BUSINESS ANALYTICS (MBA-7302) HPTU SYLLABUS OF MBA 3RD SEM

 

⭐ UNIT – I (FULL DETAILED NOTES, VERY EASY LANGUAGE)

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1️⃣ STATISTICS – BASIC INTRODUCTION

Definition (Easy English):

Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data for decision making.

Why Statistics is Important in Business?

• Sales forecasting

• Market analysis

• Quality control

• Inventory management

• Financial analysis

• Demand prediction

• Risk assessment

Types of Statistics

1. Descriptive Statistics – describes data (mean, median, charts).

2. Inferential Statistics – draws conclusions from sample to population (probability, hypothesis, regression).

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2️⃣ MEASURES OF CENTRAL TENDENCY (Center of Data)

Yeh batata hai data ka “centre” kahan lie karta hai.

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A) MEAN (Arithmetic Mean)

Mean = Data values ka simple average

Formula:

$$\text{Mean} = \frac{\sum X}{N}$$

Example (easy):

Data: 5, 10, 15, 20
Mean = (5+10+15+20)/4 = 12.5

Advantages:

✔ Easy to calculate
✔ Uses all data

Disadvantages:

✘ Outliers se effect hota hai
Example:
10, 12, 14, 100 → mean grows too much.

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B) MEDIAN

Median = Middle value (jab data ko ascending me arrange karein)

Steps:

1. Arrange data

2. If odd number → middle value

3. If even number → middle 2 values ka average

Example:

Data: 2, 4, 7
Median = 4

Even example:
12, 15, 18, 27
Median = (15+18)/2 = 16.5

Why important?

Median outliers se affect nahi hota → e.g., income distribution.

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C) MODE

Most frequently occurring value.

Example:

5, 7, 7, 9, 11
Mode = 7

Use:

✔ shoe size
✔ customer buying pattern
✔ product color preference

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3️⃣ MEASURES OF DISPERSION (Data Spread)

Center ke alawa hume yeh bhi jaana hota hai ki data kitna spread/variability show karta hai.

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A) RANGE

$$\text{Range} = \text{Maximum} - \text{Minimum}$$

Very basic measure.

Example:

Prices: 100, 150, 200
Range = 200 – 100 = 100

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B) QUARTILE DEVIATION (Optional – extra)

Middle 50% data ka spread.

$$QD = \frac{Q3 - Q1}{2}$$

Example:
Q3 = 80, Q1 = 60
QD = (80 – 60)/2 = 10

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C) MEAN DEVIATION (MD)

Deviation from mean/median ka average.

$$MD = \frac{\sum |X - \bar{X}|}{N}$$

Example:

Data: 4, 6, 8
Mean = 6
|4-6|=2, |6-6|=0, |8-6|=2
MD = (2+0+2)/3 = 1.33

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D) VARIANCE & STANDARD DEVIATION (Most Important)

Variance:

Data mean se on average kitna far hai.

$$\sigma^2 = \frac{\sum (X - \bar{X})^2}{N}$$

Standard Deviation (SD):

Variance ka square root

$$SD=\sqrt{\text{Variance}}$$

Example:

Data: 2, 4, 6
Mean = 4

(2–4)² = 4
(4–4)² = 0
(6–4)² = 4

Variance = (4+0+4)/3 = 2.66
SD = √2.66 = 1.63

Importance:

✔ Best measure of reliability
✔ Used in finance (risk), inventory, sales fluctuations

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4️⃣ MEASURES OF SHAPE (Skewness)

Data symmetric hai ya tilted?

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A) Skewness

Skewness tells:

• data right side tilt hai?

• data left side tilt hai?

Types:

1. Positive (Right) Skewness

Tail right side → long right tail
Mean > Median > Mode

Example: Income data
(bohot log low income, few very high)

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2. Negative (Left) Skewness

Tail left side → long left tail
Mode > Median > Mean

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3. Zero Skewness (Symmetric)

Mean = Median = Mode
Example: Normal distribution (bell curve)

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5️⃣ KURTOSIS (Peak of Data)

Definition:

Kurtosis shows data curve kitni peaked ya flat hai.

