STATISTICS

INTRODUCTION

Statistics is the method of conducting a study about a particular topic by collecting, organizing, interpreting, and finally presenting data. Being a statistician at an elementary level may simply mean noticing patterns in daily circumstances and drawing conclusions about those patterns. On a grander scale, statisticians may spend months or years conducting a study before they can produce meaningful analysis of information. Statistics is its own community, with rules, procedures, and policies all built on simple mathematical principles.

Stages in the Statistical Process

The statistical process guides genuine study, and statisticians are exacting in their methodologies. The major steps of statistics are explained in a simplistic form as follows:

1. Planning a study: There must be a subject that requires investigation. Planning entails deciding what instruments (interviews, surveys, etc.) to use, who to speak with, and how to analyze findings. Instruments, in this case, are tools used in conducting a study like surveys, interviews, etc. Do you remember Timmy? In this stage, he plans to interview shoppers and count people.
2. Organizing the data: The best way to obtain the valid answers is to organize the information effectively to help expose patterns and other significant relationships. There are a variety of software programs that can help with this step. Once Timmy has gathered data, he could perform calculations of the mean, mode, and median visitors.
3. Interpreting the data: This is the heartbeat of statistics. Interpretations can have lasting repercussions, and it's important to make sure they are valid assumptions and supported by mathematical reasoning. Timmy, based on his interpretations of the numbers, could make plans to have special sales on days with the most traffic.
4. Presenting the data: The methods you chose to present the data can make findings more interesting or powerful. People use graphs, tables, and various diagrams to show relationships between data. With this information, Timmy could present compelling arguments using his analysis so that he and his business partners can discuss the most profitable possibilities for the pizza shop.

Applications of Statistics

Other than individuals and small businesses owners like Timmy who conducted their own studies, there are some entities who thrive on statistics. Here are a few major examples.

Government Agencies

The government uses statistics to make decisions about populations, health, education, etc. It may conduct research on education to check the progress of high schools students using a specific curriculum or collect characteristic information about the population using a census.

Statistical laws

Statistical law or (in popular terminology) a law of statistics represents a type of behaviour that has been found across a number of datasets and, indeed, across a range of types of data sets. Many of these observances have been formulated and proved as statistical or probabilistic theorems and the term "law" has been carried over to these theorems. There are other statistical and probabilistic theorems that also have "law" as a part of their names that have not obviously derived from empirical observations. However, both types of "law" may be considered instances of a scientific law in the field of statistics. What distinguishes an empirical statistical law from a formal statistical theorem is the way these patterns simply appear in natural distributions, without a prior theoretical reasoning about the data.

Examples

There are several such popular "laws of statistics".

The Pareto principle is a popular example of such a "law". It states that roughly 80% of the effects come from 20% of the causes, and is thusly also known as the 80/20 rule. In business, the 80/20 rule says that 80% of your business comes from just 20% of your customers. In software engineering, it's often said that 80% of the errors are caused by just 20% of the bugs. 20% of the world creates roughly 80% of worldwide GDP. 80% of healthcare expenses in the US are caused by 20% of the population.

Zipf's law, described as an "empirical statistical law" of linguistics, is another example. According to the "law", given some dataset of text, the frequency of a word is inversely proportional to its frequency rank. In other words, the second most common word should appear about half as often as the most common word, and the fifth most common world would appear about once every five times the most common word appears. However, what sets Zipf's law as an "empirical statistical law" rather than just a theorem of linguistics is that it applies to phenomena outside of its field, too. For example, a ranked list of US metropolitan populations also follow Zipf's law, and even forgetting follows Zipf's law. This act of summarizing several natural data patterns with simple rules is a defining characteristic of these "empirical statistical laws".

Examples of empirically inspired statistical laws that have a firm theoretical basis include:

·         Statistical regularity

·         Law of large numbers

·         Law of truly large numbers

·         Central limit theorem

·         Regression towards the mean

Examples of "laws" with a weaker foundation include:

·         Safety in numbers

·         Benford's law

Examples of "laws" which are more general observations than having a theoretical background:

·         Rank-size distribution

Examples of supposed "laws" which are incorrect include:

·         Law of averages

APPLIED LAWS OF STATISTICS IN REAL LIFE

You can use statistics in everyday life in the following way.

1.      Applying decision theorem in making daily decisions by calculating probability of each decision with its likelihood

2.      Using sampling method in selection of items

3.      Using transportation model in planning your daily movement

4.      Calculating the risk of taking or not taking a decision

5.      Calculate the chances of success or failure in trying a new method using binomial distribution model etc

·         Every time you go to an online shopping site like Flipkart or Amazon, you see the ratings of the products, the reviews of the customers etc. All this data that you see is nothing but statistics.

·         Every time you go to cast your vote, you compare the performance of the current government to that of the other previous governments. You also decide whom to vote on the basis on the promises made by the other party leaders which often use phrases like “We will try to improve the education rates to ……….”. All this data is part of statistics.

·         Whenever you are planning a trip or a journey, you take in account the weather conditions of the place. Since future telling machines haven’t been invented till now, all the data you see is due to the goodwill of statistics.

·         You know that in order to drive your car you are required by law to have car insurance. If you have a mortgage on your house, you must have it insured as well. The rate that an insurance company charges you is based upon statistics from all drivers or homeowners in your area.

·         Stock market is a concept we all hear about in our day to day lives and it will not come as a surprise to you that it is completely based on statistics as stock analysts also use statistical computer models to forecast what is happening in the economy.

·         Sport selections are mostly done on the basis of data about the performance and the form of the player. Also tin the modern world that we live in statistics of player make the match or game more interesting and provide ground for fans to argue about the dominance of their favorite player in the game.

REFERENCES

Kitcher, P., Salmon, W.C. (Editors) (2009) Scientific Explanation. University of                                   Minnesota Press. ISBN 978-0-8166-5765-0

Gelbukh, A., Sidorov,G. (2008). Zipf and Heaps Laws’ Coefficients Depend on          Language. In:Computational Linguistics and Intelligent Text Processing (pp. 332–335),     Springer. ISBN 978-3-540-41687-6 . link to abstract

Kitcher & Salmon (2009) p.51

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Rooney, Paula (2002-10-03). "Microsoft's CEO: 80-20 Rule Applies To Bugs, Not Just             Features". CRN. Retrieved 2017-05-05.

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"Percent of Total Health Care Expenses Incurred by Different Percentiles of U.S.         Population: 2002". Research in Action. Issue 19: Figure 1. June 2006.

Gelbukh & Sidorov (2008)              

Gabaix, Xavier (2011). "The Area and Population of Cities: New Insights          from a Different Perspective on Cities" (PDF). American Economic Review. vol 101(5):            2205–2225.

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