Meaning and Definition of Statistics in Maths

Statistics is a living subject full of challenging problems and exciting developments. Through statistics, you would have the thrill of discovering, learning, and challenging your own assumptions. With statistics, new knowledge is created by pushing the frontier of what is known.

The Power of Data

Data is all around us. The number of people in a country, sales figures of an organization, and the number of hits on a website are data that lets a business or a nation make informed decisions. 

The field of statistics is all about learning from data. It is the process of converting raw data into a meaningful, organized, and informative form. Statistical knowledge is the basis on which proper methods of collecting data, employing the right analysis, and effectively presenting the results are built. The discoveries in science and many predictions are all based on statistical methods. If you want to understand a subject deeply, you need to get into the statistics of it all.

If you are looking to learn and gather statistics notes, you must go through this article where you will learn the meaning and definition of statistics and the classification of statistics.

Meaning and Definition of Statistics

Statistics means studying, collecting, analyzing, interpreting, and organizing data. Statistics is a science that helps to gather and analyze numerical data in huge quantities. With the help of statistics, you can measure, control, and communicate uncertainty. It allows you to infer proportions in a whole, derived from a representative sample. In other words, statistics could be described as the feature or characteristic of a sample and is generally used to estimate a population parameter's value.

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The Need for Statistics

The early impetus for statistical data arose from the government’s needs for data like census and the need for information about various economic activities. In modern times, the necessity to turn large volumes of data available in many applied fields into meaningful and useful information has resulted in the evolution of both practical and theoretical statistics.

Terms Used in Statistics

Statistics is applied in many real-life situations to make it easy to understand data when data is represented in a particular number (that represents all numbers). This number is termed as a measure of central tendency, and a few common central tendencies are:

• Mean 

This is the average of given numbers and is measured by adding all the numbers and then dividing by the total count of numbers. So if a1, a2, a3, a4,...., an are n numbers then their mean \[\bar{a}\] = (a1 + a2 + a3 + …+ an)/n = \[\sum_{i=1}^{n}\] ai/n

• Median

If all the n numbers are arranged either in ascending or descending manner, then the middle number of that series denotes the median of the group. In the case of n being an odd number, the median is the observation at the ((n + 1)/2)th position. In the case of n being an even number, we get the median by taking the average of both the middle numbers i.e. the average of observations at (n/2)th and ((n + 1)/2)th observations.

• Mode 

The mode of n numbers is the number that has the highest frequency in the given sample. In case there are no numbers that are repeated in the list, then that sample has no mode.

• Range  

The range of observations is the difference between the highest and the lowest number in the list.

Example Problem on Finding Mean, Median, Mode, and Range

From the list of values given below, let us find their mean, median, mode, and range.

12, 16, 13, 14, 13, 18, 14, 21, 13

Mean - 12 + 16 + 13 + 14 + 13 + 18 + 14 + 21 + 13/9 (since there are 9 numbers in the list) = 14.88

Median - To find median we will first write down the list in ascending order: 12, 13, 13, 13, 14, 14, 16, 18, 21

Here n = 9 so it is an odd number. So the median is the number at the position (9+1)/2 = 10/2 = 5. So, the median is 14.

Mode - Since the number 13 is repeated the maximum number of times (3 times) in the list, 13 is the mode of this sample.

Range - In the list the highest value is 21 and smallest value is 12 hence range = 21 - 12 = 9

Classification of Statistics

Statistics has three broad categories as outlined below:

• Descriptive Statistics 

This is the methodology where data is effectively collected, organized, and described.

• Inferential or Inductive Statistics 

In this process, conclusions are drawn about unknown sample features taken from a population. This involves an interpretation of the descriptive stats.

• Predictive Statistics  

This is the process where future values are predicted based on historical data.

Application of Statistics

Statistics provides a clear picture of the work we do on a day-to-day basis, and it has wide applications in the following areas:

• Mathematics 

We use statistical methods like probability and dispersion, to get more accurate information.