Types:

1. Leptokurtic → sharp peak (more concentrated)

2. Mesokurtic → normal peak

3. Platykurtic → flat peak (more spread)

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6️⃣ CHEBYSHEV’S THEOREM (VERY IMPORTANT)

Chebyshev’s rule applies to all types of data (normal or not normal).

Formula:

$$\text{At least } \left(1-\frac{1}{k^2}\right) \text{ observations lie within } k\text{ standard deviations of mean}$$

Remember Values:

k (SD)	At least within Mean ± k SD
2 SD	75%
3 SD	88.9% ≈ 89%
4 SD	93.75%

Example:

If mean = 50 and SD = 10
k = 2
Range = 50 ± 2×10 = 50 ± 20 = 30 to 70
At least 75% data will lie in this range.

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7️⃣ Additional Concepts (Exam me puchte hain)

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Population vs Sample

Population:

Entire group of interest
→ example: all customers

Sample:

Part of population
→ example: 100 customers out of 10,000

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Parameter vs Statistic

● Parameter → population ka measure (mean = μ)
● Statistic → sample ka measure (mean = X̄)

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Primary vs Secondary Data

Primary data: collected firsthand
Example: surveys, interviews

Secondary: already available
Example: newspaper, report, website

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⭐ UNIT–I Summary Table (Exam Writing Ready)

Topic	Meaning	Best For	Example
Mean	Average	numerical data	sales avg
Median	Mid value	skewed data	income data
Mode	Most frequent	categorical	shoe size
Range	Max–Min	quick spread	100–10
Variance	Avg squared deviation	accuracy	finance risk
SD	Square root of variance	reliability	price fluctuation
Skewness	Tilt	distribution shape	right skew incomes
Kurtosis	Peak	shape	leptokurtic peak
Chebyshev	Min % within SD	non-normal data	75% within 2S

⭐ UNIT – II : PROBABILITY & PROBABILITY DISTRIBUTIONS (FULL DETAILED NOTES)

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1️⃣ PROBABILITY – BASIC INTRODUCTION

Definition (Easy):

Probability tells the likelihood/chance of an event happening.
Values lie between 0 and 1.

• 0 → Impossible event

• 1 → Certain event

Example:

Chance of getting head in coin toss = ½ = 0.5

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2️⃣ IMPORTANT TERMS

Experiment:

Any action which produces outcomes.
E.g., tossing a coin.

Sample Space (S):

All possible outcomes.
Coin → S = {H, T}

Event (E):

Subset of sample space.
Event = getting head = {H}

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3️⃣ TYPES OF PROBABILITY

A) Classical Probability (Theoretical)

Formula:

$$P(E) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}}$$

Example:
Rolling a die → probability of 4 = 1/6.

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B) Empirical Probability (Experimental)

Based on observation.
Example: Cricket match mein “win percentage”.

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C) Subjective Probability

Based on judgment/experience.
Example: Market trend prediction.

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⭐ 4️⃣ LAWS OF PROBABILITY

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A) ADDITION LAW (Union of Events)

1) For Mutually Exclusive Events

Events that cannot occur together.
Example: Getting head and tail at same time.

Formula:

$$P(A \cup B) = P(A) + P(B)$$

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2) For Non-Mutually Exclusive Events

Example: Rolling a die → event A: even number, event B: number > 3.

Formula:

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

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B) MULTIPLICATION LAW (Intersection of Events)

1) Independent Events

One event does not affect other.
Example: Coin + die.

$$P(A \cap B) = P(A) \times P(B)$$

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2) Dependent Events

Example: drawing cards without replacement.

$$P(A \cap B) = P(A) \times P(B|A)$$

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⭐ 5️⃣ BAYES' THEOREM (Very Important)

Used when:
● Reverse probability chaiye
● Condition-based questions

Formula:

$$P(A|B) = \frac{P(A) P(B|A)}{P(A) P(B|A) + P(A') P(B|A')}$$

Example (easy):

A machine A makes 60% items, B makes 40%.
Defective rate: A → 2%, B → 3%.
Find: Probability defective item came from machine A.

