Quantitative Techniques Notes
Subject Overview
Quantitative Techniques equips M.Com students with the statistical and operations-research toolkit used throughout the program — central tendency, dispersion, correlation and regression, probability distributions, linear programming and game theory, and transportation, assignment and project scheduling (PERT/
Subject at a glance
4
Units
35
Topics
4
Credits
4
Infographics
Unit-wise Syllabus
4 units — open any unit for detailed topic-wise notes, diagrams and important exam questions
- Meaning
- features
- functions
- scope and limitations of statistics
- measures of central tendency (arithmetic/geometric/harmonic mean, mode, median, quartiles/deciles/percentiles)
- measures of variation (range, quartile deviation, mean deviation, standard deviation and coefficients)
- moments
- skewness (Karl Pearson and Bowley measures) and kurtosis
Standard deviation
σ = √[Σ(x − x̄)² / n]
Coefficient of variation
(σ / x̄) × 100
Karl Pearson skewness
(Mean − Mode) / σ
Bowley skewness
(Q3 + Q1 − 2 Median) / (Q3 − Q1)
Kurtosis
β2 = μ4 / μ2²
3 = mesokurtic
Study guide
This unit covers descriptive statistics: means, mode, median and positional measures, measures of variation, moments, skewness (Karl Pearson and Bowley) and kurtosis. Practise computing and interpreting skewness.
- Simple/multiple/partial and linear/non-linear correlation
- scatter diagrams
- Pearson's correlation coefficient
- rank correlation
- simple regression via least squares
- relationship between correlation and regression
- approaches to probability
- addition and multiplication laws
- conditional probability and Bayes' theorem
Pearson's r
Cov(x, y) / (σx σy)
Spearman's rank
1 − 6Σd² / [n(n² − 1)]
Regression coefficient
byx = r × σy / σx
Bayes' theorem
P(Ai given B) = P(Ai) P(B given Ai) / Σ P(Aj) P(B given Aj)
Study guide
You study correlation and regression (simple, multiple, partial), rank correlation, least squares, the relation between correlation and regression, approaches to probability, probability laws, conditional probability and Bayes' theorem. Work Bayes' theorem problems with a tree diagram.
- Binomial
- Poisson and Normal distributions with properties and applications
- formulation of linear programming problems
- graphic and Simplex (including Big-M) solution methods
- degeneracy
- duality
- post-optimality analysis
- two-person zero-sum games
- pure and mixed strategies
- dominance rule
- graphic solution to games
- 1Standard form
Add slack, surplus, artificial variables
- 2Initial table
Basic feasible solution
- 3Key column
Most negative Cj − Zj (max problem)
- 4Key row
Minimum ratio test
- 5Pivot and iterate
Until no improvement is possible
Study guide
You study the binomial, Poisson and normal distributions, formulation and solution of linear programming problems (graphical, simplex, Big-M), degeneracy, duality, post-optimality analysis and game theory with pure and mixed strategies and dominance. Practise at least one simplex problem fully.
- Transportation problem — North-West Corner
- Least Cost and Vogel's Approximation methods
- optimality testing via MODI method
- assignment problem via the Hungarian method
- PERT/CPM project networks
- scheduling with known activity times
- critical path
- 1Row reduction
Subtract row minimum
- 2Column reduction
Subtract column minimum
- 3Cover zeros
With minimum lines
- 4Lines = n?
If yes, assign; if no, adjust
- 5Adjust
Subtract smallest uncovered, add at intersections
Study guide
You study the transportation problem (North-West Corner, Least Cost, Vogel, MODI), the assignment problem (Hungarian method) and PERT/CPM networks and critical path. Set up each problem in a table and check feasibility.
Why Quantitative Techniques Matters
Quantitative methods underpin research, analytics and operations decisions, and they are tested in management entrance exams and UGC-NET.
How to Prepare for Quantitative Techniques
- Solve numericals daily and keep a formula sheet.
- Practise LP, transportation and assignment problems from start to finish.
- Use Excel or Python to check your answers.
Quantitative Techniques: Frequently Asked Questions
What is skewness?
Skewness measures the asymmetry of a distribution around its mean; it can be positive, negative or zero.
What is the MODI method?
MODI (modified distribution) is a method to test whether a transportation solution is optimal and to improve it if not.