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Statistics — syllabus topic — of 10 · Background only. Not one of the 10 syllabus topics.

⬜ FOUNDATION — General Concepts

Background only — meaning, characteristics, limitations and basic vocabulary. Not one of the 10 syllabus topics. Topic (i) begins after this.

1. Five Basics / Fundamentals of Statistics

1.1 Variable

An attribute or characteristic of an item being analysed.

Type	Number of variables	Example
Univariate	One	Height of a person in a country
Bivariate	Two	Height with respect to age
Multivariate	More than two	Height w.r.t. gender w.r.t. age

1.2 Population / Universe

All the members, or the entire group of units, which is the focus of study. Example: all the citizens of a country; the residents of a particular geographical location.

1.3 Parameter

A characteristic used to define a given population — a numeric measure. Example: average income of every individual in a country.

1.4 Sample

A set of observations drawn from a population — a subset of the population selected for analysis. Example: a sample of a medicine.

1.5 Statistic

A characteristic that defines the given sample — a numerical measure of the sample. Example: number of RBCs in a blood sample.

The pairing to remember: a parameter describes a population; a statistic describes a sample.

2. Origin and Definition

Derivation of the word "Statistics":

graph TD
    A[Word: Statistics] --> B["==Status==<br>(Latin word)"]
    A --> C["==Statista==<br>(Italian word)"]
    B --> D["Political State<br>(Political status)"]
    C --> E["(Statesman)"]

Definition — Statistics is the study of:

graph TD
    A["==Collection=="] --> B["==Classification / organisation=="]
    B --> C["==Analysis=="]
    C --> D["==Presentation / Interpretation=="]
    D -.-> E[of Data]

Key people

Title	Person
Founder of Statistics	John Graunt and William Petty (1662)
Father of Statistics	Sir Ronald Fisher (Fisher Principle / ANOVA) · Karl Pearson (graphical statistical techniques)
Father of Indian Statistics	Prasanta Chandra Mahalanobis (Mahalanobis distance · Kolkata Statistical Institute · Industrialisation Policy, 2nd FYP)

What statistics is, and what it deals with

Statistics is a branch of Science / Mathematics / Mathematical Science.

graph TD
    A[Data] --> B["Qualitative data<br>(Attributes / characteristics)"]
    A --> C["Quantitative data<br>(Number / Quantity)"]

Data + Statistical Techniques = Statistics

Characteristics of statistics

Data is numerically expressed
A systematic manner is followed
Expresses relations within the data (comparison)
Provides metrical results
Complexities in data are simplified

Fields of application

Economics · Commerce · Banking & Insurance · Public Opinion (exit polls, etc.)

Limitations — what statistics cannot do

❌ Study qualitative phenomena
❌ Reveal the entire background
❌ Be precise and exact (it works on averages)
❌ Resist misuse — the full context is always needed

3. Other Important Terms

Term	Meaning
Generalizability	The ability to draw conclusions about the whole population from the results of a sample
Distribution	An arrangement of data by the values of one variable, in order from low to high
Skewness	The asymmetry of a distribution — see below

Skewness and normal distribution

      Height of                             Income
      Students
          . ˙ .                           . ˙ .       . ˙ .
        ˙       ˙    Normal     Bihar   ˙       ˙   ˙       ˙   J&K
      ˙           ˙  Distribution     ˙           ˙           ˙
  +---+---+---+---+---+---+---+    +---+---+---+---+---+---+---+---+
 0.8 1.0 1.2 1.4 1.6 1.8 2.0      5K  10K 15K 20K 25K 30K 40K
                                  ^ Left Tail            Right Tail ^
                                  (Negative)             (Positive)

Tail direction	Skew
Tail on the left	Negative skew
Tail on the right	Positive skew