(Ye exam me bohot common hai.)

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⭐ 6️⃣ PROBABILITY DISTRIBUTIONS (Discrete & Continuous)

Unit-II me 3 main distributions hain:
✔ Binomial
✔ Poisson
✔ Normal

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A) BINOMIAL DISTRIBUTION

Situation jahan:

• experiment repeat hota hai

• 2 possible outcomes (success/failure)

• probability = constant

• trials independent

Example:

Coin toss 10 times
Success = head
p = 0.5

Formula:

$$P(X = k) = nCk \, p^k \, q^{n-k}$$

where
p = success probability
q = 1 − p
n = trials

Example:

Probability of getting exactly 3 heads in 5 tosses
n = 5, k = 3, p = 0.5

$$P(3) = 10 × (0.5)^3 × (0.5)^2 = 10 × 0.03125 = 0.3125$$

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B) POISSON DISTRIBUTION

Used when rare events occur.

Examples:

✔ No. of road accidents per day
✔ No. of telephone calls per minute
✔ No. of defects in cloth

Formula:

$$P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$$

where λ = mean = variance

Example:

λ = 2 (mean calls per minute = 2)
Find probability of 0 calls:

$$P(0) = e^{-2}$$

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⭐ Difference: Binomial vs Poisson

Binomial	Poisson
Two outcomes	Rare event count
Fixed n	No fixed n
p constant	p very small
k successes in n trials	k occurrences in interval

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C) NORMAL DISTRIBUTION (MOST IMPORTANT)

Also called Gaussian distribution.

Characteristics:

✔ Bell-shaped curve
✔ Symmetric
✔ Mean = Median = Mode
✔ Total area = 1
✔ 68–95–99.7 Rule

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⭐ Empirical Rule (VERY IMPORTANT)

For normal distribution:

Range	Percentage
Mean ± 1 SD	68%
Mean ± 2 SD	95%
Mean ± 3 SD	99.7%

Example:

Mean = 50, SD = 10
95% values lie between
50 ± 20 → 30 to 70

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⭐ Z-SCORE (STANDARD SCORE)

Converts normal data into standard normal form.

$$Z = \frac{X - \mu}{\sigma}$$

Example:
X = 70, mean = 50, SD = 10

$$Z = 2$$

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⭐ 7️⃣ Comparison Table (Exam ke liye best)

Distribution	Type	When used	Example
Binomial	Discrete	Success/failure	Heads in 10 tosses
Poisson	Discrete	Rare events	Accidents/day
Normal	Continuous	Natural data	Height, weight

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⭐ 8️⃣ UNIT–II Ready-Made 5 Mark Answer Structure

Q. Explain Bayes' Theorem.

Intro:
Bayes’ theorem is used to find reverse or conditional probabilities.

Formula:

$$P(A|B) = \frac{P(A)P(B|A)}{P(A)P(B|A) + P(A')P(B|A')}$$

Example: (Write machine example)

Conclusion:
It is widely used in business analytics, machine learning, medical testing, and classification.

⭐ UNIT – III : CORRELATION & REGRESSION (FULL NOTES)

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1️⃣ CORRELATION ANALYSIS

Correlation measures:
✔ two variables ke beech strength kitni hai
✔ direction (positive/negative)
✔ linear relationship

Easy Definition:

Correlation tells how strongly two variables move together.

Example:

• Height ↑ → Weight ↑ (positive correlation)

• Price ↑ → Demand ↓ (negative correlation)

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⭐ Types of Correlation

1) Positive Correlation

Both variables increase or decrease together.

Examples:
✔ income & expenditure
✔ length & weight

2) Negative Correlation

One increases, the other decreases.

