#### Topics

##### Mathematical Logic

##### Mathematical Logic

##### Matrices

##### Differentiation

##### Applications of Derivatives

##### Integration

##### Definite Integration

##### Applications of Definite Integration

##### Differential Equation and Applications

##### Matrices

##### Commission, Brokerage and Discount

##### Insurance and Annuity

##### Linear Regression

##### Time Series

##### Index Numbers

- Index Numbers
- Types of Index Numbers
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Simple Aggregate Method
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number

##### Linear Programming

##### Assignment Problem and Sequencing

##### Probability Distributions

- Mean of a Random Variable
- Types of Random Variables
- Random Variables and Its Probability Distributions
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution
- Expected Value and Variance of a Random Variable

##### Continuity

##### Differentiation

##### Applications of Derivative

##### Indefinite Integration

##### Definite Integrals

##### Ratio, Proportion and Partnership

##### Commission, Brokerage and Discount

##### Insurance and Annuity

##### Demography

##### Bivariate Data and Correlation

##### Regression Analysis Introduction

##### Random Variable and Probability Distribution

##### Management Mathematics

## Notes

**Introduction : **

Index numbers are one of the most used statistical tools in economics. An index number is a device to measure changes in an economic variable (or group of variables) over a period of time. Index numbers were originally developed to measure changes in the price level. In the present context, it is also used to measure trends in a wide variety of areas that includes stock market prices, cost of living, industrial and agricultural production, changes in exports and imports etc. Index numbers are not directly measurable, but represent relative changes.

**Definitions of Index Numbers :**

**1) Spiegel :**

“An index number is a statistical measure designed to show changes in a variable or a group of related variables with reference to time, geographical location and other characteristics such as income, profession etc.”

**2) Croxton and Cowden :**

“Index Numbers are devices for measuring differences in the magnitude of a group of related variables.”

**Features of Index Numbers :**

1) Index numbers are statistical devices.

2) Index numbers are specialized averages which are capable of being expressed in percentages.

3) Index numbers measure the net change in one or more related variables over a period of time or between two different time periods or two different localities.

4) Index number which is computed from a single variable is called a ‘univariate index’,whereas an index which is constructed from a group of variables is called a ‘composite index’.

5) The year for which the index number is prepared is the current year.

6) The year with which the changes are measured is called the base year.

7) The base year’s index is assumed as 100 and accordingly the value of the current year is calculated.

8) Index numbers are also referred to as ‘barometers of economic activity’, since it is used to measure the trends and changes in the economy.