## Explain the Statistics with different definitions

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. Statisticians, people who do statistics, are 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.

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.

Some common statistical tools and procedures include the following:

• Descriptive
• Mean (average)
• Variance
• Skewness
• Kurtosis
• Inferential
• Linear regression analysis
• Analysis of variance (ANOVA)
• Logit/Probit models
• Null hypothesis testing
• 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 used to make better-informed business and investing decisions.

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 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). Because in many cases gathering comprehensive data about an entire population is too costly, difficult, or flat out impossible, statistics start with a sample that can conveniently or affordably be observed.

Two types of statistical methods are used in analyzing data: descriptive statistics and inferential statistics. Statisticians measure and gather data about the individuals or elements of a sample, then 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.

(b)    What is the importance of Statistics?

The field of statistics is the science of learning from data. Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions. Statistics allows you to understand a subject much more deeply.

First, statisticians are guides for learning from data and navigating common problems that can lead you to incorrect conclusions. Second, given the growing importance of decisions and opinions based on data, it’s crucial that you can critically assess the quality of analyses that others present to you.

Personally, I think statistics is an exciting field about the thrill of discovery, learning, and challenging your assumptions. Statistics facilitates the creation of new knowledge. Bit by bit, we push back the frontier of what is known.

Statistics are not just numbers and facts. You know, things like 4 out of 5 dentists prefer a specific toothpaste. Instead, it’s an array of knowledge and procedures that allow you to learn from data reliably. Statistics allow you to evaluate claims based on quantitative evidence and help you differentiate between reasonable and dubious conclusions. That aspect is particularly vital these days because data are so plentiful along with interpretations presented by people with unknown motivations.

Statisticians offer critical guidance in producing trustworthy analyses and predictions. Along the way, statisticians can help investigators avoid a wide variety of analytical traps.

When analysts use statistical procedures correctly, they tend to produce accurate results. In fact, statistical analyses account for uncertainty and error in the results. Statisticians ensure that all aspects of a study follow the appropriate methods to produce trustworthy results. These methods include:

• Producing reliable data.
• Analyzing the data appropriately.
• Drawing reasonable conclusions.

Statisticians Know How to Avoid Common Pitfalls

Using statistical analyses to produce findings for a study is the culmination of a long process. This process includes constructing the study design, selecting and measuring the variables, devising the sampling technique and sample size, cleaning the data, and determining the analysis methodology among numerous other issues. The overall quality of the results depends on the entire chain of events. A single weak link might produce unreliable results. The following list provides a small taste of potential problems and analytical errors that can affect a study.

Biased samples:

An incorrectly drawn sample can bias the conclusions from the start. For example, if a study uses human subjects, the subjects might be different than non-subjects in a way that affects the results. See Populations, Parameters, and Samples in Inferential Statistics.

Overgeneralization:

Findings from one population might not apply to another population. Unfortunately, it’s not necessarily clear what differentiates one population from another. Statistical inferences are always limited, and you must understand the limitations.

Causality:

How do you determine when X causes a change in Y? Statisticians need tight standards to assume causality whereas others accept causal relationships more easily. When A precedes B, and A is correlated with B, many mistakenly believe it is a causal connection! However, you’ll need to use an experimental design that includes random assignment to assume confidently that the results represent causality. Learn how to determine whether you’re observing causation or correlation!

Incorrect analysis:

Are you analyzing a multivariate study area with only one variable? Or, using an inadequate set of variables? Perhaps you’re assessing the mean when the median might be better? Or, did you fit a linear relationship to data that are nonlinear? You can use a wide range of analytical tools, but not all of them are correct for a specific situation.

Violating the assumptions for an analysis:

Most statistical analyses have assumptions. These assumptions often involve properties of the sample, variables, data, and the model. Adding to the complexity, you can waive some assumptions under specific conditions—sometimes thanks to the central limit theorem. When you violate an important assumption, you risk producing misleading results.

Data mining:

Even when analysts do everything else correctly, they can produce falsely significant results by investigating a dataset for too long. When analysts conduct many tests, some will be statistically significant due to chance patterns in the data. Fastidious statisticians track the number of tests performed during a study and place the results in the proper context.