Examples:
✔ price & demand
✔ speed & time taken

3) Zero Correlation

No relationship.
Example: height & intelligence

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⭐ Methods of Correlation (Syllabus ke according 2 methods)

✔ Rank Correlation

✔ Karl Pearson’s Coefficient of Correlation

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2️⃣ Rank Correlation (Spearman’s Rank Correlation)

Used when:
✔ data ranked form me ho
✔ small samples
✔ qualitative data (performance, preference)

Formula:

$$r_s = 1 - \frac{6 \sum d^2}{n(n^2 - 1)}$$

where:
d = difference of ranks
n = number of observations

Example (Easy):

Students rank in Maths & English:

Student	Maths Rank	English Rank
A	1	2
B	2	1
C	3	3

d = difference
A → 1 - 2 = -1 → d² = 1
B → 2 - 1 = 1 → d² = 1
C → 3 - 3 = 0 → d² = 0
Total = 2

$$r_s = 1 - \frac{6(2)}{3(9-1)} = 1 - \frac{12}{24} = 1 - 0.5 = 0.5$$

→ Moderate positive correlation.

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3️⃣ KARL PEARSON’S COEFFICIENT OF CORRELATION (r)

Used when:
✔ data in numeric form
✔ finding linear correlation

Formula:

$$r = \frac{\sum (X - \bar{X})(Y - \bar{Y})}{\sqrt{\sum (X - \bar{X})^2 \sum (Y - \bar{Y})^2}}$$

But exam me shortcut formula likho:

$$r = \frac{n\sum XY - (\sum X)(\sum Y)}{\sqrt{[n\sum X^2 - (\sum X)^2][n\sum Y^2 - (\sum Y)^2]}}$$

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⭐ Interpretation of r

Value of r	Interpretation
+1	Perfect positive
0.7 to 0.9	High positive
0.3 to 0.6	Moderate positive
0 to 0.3	Low positive
0	No correlation
–0.3 to –0.6	Moderate negative
–0.7 to –1	High/Perfect negative

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⭐ Properties of Correlation

1. r lies between –1 and +1

2. r has no units

3. r is symmetric ⇒ r(X,Y) = r(Y,X)

4. r only measures linear relationship

5. If r = 0 ⇒ no linear relation

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⭐ Difference Between Rank & Pearson Correlation

Rank Correlation	Pearson Correlation
Uses ranks	Uses actual values
For qualitative data	For quantitative data
Based on differences in ranks	Based on covariance
Less accurate	More accurate
Non-parametric	Parametric

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4️⃣ REGRESSION ANALYSIS

Regression tells:
✔ effect of one variable on another
✔ prediction/estimation
✔ direction & magnitude of impact

Easy Definition:

Regression is a statistical method for predicting the value of one variable using another variable.

Example:
Predicting sales from advertisement expenditure.

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⭐ Types of Regression (Unit syllabus – simple linear regression)

1. Regression of Y on X

2. Regression of X on Y

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Regression Line of Y on X

Formula:

$$Y = a + bX$$

Where:
a = intercept
b = slope (regression coefficient)

b (regression coefficient)

$$b = \frac{n\sum XY - (\sum X)(\sum Y)}{n\sum X^2 - (\sum X)^2}$$

a

$$a = \bar{Y} - b\bar{X}$$

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Regression Line of X on Y

Formula:

$$X = a + bY$$

where

$$b = \frac{n\sum XY - (\sum X)(\sum Y)}{n\sum Y^2 - (\sum Y)^2}$$

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⭐ Interpretation of Regression Coefficient (b)

b tells:

• change in dependent variable due to 1 unit change in independent variable.

Example:
b = 0.8
→ X increases by 1 → Y increases by 0.8

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⭐ Properties of Regression Coefficients

1. Both regression coefficients generally have same sign as correlation

2. If r = 0 → both regression coefficients = 0

3. b(yx) × b(xy) = r²

4. Regression coefficients are not symmetric

5. Value can be greater than 1

6. Averages always lie on regression line

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⭐ Relationship Between Correlation & Regression

$$r = \sqrt{b_{yx} \times b_{xy}}$$

If both b positive ⇒ r positive
If both negative ⇒ r negative

Important:

Regression can exist even when correlation is weak, but prediction accuracy low hogi.

