Introduction to Statistics | Additional Topics for IIT JAM Mathematics PDF Download

Introduction:-
Statistics is a branch of mathematics that deals with the collection, analysis and interpretation of data.
Data can be defined as groups of information that represent the qualitative or quantitative attributes of a variable or set of variables. In layman's terms, data in statistics can be any set of information that describes a given entity. An example of data can be the ages of the students in a given class. When you collect those ages, that becomes your data.
A set in statistics is referred to as a population. Though this term is commonly used to refer to the number of people in a given place, in statistics, a population refers to any entire set from which you collect data.

Data Collection Methods:-
As we have seen in the definition of statistics, data collection is a fundamental aspect and as a consequence, there are different methods of collecting data which when used on one particular set will result in different kinds of data. Let's move on to look at these individual methods of collection in order to better understand the types of data that will result.

Census Data Collection:-
Census data collection is a method of collecting data whereby all the data from each and every member of the population is collected.
For example, when you collect the ages of all the students in a given class, you are using the census data collection method since you are including all the members of the population (which is the class in this case).
This method of data collection is very expensive (tedious, time consuming and costly) if the number of elements (population size) is very large. To understand the scope of how expensive it is, think of trying to count all the ten year old boys in the country. That would take a lot of time and resources, which you may not have.

Sample Data Collection:-
Sample data collection, which is commonly just referred to as sampling, is a method which collects data from only a chosen portion of the population.
Sampling assumes that the portion that is chosen to be sampled is a good estimate of the entire population. Thus one can save resources and time by only collecting data from a small part of the population. But this raises the question of whether sampling is accurate or not. The answer is that for the most part, sampling is approximately accurate. This is only true if you choose your sample carefully to be able to closely approximate what the true population consists of.
Sampling is used commonly in everyday life, for example, all the different research polls that are conducted before elections. Pollsters don't ask all the people in a given state who they'll vote for, but they choose a small sample and assume that these people represent how the entire population of the state is likely to vote. History has shown that these polls are almost always close to accuracy, and as such sampling is a very powerful tool in statistics.

Experimental Data Collection:-
Experimental data collection involves one performing an experiment and then collecting the data to be further analyzed. Experiments involve tests and the results of these tests are your data.
An example of experimental data collection is rolling a die one hundred times while recording the outcomes. Your data would be the results you get in each roll. The experiment could involve rolling the die in different ways and recording the results for each of those different ways.
Experimental data collection is useful in testing theories and different products and is a very fundamental aspect of mathematics and all science as a whole.

Observational Data Collection:-
Observational data collection method involves not carrying out an experiment but observing without influencing the population at all. Observational data collection is popular in studying trends and behaviors of society where, for example, the lives of a bunch of people are observed and data is collected for the different aspects of their lives.