unit 3

Unit 3

Bhuvanesh R 

I b.com

Statistics in Math: Definition, Types, and Important 

What Is Statistics?

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory.

People who do statistics are referred to as statisticians. They're particularly concerned with determining how to draw reliable conclusions about large groups and general 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 instances of a general phenomenon.

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 descriptive and inferential statistics.
• Statistics can be communicated at different levels ranging from non-numerical descriptor (nominal-level) to numerical in reference to a zero-point (ratio-level).
• Several sampling techniques can be used to compile statistical data, including simple random, systematic, stratified, or cluster sampling.
• Statistics are present in almost every department of every company and are an integral part of investing as well.

Investopedia / Dennis Madamba

Understanding Statistics

Statistics are used in virtually all scientific disciplines, such as the physical and social sciences as well as in business, the humanities, government, and manufacturing. Statistics is fundamentally a branch of applied mathematics that developed from the application of mathematical tools, including calculus and linear algebra to probability theory.

In practice, statistics is the idea that we can learn about the properties of large sets of objects or events (a population) by studying the characteristics of a smaller number of similar objects or events (a sample). Gathering comprehensive data about an entire population is too costly, difficult, or impossible in many cases so statistics start with a sample that can be conveniently or affordably observed

Statisticians measure and gather data about the individuals or elements of a sample, then they analyze this data to generate descriptive statistics. They can then use these observed characteristics of the sample data, which are properly called "statistics," to make inferences or educated guesses about the unmeasured (or unmeasured) characteristics of the broader population, known as the parameters.

Statistics informally dates back centuries. An early record of correspondence between French mathematicians Pierre de Fermat and Blaise Pascal in 1654 is often cited as an early example of statistical probability analysis.1

Descriptive and Inferential Statistics

The two major areas of statistics are known as descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions. Descriptive statistics include mean (average), variance, skewness, and kurtosis. Inferential statistics include linear regression analysis, analysis of variance (ANOVA), logit/Probit models, and null hypothesis testing.

Descriptive Statistics

Descriptive statistics mostly focus on the central tendency, variability, and distribution of sample data. Central tendency means the estimate of the characteristics, a typical element of a sample or population. It includes descriptive statistics such as mean, median, and mode.

Variability refers to a set of statistics that show how much difference there is among the elements of a sample or population along the characteristics measured. It includes metrics 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 a dot plot, and includes properties such as the probability distribution function, skewness, and kurtosis. Descriptive statistics can also describe differences between observed characteristics of the elements of a data set. They can help us understand the collective properties of the elements of a data sample and form the basis for testing hypotheses and making predictions using inferential statistics.

Inferential Statistics

Inferential statistics are tools that statisticians use to draw conclusions about the characteristics of a population, drawn from the characteristics of a sample, and to determine how certain they can be of the reliability of those conclusions. Based on the sample size and distribution, statisticians can calculate the probability that statistics, which measure the central tendency, variability, distribution, and relationships between characteristics within a data sample, provide an accurate picture of the corresponding parameters of the whole population from which the sample is drawn.

Inferential statistics are used to make generalizations about large groups, such as estimating average demand for a product by surveying a sample of consumers' buying habits or attempting to predict future events. This might mean 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 statistical inference used to determine the strength and nature of the relationship (the correlation) between a dependent variable and one or more explanatory (independent) variables. The output of a regression model is often analyzed for statistical significance, which refers to the claim that a result from findings generated by testing or experimentation is not likely to have occurred randomly or by chance. It's likely to be attributable to a

 Bhuvanesh R  23ucm03

I b.com 

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