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⭐ 5️⃣ Solved Example of Regression (Very Easy)

Given data:

X	Y
2	4
4	6
6	8

Step 1: Calculate sums

∑X = 12
∑Y = 18
∑XY = (2×4)+(4×6)+(6×8)=8+24+48=80
∑X² = 4+16+36 = 56
n = 3

Step 2: Find b (slope)

$$b = \frac{3(80) - (12)(18)}{3(56) - (12)^2} = \frac{240 - 216}{168 - 144} = \frac{24}{24} = 1$$

Step 3: Find a

$$\bar{X} = 4,\quad \bar{Y}=6$$ $$a = 6 - 1(4) = 2$$

Regression line of Y on X:

$$Y = 2 + 1X$$

Means:
X me har 1 unit increase → Y me 1 unit increase.

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⭐ 6️⃣ Difference: Correlation vs Regression

Correlation	Regression
Relationship shows	Prediction shows
No direction	One-way direction
r is unitless	regression has units
r between –1 to +1	b any value
Shows strength	Shows rate of change

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⭐ Unit–III Summary (Exam time 2 min revision)

• Correlation → degree of relationship

• Pearson r → numerical method (–1 to +1)

• Rank correlation → qualitative data

• Regression → prediction + equation

• Two equations: Y on X, X on Y

• Regression coefficients related by r² = bxy × byx

UNIT 4 FULL NOTES

(Super Easy + Examples + Exam Oriented)

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⭐ PART–A : LINEAR PROGRAMMING (LPP)

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1. Linear Programming – Meaning

Definition (Easy English):
Linear Programming is a mathematical technique used to find the best possible solution (maximum profit or minimum cost) under given constraints.

Key Elements:

1. Objective function – Maximize profit OR minimize cost

2. Decision variables – What to produce (x, y etc.)

3. Constraints – Limitations (resources, time, budget)

4. Non-negativity – x, y ≥ 0

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⭐ 2. LPP Formulation (How to write LPP)

Steps:

1. Identify decision variables → Let x = product A, y = product B

2. Write objective function

   • Max Z = … OR Min Z = …

3. Identify constraints (resource limits)

4. Add non-negativity (x ≥ 0, y ≥ 0)

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⭐ 3. Graphical Method (Only for 2 variables)

Steps:

1. Convert constraints into equations

2. Draw lines on graph

3. Identify feasible region

4. Check corner points

5. Put corner points in objective function

6. Highest value = maximum solution || lowest = minimum

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⭐ 4. Simplex Method (For more than 2 variables)

Definition:
Simplex is an iterative mathematical method to solve complex LPP problems.

Steps (Simple Language):

1. Convert constraints into equalities (add slack variables)

2. Make initial simplex table

3. Identify entering & leaving variables

4. Perform pivot operations

5. Continue until no negative value in Z-row

(Exam में mostly theory पूछते हैं)

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⭐ 5. Sensitivity Analysis

Definition:
Checking how optimal solution changes when parameters (cost, resources, coefficients) are changed.

Why needed?

• Better decision making

• Risk reduction

• Future planning

Components:

• Shadow price

• Range of optimality

• Range of feasibility

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⭐ 6. Transportation Problem

Objective: Minimize cost of transporting goods from sources to destinations.

Methods:

1. Initial Solution Methods

   • North West Corner

   • Least Cost Method

   • Vogel’s Approximation Method (Best)

2. Optimality Test

   • MODI method

   • Stepping-stone method

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⭐ 7. Assignment Problem

Definition: Assigning persons/jobs in such a way that total cost is minimum or total profit is maximum.

Method Used:
👉 Hungarian Method

Applications:

• Assigning workers to tasks

• Machine to jobs

• Salesmen to territories

• Teachers to classrooms

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⭐ PART–B : DATA ANALYTICS

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⭐ 1. Introduction to Analytics

Analytics: Process of collecting, cleaning, analyzing data to find patterns and support decisions.

