Topics
Mathematical Logic
Matrices
Differentiation
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Inverse Functions
- Derivatives of Logarithmic Functions
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Second Order Derivative
- Overview of Differentiation
Applications of Derivatives
Integration
Definite Integration
Applications of Definite Integration
- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves
- Overview of Application of Definite Integration
Differential Equation and Applications
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations
- Overview of Differential Equations
Commission, Brokerage and Discount
- Commission and Brokerage Agent
- Concept of Discount
- Overview of Commission, Brokerage and Discount
Insurance and Annuity
- Insurance
- Types of Insurance
- Annuity
- Overview of Insurance and Annuity
Linear Regression
- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients
- Overview: Linear Regression
Time Series
- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend
- Overview of Time Series
Index Numbers
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Overview of Index Numbers
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
Linear Programming
- Introduction of Linear Programming
- Linear Programming Problem (L.P.P.)
- Mathematical Formulation of Linear Programming Problem
- Overview of Linear Programming
Assignment Problem and Sequencing
- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence
- Overview of Assignment Problem and Sequencing
Probability Distributions
- Poisson Distribution
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
- Overview of Binomial Distribution
Definition: Index Number
- An Index Number is a statistical measure of changes in a variable or a group of variables with respect to time, geographical location, or some other characteristic, such as production, income, etc.
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An Index Number is used for measuring changes in a quantity that can not be measured directly.
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An Index Number is a single ratio, usually expressed as a percentage, that measures aggregate (or average) change in several variables between two different times, places, or situations.
Key Points: Types of Index Numbers
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Price Index Number – Measures change in prices (Inflation indicator)
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Quantity Index Number – Measures change in output/quantity
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Value Index Number – Measures change in total value (Price × Quantity)
Definition: Base Period
The base period of an index number is the period against which comparisons are made.
Key Points: Important Terminology
| Symbol | Meaning |
|---|---|
| p0 | Price in base year |
| p1 | Price in current year |
| q0 | Quantity in base year |
| q1 | Quantity in current year |
| w | Weight |
| I | Price Relative |
| Base Year | Year taken as 100 |
| Current Year | Year under comparison |
Formula: Simple Aggregate Method
Price Index:
\[P_{01}=\frac{\sum p_1}{\sum p_0}\times100\]
Quantity Index:
\[Q_{01}=\frac{\sum q_1}{\sum q_0}\times100\]
Value Index:
\[V_{01}=\frac{\sum p_1q_1}{\sum p_0q_0}\times100\]
Formula: Weighted Aggregate Method
\[P_{01}=\frac{\sum p_1w}{\sum p_0w}\times100\]
Formula: Price Index Numbers
Laspeyre’s Price Index Number:
\[P_{01}(L)=\frac{\sum p_1q_0}{\sum p_0q_0}\times100\]
Paasche’s Price Index Number:
\[P_{01}(P)=\frac{\sum p_1q_1}{\sum p_0q_1}\times100\]
Dorbish-Bowley’s Price Index Number:
\[P_{01}(D-B)=\frac{P_{01}(L)+P_{01}(P)}{2}\]
Fisher’s Ideal Price Index Number:
\[P_{01}(F)=\sqrt{P_{01}(L)\times P_{01}(P)}\]
Marshall-Edgeworth’s Price Index Number:
\[P_{01}(M-E)=\frac{\sum p_1(q_0+q_1)}{\sum p_0(q_0+q_1)}\times100\]
Walsh’s Price Index Number:
\[P_{01}(W)=\frac{\sum p_1\sqrt{q_0q_1}}{\sum p_0\sqrt{q_0q_1}}\times100\]
Definition: Cost of Living Index Number
Cost of Living Index Number, also known as Consumer Price Index Number, is an index number of the cost of buying goods and services in day-to-day life for a specific consumer class.
Formula: Aggregative Expenditure Method (Weighted Aggregate Method)
\[CLI=\frac{\sum p_1q_0}{\sum p_0q_0}\times100\]
Same as Laspeyre’s Price Index
Formula: Family Budget Method
\[CLI=\frac{\sum IW}{\sum W}\]
Where,
\[I=\frac{p_1}{p_0}\times100\]
W = p0q0
Formula: Purchasing Power of Money
\[\text{Purchasing Power}=\frac{1}{CLI}\]
Formula: Real Wages
\[\mathrm{Real~Wages}=\frac{\text{Money Wages}}{CLI}\times100\]
