1. Introduction to Statistics Basic Important Concepts

In this post, we are going to discuss, Introduction to Statistics Basic Important Concepts such as branches of statistics, population, statistic, parameter & statistic, types of variables, types of data etc. These concepts are asked in the papers of Business Statistics, Statistics or Business Statistics and Mathematics, Quantitative Techniques in Business in all major boards such as FBISE, BISELHR, BISERWP, Punjab University, University of Sargodha and in all major Indian Universities and Boards. On the other hand these concepts are equally important for data scientists and many tests related to data scientists.

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Introduction to Statistics Basic Important Concepts

Introduction

Statistics is a branch of applied mathematics.
It deals with data e.g. collection of data, organization of the data, interpretation or analysis of the data and presentation of the data.
Mainly it deals with quantitative analysis of the data and rarely touches qualitative aspect of the data.
It is the science of getting average and probability but overall field of statistical analysis is so vast.
Governments, Corporate Sectors, Natural & Physical Sciences and Social Sciences direly need the Statistics to analyze the data and making and implementation of their decision on practical ground.

Branches of Statistics

There are two main branches of Statistics:

Descriptive Statistics & Inferential Statistics

(i) Descriptive Statistics

It is first branch of statistics in which collected data is presented in the form of tables, graphs and charts. We can say that it is the branch of collection and presentation of the data.

(ii) Inferential Statistics

In inferential statistics, gathered data is concluded after making hypothesis while using sample and populations so it is the science of inference that is why it is called inferential statistics.

Population & Sample

Population: Whole group under discussion is called population. For example if you want to study some specific issue which is related to a persons of the state whose age is from 20 to 30 then all the persons of a state having age 20 to 30 is your population.

For example if you want to study some character of your college students then all your college students who are studying with you are your population.

Sample: The part of population is called sample. For example there are 500 students in your college and you take only 50 students for your analysis, then 50 students will be sample for you.

Why Sample? Because it is too much costly and time consuming to take the data of whole college so you can take a sample because it is time and cost efficient.

Is Sample a true representative of population or not?

Yes sample is a true representative of a population if you select the sample correctly out of well shuffled data or your proportion of selection is truly associated with the demography of the data.

Think about it!

When you cook food in your kitchen, you taste the food before serving either it is good or not.

Do you taste the whole dish or just taste the part of it?

Is well shuffled food a good representative of your whole food?

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Parameter & Statistic

Parameter

Any statistical estimator which represents a population is called parameter. For example population average and variance are parameters.

$Population\ Average = \ \mu = \frac{\sum X}{N}$

$Population\ Variance = \ \sigma^{2} = \frac{\sum X^{2}}{N} - \left( \frac{\sum X}{N} \right)^{2}\$

Statistic

Any statistical estimator which represents the sample is called statistic. For example sample average and variance are statistic.

$Sample\ Average = \ \overline{X} = \frac{\sum x}{n}$

$Sample\ Variance = \ S^{2} = \frac{\sum x^{2}}{n} - \left( \frac{\sum x}{n} \right)^{2}$

Data and its Types

Data: A set of numbers, digits, facts and figures which researchers gather during survey is called data.

Editing of Data: Editing of data means changing, correction of errors, addition of missing frequencies or removal of duplicates or errors from the gathered data.

Types of Data:

Primary data
Secondary data
Quantitative data
Qualitative data
Discrete data
Continuous data

Primary Data

Primary data is a type of data which is not collected by someone previously or it is fresh newly collected data. Ungrouped data is also called primary data. For example if you collect the fresh data from your college students which is not collected by someone previously then it will be primary data for you.

Sources of Collection of Primary Data:

Questionnaire
Personal Investigation
Through Telephone
Through SMS
Through Email

Secondary Data

Secondary data is a type of data which is collected by someone previously or it is old previously collected data. Grouped data is also called secondary data. For example if you need the inflation historical past data record, you can take this from monetary authorities of your country or from research and data oriented magazine or website.

Sources of Collection of Secondary Data:

Research Organizations
Research Magazines & Journals
Monetary Authorities
Statistical Departments
State Bank
Research based Websites

Quantitative Data

A data which is represented in terms of quantity is called quantitative data. For Example data regarding salary, income, consumption, saving, GDP, NNP, Growth Rate etc.

Qualitative Data

A data which is represented in terms of quality or attribute is called qualitative data. For example color of eyes, color of hairs etc.

Discrete Data

Data which has some specific value within a given range is called discrete data. For Example Number of persons, Number of Oranges, Number of pencils etc.

e.g. 2, 4, 6, 8, 10 etc.

Continuous Data

Data which has any value within a given range is called continuous data. For Example weight, height etc.

e.g. 30.1, 20.34, 60.19 etc.

Variable Vs Constant

Constant:

A value which remains fix is called constant or something that is not variable. For example Value of pi π which is 22/7, Avogadro number and mass of earth etc.

Variable:

A value which does not remain fix is called variable or something that is not constant. For example income, saving, consumption, GDP, NNP, Growth rate, Inflation, Interest rate etc.

Types of Variables

Dependent or Responding Variable
Independent Variable and Explanatory Variable
Discrete Variable
Continuous Variable
Quantitative Variable
Qualitative Variable
Categorical or Nominal Variable
Confounding Variable
Endogenous Variable
Exogenous Variable
Binary or Dichotomous Variable
Random Variable
Intervening Variable

Dependent or Responding Variable

Variable which depends on another variable is called dependent or in informal term a responding variable. For Example in case of income and consumption, consumption is dependent on income.

Independent and Explanatory Variable

Independent variable is a variable which does not depend on any other variable is called independent variable and explanatory variable is also independent but there is a minor difference and that difference is that explanatory variable is independent to some other variables but for some it may be not.

Discrete Variable

A variable in which a data has some specific value within a given range is called discrete variable. For Example Number of persons, Number of Oranges, Number of pencils etc.

e.g. 2, 4, 6, 8, 10 etc.

Continuous Variable

A variable in which a data which has any value within a given range is called continuous data. For Example weight, height, age etc.

e.g. 30.1, 20.34, 60.19 etc.

Quantitative Variable

A variable which is described in terms of quantity is called quantitative variable. For example income, consumption, saving, weight, age, blood pressure etc.

Qualitative Variable

A variable which can be described in terms of quality or attribute is called qualitative variable. For example color of eyes, color of hair, face complexion etc.

Categorical or Nominal Variable

A variable which can be subdivided into further categories. For example in case of gender male and female are categories.

Confounding Variable

Confounding variables are those hidden variables which impose the hidden effect on your experiment but not shown directly.

Endogenous Variable

Endogenous variables are just like dependent variables and they also affected by different other variables in the system. These variables are exclusively used in advance topics of Econometrics.

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Exogenous Variables

Exogenous variable are just opposite to the endogenous variables these are not affected by others in a system but they put impact on other variables in a system.

Binary or Dichotomous Variables

Binary or Dichotomous variables are those variables in which outcomes are assigned by the values 0 and 1 so that is why these are called binary or dichotomous.

Random Variables

Random variables are those variables in which event outcomes of a random experiment are gathered so they are typically associated with the outcomes of a random experiments that is why these are called random variables.

Intervening Variables

Intervening variables are hypothetical variables. These variables are used to explore the causal link between other variables. These are hypothetical so they are not observed in an experiment.

Census:

Complete enumeration or count of the population of the whole country after some specific time period 5 years or 10 years is called census. It is a time consuming and costly process. Each country in the world must do a census after some specific time period to know the data and information about population.

All the information which I presented to you is least but not last.

I defined these terms in a way through my teaching experience that these must be understood by you before going deep into Statistics.

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