3 Types:

1. Descriptive Analytics – What happened?

2. Predictive Analytics – What will happen?

3. Prescriptive Analytics – What should be done?

(Exam में mostly first two पूछते हैं)

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⭐ 2. Sources of Data

1. Internal data: Sales, HR, finance

2. External data: Government reports, websites

3. Primary data: Surveys, interviews

4. Secondary data: Books, newspapers

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⭐ 3. Data Quality Issues

• Missing data

• Duplicate values

• Inconsistency

• Outliers

• Human errors

• Incorrect formats

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⭐ 4. Dealing with Missing Data

Methods:

1. Deletion method – Remove missing rows

2. Mean/Median imputation

3. Regression imputation

4. Interpolation

5. Using default values

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⭐ 5. Data Classification

Dividing data into categories (classes).

Types:

• Binary classification – Yes/No

• Multi-class classification – A/B/C etc.

• Ordinal classification – Low/Medium/High

• Nominal classification – Male/Female

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⭐ 6. Descriptive Analytics

Definition: Analyzing historical data to understand what happened.

Tools:

• Mean, median, mode

• Charts, graphs

• Pivot tables

• Summary statistics

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⭐ 7. Predictive Analytics

Definition: Using past data to predict future outcomes.

Types:

1. Univariate Analysis
   (Prediction using single variable)
   – Example: Predict sales using past sales only.

2. Multivariate Analysis
   (Prediction using multiple variables)
   – Example: Predict sales using price + promotions + season.

Techniques:

• Regression

• Time series forecasting

• Machine learning models

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⭐ UNIT 4 → SUPER SHORT SUMMARY

LPP

• Objective → Max/Min

• Method → Graphical, Simplex

• Tools → Slack variable, Feasible region

• Related → Transportation, Assignment

Data Analytics

• Types → Descriptive, Predictive

• Missing data → Mean/median, deletion

• Classification → Binary, multi-class

• Predictive → Regression, models

⭐ BUSINESS ANALYTICS (MBA-7302) – COMPLETE NOTES (UNIT 1 to UNIT 4)

(Hinglish + Examples + Super Easy)

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➤ UNIT 1 – BASIC STATISTICS

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⭐ 1. Measures of Central Tendency

Meaning:

Central tendency = वो value जो पूरी data का “center” represent करती है.

Types:

1. Mean (Average)

$$\text{Mean} = \frac{\sum X}{N}$$

Example: 2,4,6 → Mean = 4

2. Median

Middle value after arranging data.

Example: 3,5,7 → Median = 5

3. Mode

Most frequently occurring value
Example: 2,3,3,4 → Mode = 3

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⭐ 2. Measures of Dispersion

Dispersion = Data कितना spread है.

Types:

1. Range = Max – Min

2. Quartile Deviation = Q3 – Q1 / 2

3. Mean Deviation

4. Variance

5. Standard Deviation (σ)
   $\sigma = \sqrt{\frac{\sum (X - \bar{X})^2}{N}}$

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⭐ 3. Skewness & Kurtosis

Skewness – Shape of distribution

• Positive skew → Tail right side

• Negative skew → Tail left side

• Zero skew → Symmetrical

Kurtosis – Peakedness of curve

• Leptokurtic → Tall, sharp

• Platykurtic → Flat

• Mesokurtic → Normal curve

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⭐ 4. Chebyshev's Theorem

For any distribution:

• At least 75% values lie within 2 SD

• At least 89% values lie within 3 SD

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➤ UNIT 2 – PROBABILITY & DISTRIBUTIONS

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⭐ 1. Probability Theory

Probability = Likelihood of an event

$$P(E) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}}$$

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⭐ 2. Addition Law

Mutually exclusive:

$$P(A \cup B) = P(A) + P(B)$$

Not mutually exclusive:

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

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⭐ 3. Multiplication Law

Independent:

$$P(A \cap B) = P(A) \times P(B)$$

Dependent:

$$P(A \cap B) = P(A) \times P(B|A)$$

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⭐ 4. Bayes Theorem

Used to find reverse probability

$$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$

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⭐ 5. Probability Distributions

(A) Binomial Distribution

Used when:

• Fixed trials

• Success/Failure

• Probability constant

Example: Coin toss.

