# Statistics

Sub Topics
Statistics can be defined as the study of data which includes its collection, organization, analysis, and interpretation. It includes the planning of the ways by which data can be collected in terms of the design of the experiment used. It can be taken as a systematic ways of obtaining information from the data.

By definition given by Fraser(1958) “The branch of the scientific method which deals with the data obtained by counting or measuring the properties of populations”

The word statistics has been originated from the Latin word “status,” which means “state”.

Statistics is a organized set of concepts, procedures, rules that helps us to organise, understand and make informed decisions. It involves measurement of data and catogorical data. Statistics involves putting data in the form of tables, pie charts, histograms and graphs.

The word statistics come from the Italian word statista (which means “statesman”) or the German word statistik which also means political state. It was defined as the political science of the several countries by Professor Gottfried Achenwall. In the famous book Elements of Universal Erudition statistics is defined as “the science that teaches us the political arrangement of all the modern states of the known world." We cover this and more when yoiu get statistics homework help .

The science of statistics originates mainly from two sources:

1. Government Records, and
2. Mathematics.

In government records statistics appeared recording the census of population, military strength, taxable capacity of the people, births and deaths, etc. Since this statistical data was collected for governmental purposes, statistics was then described as the science of kings or the science of statecraft.

In applied mathematics the present statistical methods, particularly those concerned with drawing inferences, are based on the mathematical theory of probability. Statistical techniques in the form of regression, normal curve, chi-square, the goodness of fit test and so on were all developed during the last century using mathematical theories.

## Statistics in Everyday Life

Today's society is completely covered by the usage of numbers. Numbers represents many data facts linked with different areas in the society. Statistics helps to organize all these data in a systematic order so that it can be used for further use.

Statistics has great application in day to day life. It has different means by which an unorganized set of data can be made into meaning information which can be saved for later use.

Lets take some examples in statistics to see its daily application.

Mean is a way of comparing sets of data provided. It has many uses. Some of them are
• It helps to understand the average mark obtained by students in a particular time.
• It can be used to compare the different salaries of workers in a company.
• It can be used understand their expenses with the average income of a family.

Median is another way by which we can show the importance of statistics in day to day life.
• As its main idea is to find the middle most value of a set of observations, it can be used to find the height of players in games like basketball, foot ball, etc.
• It can be used to find the middle age group of students in a class.

Mode plays a very important part in statistic as it shows the highest frequency in any provided data.
• It tells the number of games succeeded or failed by any team of players.
• It tells the number of infant death in a hospital. It also helps in finding the means of traveling used frequently, number of people attending the hospitals, etc.

## Importance of Statistics

The main importance of statistics is to make an inference about a population based on information contained in a sample and to provide an associated measure of goodness for the inference.

## Statistics for Scientists and Engineers

Any scientific inquiry denotes to a systematic process of learning. A researcher sets the goal of an experiment, collects relevant datas, analyzes it, draws conclusions, and decides further courses of action. It must be realized that a scientific investigation consists of a process of trial and error. It is very rare that a phenomenon be completely understood or a theory perfected by means of a single, definite experiment.

It is too much to expect to get it all right in one shot. Data obtained from an experiment provide new knowledge. This new knowledge often suggests a rechecking of already existing theory, and hence further experiment may be conducted by analysis of data.

## Descriptive Statistics

Descriptive statistics helps in describing a particular pattern as well as a general trend in any set of data. In most situations, descriptive statistics are used to examine one variable at a time. However, in certain situation, the relationship between two variables can be described using the correlation and regression.

In other words, it is used simply to describe the sample you are concerned with. Descriptive statistics gives a clear summary about the sample and about the observations that have been made. These may either be quantitative or visual, i.e. like graphs. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.

The distribution can be taken as a summary of the frequency of individual or ranges of values for a variable. The simplest distribution would list each value of a variable and all the cases that had that value.

Frequency distributions can be defined as a table. Quantities that summarize a distribution are as follows:
1. measures of central tendency: It represents a"particular value" for a member of a population. The three main types of central tendencies are the mean, the median, and the mode.
2. measures of dispersion: It describes how different members of a sample are among themselves. Common measures of dispersion contain the absolute deviation, the standard deviation, and the interquartile range.
3. measures of distribution shape, like skewness.
4. measures which is aimed at describing the most unusual data contained in any population, Statistical sampling can be taken as the study of populations obtained by gathering information about and analyzing it.

## Statistical Sampling

Statistical sampling plays a important role for a great deal of information, which ranges from estimates of average height of a set of population to studies on the impact of marketing. Statistical sampling, can be used in many area which includes psychology, anthropology, demography etc. As in case of any method, however, statistical sampling is also prone to many errors, and hence it is very important to analyze each methods used to conduct a study before accepting the results.

This process begins with a definition of the population the researcher wants to study, and the variable which he would want to measure.

For example, lets check an example to understand the average height of high school children. Next, the researcher checks on the different ways to collect the needed data. Here the researcher might travel to different schools in different areas with a estimated scale, send questionnaires out to teachers or parents, or try to access any school records about each students.  Many researchers adopted the direct method by which the results became more consistent other than depend on self responses.

In statistical sampling, the researcher first decides the population to be studied, variable to be taken for measurement, and method to be used, then only he decides how to accurately sample the population in order that the collected data should completely represent the whole population. As the sample size gets larger, the result becomes better.