample or population, and includs descriptive such as Mean , Media and Mode. Variability refers to a set of statistics that show much diffrence there is among the elements of a sample or population along the characteristics measured, and includs metircs such as range, variance, and standard deviation.
The distribution refers to the overall "shape" of the data, which can be depicted on a chart such as a histogram or dot plot, and includes properties such as the probabilty distribution functon, skewness, and kurtosis. Descriptive statistics can also descrieb diffrences between observed characteristiscs of the element of a data set. Descriptive statistics help us understand the collective properties of the elements of a data sample and from the basis for testing hypotheses and making prediction using inferential statistic.
Inferential Statistics
Inferntial statistics are tools that statisticans use to draw conclusion about the characteristics of a population, drawn from the charactesriestics of a sample, and to decide how certain they can be of the reliability of those cinclusion.Based on the sample size and distribution statistics can calculate the probabilty that statistics, which measure the central tendency, varability, distribution, and relationship between characteristics within a data sample, provide an accurate picture of the croesponding parameters of the whole population from which the sample is drawn.
Inferntial statistic are used to make generlization about large group, such as estimating average demand for a product by surveying a sample of cinsumers buying habists or to attempt to predict future events, such as projecting the future return of a security or asset class based on returns in a sample period.
Regression analysis is a widely used technique of statustics inference used to determine the strength and nature of the relationship between a depenent variable and one of more explanatory variables. The output of a regression modle is often analyzed for a statistics singnificance, which is refers to the claim that a result from findings genratedby testing or experimention is not likely to have occured randomly or by chance but is likely to be attributable to specific cause elucidated by the data. Having statistical significance is important for acadmic diciplines or practitioner that rely heavily on analying data and reserch.
What is the Difference between Descriptive and inferential statistics?
Descriptive statistics are used to describe or summarize the characteristics of a sample data set, such as veriable's means, standar deviation, or frequency. Ibferential statistics , in contrast, employs and number of techniques to relate variables in a data set to one another, for example using correlation or regression analysis. These can then be used to estimate forecasts or infer causality.
who use statistics?
Statistics are used widely across an array and professions. Any time data are collected and analyzed, statistics are being done. This can range from government agencies to acadmeic reserch to analying investment.
How are used statistics used in economics and finance?
Economists collect and look at all sorts of data, ranging from consumer spending to housing starts to inflation to GDP growth. In finance, analysts and investors collect data about companies, industries, sentiments, and market data on price and volume. Together, the use of inferential statistics in these field is known as econometircs. Severl important financial models from CAPM to Modren portfolio theory and the black scholes option pricing model, rely on statistics inference.