Formula:

$$P(X=k)=\binom{n}{k} p^k (1-p)^{n-k}$$

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(B) Poisson Distribution

Used for rare events
Example: Accident, calls, arrivals.

Formula:

$$P(X=k)=\frac{e^{-\lambda}\lambda^k}{k!}$$

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(C) Normal Distribution

Bell-shaped, symmetric, mean = median = mode.

Uses:

• Z-score

• Probability estimates

• Quality control

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➤ UNIT 3 – CORRELATION & REGRESSION

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⭐ 1. Correlation

Measures relationship between two variables.

Range: –1 to +1

Types:

• +1 → Perfect positive

• –1 → Perfect negative

• 0 → No relation

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⭐ 2. Karl Pearson’s Correlation (r)

$$r = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sqrt{\sum (x-\bar{x})^2 \sum (y-\bar{y})^2}}$$

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⭐ 3. Rank Correlation (Spearman)

Used for ranking data.

$$r_s = 1 - \frac{6\sum D^2}{N(N^2-1)}$$

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⭐ 4. Regression Analysis

Predicting value of one variable using another.

Regression Equation

$$Y = a + bX$$

Regression Coefficient (b)

Indicates slope
If b = 2 → X increases 1 unit → Y increases 2 units

Properties:

• bxy × byx = r²

• Same sign as correlation

• One regression line passes through mean point (x̄, ȳ)

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➤ UNIT 4 – LINEAR PROGRAMMING + DATA ANALYTICS

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⭐ A. LINEAR PROGRAMMING (LPP)

1. Definition:

A method to maximize profit or minimize cost under given constraints.

2. Components

• Decision variables

• Objective function

• Constraints

• Non-negativity

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⭐ 3. Graphical Method

Steps:

1. Convert constraints

2. Draw lines

3. Feasible region

4. Check corner points

5. Highest value = max / lowest = min

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⭐ 4. Simplex Method (Theory)

Used for problems with more than 2 variables.

Steps:

• Add slack variables

• Form initial table

• Entering/leaving variable

• Pivot

• Continue until optimum reached

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⭐ 5. Transportation Problem

Objective: Minimize cost of transporting goods.

Methods:

• NWC

• Least Cost

• VAM (best)

• MODI (optimality test)

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⭐ 6. Assignment Problem

Objective: Minimum cost assignment.

Method: Hungarian Method

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⭐ B. DATA ANALYTICS

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⭐ 1. Introduction

Analytics = Converting data into insights.

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⭐ 2. Types of Analytics

✔ Descriptive

“What happened?”
Uses: charts, mean, median, reports.

✔ Predictive

“What will happen?”
Uses: regression, forecasting.

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⭐ 3. Data Sources

• Internal

• External

• Primary

• Secondary

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⭐ 4. Data Quality Issues

• Missing values

• Duplicates

• Inconsistency

• Outliers

• Wrong entry

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⭐ 5. Handling Missing Data

• Deletion

• Mean/median substitution

• Regression imputation

• Interpolation

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⭐ 6. Data Classification

• Binary

• Multi-class

• Ordinal

• Nominal

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⭐ 7. Predictive Analytics Methods

• Regression

• Machine learning models

• Time series

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⭐ 8. Univariate & Multivariate

• Univariate → one variable

• Multivariate → multiple variables

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⭐ FINAL SUPER SUMMARY

(10 minutes revision)

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UNIT 1 – Stats

Central tendency → Mean/Median/Mode
Dispersion → Range, SD, Variance
Skewness → shape
Kurtosis → peak
Chebyshev → 75% in 2SD

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UNIT 2 – Probability

Addition law
Multiplication law
Bayes theorem
Distributions:

• Binomial → success/failure

• Poisson → rare events

• Normal → bell curve

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UNIT 3 – Correlation & Regression

Correlation (r → –1 to +1)
Rank correlation
Regression: Y = a + bX
Properties: bxy × byx = r²

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UNIT 4 – LPP + Analytics

LPP → maximize/minimize
Graphical method
Simplex (steps)
Transportation (VAM, MODI)
Assignment (Hungarian)
Analytics → descriptive, predictive
Missing data handling
Classification