Statistics definition & variable introduction

What is Statistics?

Table of Contents.

The word Statistics is derived from the Latin word ‘Status’ or the Italian word ‘Statista’ or the German word ‘Statistik’ meaning a Political State.
Statistics consists of conducting studies to collect, organize, summarize, analyze, and draw conclusions

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of data.

- - Statistics may lightly be called the science of averages –A.L Bowley
  - Statistics are the classified facts respecting the conditions of the people in a state- Webster
  - Statistics have to bring order out of chaos.
  - Statistics may be called the science of counting – A.L Bowley
  - The term statistics is used to refer to methods for organizing, summarizing, and interpreting data.

Data

Data are individual pieces of factual information collected, recorded, and used for the purpose of analysis. It is the raw information from which statistics are created. There is two categories of data.

Continuous data
Discrete data

a) Continuous data

There are an infinite number of possible values that fall between any two observed values. A continuous variable is divisible into an infinite number of fractional parts.

Example 1

1, 2,3,4,5, 6….

Between 5 & 6 there can be 5.5

1,2,3,4,5, 5.5, 6

Between 5 & 5.5 there can be a value of 5.25

1,2,3,4,5, 5.25, 5.5, 6

Similarly, between 5.5 & 6, there can be a value of 5.75

1,2,3,4,5, 5.25, 5.5, 5.75, 6

>> In this example you can put an infinite number of data between any two numbers. Hence it is continuous data.

Example 2

Statistics definition & variable introduction

Weight can be measured as:

- - - 49kg
    - 49.5kg
    - 49.48kg
    - 49.4812kg
    - 49.48124kg …… etc.

>> In this example measurement is possible up to infinite decimal points. Hence this data is continuous in nature.

Other Examples:

Height, ampere, Voltage, wind speed, air temperature, vehicle speed, brake force, pollution level, etc.

b) Discrete Data

Discrete data can only take certain values (like whole numbers)
Consists of separate, indivisible categories. No values can exist between two neighboring categories.

Example: No of the egg will be a whole number (cannot count eggs as 2.5 or 3.5)

One Egg

Two Egg

Three Egg

Other examples:

- - Students in a class
  - Number of likes on YouTube video
  - Number of votes in an election
  - The number of participants in JEE exam….. etc.

Variables

The values assumed by quantitative observations are called variables. A data is called variable data if the value may vary. Maybe between production batches, Variation over a period of time, etc. Examples: Weight, Temp, Age, Dimension, Humidity, Pollution level, Rainwater qty, Production volume, Depreciation, etc.

Example 1: Weight measurement in Kilogram :

45, 40, 35, 39, 41, 45, 40, 44, 43,40, 41, 42, 44, 42 …………..

Statistics definition & variable introduction

Example 2: Height measurement in Centimeters:

172 ,172 , 171 , 170 , 167, 167 , 166 , 165 ,164 , 163 ,156 ,163 , 155…………..

A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour & vehicle type are examples of variables.

A variable is a characteristic or condition that changes or has different values for different individuals.
Variables can be characteristics that differ from one individual to another, such as height, weight, gender, or personality.
Variables are classified as:
- - Independent Variable
  - Dependent Variable

a) Independent variable

A variable (X) is called an independent variable if it is not influenced by any other variable under study.

Y= 10X + 2

X is the independent variable. X can be assigned any value (Negative or positive).

Explanatory variable: Independent variable is also called the explanatory variable.

In statistics: Independent variables are the one that is being manipulated by the researcher in an experimental study.

b) Dependent variable

A variable (Y) is called a dependent variable if it is influenced by any other variable (X) under study.

Y= 10x + 2

Y is the dependent variable.
The value of Y is obtained through the value of X. Hence Y depends on the value of X.
Outcome variable: the dependent variable is also called the outcome variable or resultant variable.

c) Dependent Vs. Independent variable

An independent variable(X) stands alone and is not changed by the other variables.
Any change in the independent variable(X), either positive or negative, leads to changes (increase or decrease) in the dependent variable(Y).
Independent variables(x) are those, which are used to predict dependent variables (Y).

Example:

Refer above diagram :

- - The taste of the tea depends on the quantity of water, Tea, Milk, and sugar.
  - Therefore Tea taste is a dependent variable(Y).
  - Water, Tea, Milk & sugar quantity can be varied as per tea taste requirements. Therefore these are independent variables(X).

Independent variables :

X1= Water, X2= Milk, X3=Sugar, X4= Tea

Dependent variable :

Y = Taste of tea

- - above information can be summarized as :

What is Statistics?

The word Statistics is derived from the Latin word ‘Status’ or the Italian word ‘Statista’ or the German word ‘Statistik’ meaning a Political State.
Statistics consists of conducting studies to collect, organize, summarize, analyze, and draw conclusions

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of data.

- - Statistics may lightly be called the science of averages –A.L Bowley
  - Statistics are the classified facts respecting the conditions of the people in a state- Webster
  - Statistics have to bring order out of chaos.
  - Statistics may be called the science of counting – A.L Bowley
  - The term statistics is used to refer to methods for organizing, summarizing, and interpreting data.