• Economic 

Many economic parameters like the inflation of a country, employment status, exports, and imports, etc. are all heavily dependent on statistical methods.

• Medical 

Any drug is prescribed after it has been analyzed through statistics. Statistics measure the effectiveness of a drug. 

• Psychology 

Psychologists use statistics for figuring out things like peer pressure amongst youngsters.

• Education 

In schools and colleges, lecturers use statistics to interpret which course their students are more interested in.

• Business  

Business nowadays uses statistics to gauge customer preferences, product quality, target market, etc. Statistics in business is used to analyze past performances of business firms and markets, and hence, in turn, predict the future business strategies and practices. This helps businessmen to lead organizations and business firms very effectively. Description of markets, information about advertising, and price information about various things, customer demands, and responses are all recorded in statistical form. These are the statistical data used in business.   

Let us come to descriptive analysis for example. This takes a look at everything that has happened and gives an explanation for everything. Managers of various business sectors gather all the historical data to analyze failures and successes of the past. The proper term for this is “cause and effect analysis”. Sales, finance, marketing, operations are a few of the many areas where descriptive analytics is put to use. 

Let us now come to predictive analytics. Modeling and data mining are two of the statistical procedures that are a part of predictive analytics.  These statistical procedures are used for the prediction of future probabilities and trends. Besides, reporting the historical data also helps in the creation of the best estimates for future happenings. Detection of fraud, security, marketing, operations, and risk assessment are a few of the many areas where predictive analytics is put to use. 

Last but definitely not least; let us talk about prescriptive analytics. Prescriptive analytics determine the best course of action in a certain situation. For example, a certain business situation is described; prescriptive analytics will be used here to determine the best course of action in that given situation. The data of prescriptive analysis include future situations, the cause of those situations, and a way to navigate those situations. In prescriptive analytics, information is constantly updated. The constant update may change the course of action and the way to navigate it. The constant update helps managers to maintain and update their action plans according to the situation. 

• Quality Testing 

All the products a company produces go through a quality check by employing statistical tools.

• Banks decide to lend money to customers to increase the bank’s profits with a statistical approach to compare deposits and requests for loans.

• Astronomy 

The size, distance, and other parameters of objects in the universe are measured using statistical methods. The statistical methodology has deep roots in probability theory. This helps with a lot of analysis and quantitative procedures. Statistics is the best way to test astrophysical theories. This is because statistics and probabilities are the best ways to analyze theories. The quantitative procedures provided by probability theory are very useful in extracting scientific knowledge from astrophysics data. This knowledge and data are further used to analyze theories. 

There are several statistical methods that are used in astronomy for several purposes. Astrophysics is an area where statistical methods come in handy the most. 

• Weather Forecasting 

To predict the upcoming weather, a statistical tool is used to compare previous and current weather. Statistics play a huge role in Weather forecasting. Easy interpretability is one of the most important benefits of statistics usage in Weather forecasting. The visualization of results is easily interpreted in weather forecasting with the help of statistics. Statistics in weather forecasting also help laymen understand weather forecasts in a simpler and better way.  In fact, the very word forecasting is related to statistics. It refers to the prediction of future data with the help of data from the present and the past. The data collected is then analyzed to predict the weather. 

Let us take an example to understand this better. Let us consider the estimation of temperature in this case. For a specified date in the future, past temperature data and present temperature data are collected and then analyzed to predict future temperature. Forecasting and prediction are basically the same, but the term prediction is used here to generalize it in a better way. 

Climatology, finance, foreign exchange, are a few of the many areas where statistical forecasting methods have been used. The statistical prediction methods have been used and applied in several areas of the world for a lot of purposes. This leads to better prediction and simulation. The main thing is that, with the help of collected data, that is, statistics, we can make better predictions in every area and weather forecasting is no different. If proper rules are followed and proper methods are used, then these predictions can become pretty easy.