Introduction to Business Analytics CBMBT3T03

Syllabus topics (RTMNU)

• What Is Business Analytics?
• Evolution of Business Analytics
• Impacts and Challenges
• Scope of Business Analytics
• Software
• Support
• Data for Business Analytics
• Data Sets and Databases
• Big Data
• Metrics and Data
• Classification
• Data Reliability and Validity
• Models in Business Analytics
• Decision Models
• Model Assumptions
• Uncertainty and Risk
• Prescriptive Decision Models

What Is Business Analytics?

Definition: Business Analytics (BA) is the use of data, statistics, computer software and mathematical models to understand business problems and to take better, fact-based decisions.

In simple words, BA turns raw data (sales bills, customer records, website clicks) into useful information. Example: Big Bazaar or DMart studies its billing data to decide which products to keep near the cash counter.

BA has three main types:

1. Descriptive analytics – What happened? (reports, averages, charts).
2. Predictive analytics – What will happen? (forecasting, data mining).
3. Prescriptive analytics – What should we do? (optimization, decision models).

Evolution of Business Analytics

1. Scientific management (early 1900s) – F.W. Taylor used time-and-motion study to measure work.
2. Operations Research / Management Science (1940s–50s) – mathematical models such as linear programming, first used in World War II and later in business.
3. Decision Support Systems (1970s–80s) – computers helped managers with reports and "what-if" analysis.
4. Business Intelligence (1990s) – data warehouses, dashboards and spreadsheets (MS Excel).
5. Modern analytics (2000s onwards) – big data, data mining, machine learning and cloud tools.

Impacts and Challenges

Impacts (benefits):

1. Better and faster decisions based on facts, not guesswork.
2. Lower costs – e.g. better inventory control.
3. Higher revenue – right price, right product, right customer.
4. Better customer service – e.g. Amazon and Flipkart recommend products.
5. Risk control – banks use analytics to detect fraud and check loan default risk.

Challenges:

1. Lack of trained analysts.
2. Poor quality or incomplete data.
3. High cost of software and hardware.
4. Resistance from managers who prefer "gut feeling".
5. Data privacy and security – India's Digital Personal Data Protection Act, 2023 must be followed.

Scope of Business Analytics

BA is used in almost every department:

• Marketing – customer segmentation, campaign results, pricing.
• Finance – budgeting, credit scoring, investment analysis.
• Operations – inventory, production planning, supply chain, routing.
• Human resources – hiring, attrition prediction, performance analysis.
• Sectors – banking, insurance, retail, e-commerce, health care, sports, government.

Software and Support

Common BA software: MS Excel (with Solver and Analysis ToolPak), SPSS, SAS, R, Python, Tableau and Power BI (dashboards). Support means the help available to users: add-ins, online help, training, user communities and vendor support.

Data for Business Analytics, Data Sets and Databases

Data are raw facts and figures collected about events, people or things. Sources: sales records, surveys, government reports (RBI, Census), websites, sensors.

• Data set – a collection of data arranged in rows (records/observations) and columns (variables). Example: an Excel sheet of 500 customers with age, city and purchase amount.
• Database – a large, organised collection of related data stored in a computer, managed by a DBMS (e.g. Oracle, MySQL). A bank keeps all account data in a database.

Big Data

Big data means data sets so large and fast-changing that normal software cannot handle them. Its features are the V's:

1. Volume – huge quantity (terabytes, petabytes).
2. Velocity – data arrive very fast (UPI transactions every second).
3. Variety – numbers, text, images, videos.
4. Veracity – uncertainty about accuracy.
5. Value – useful insight from the data.

Metrics and Data Classification

A metric is a unit used to measure performance (e.g. sales per day, delivery time, defect %). A measure is the numerical value of a metric for a unit.

Data are classified into:

1. Categorical (qualitative) – labels, e.g. gender, city. Can be nominal (no order) or ordinal (order: good, better, best).
2. Numerical (quantitative) – numbers. Interval data have no true zero (temperature in °C); ratio data have a true zero (sales, weight).
3. Cross-sectional (many units at one time) and time-series (one unit over time) data.

Data Reliability and Validity

Reliability means data are measured consistently – the same method gives the same result again. Validity means data measure what they are supposed to measure. Example: a weighing machine that always shows 1 kg extra is reliable but not valid.

Models in Business Analytics and Decision Models

A model is a simplified representation of a real situation. Types: verbal (in words), graphical (charts), and mathematical (equations).

A decision model is a logical or mathematical model that links inputs (data, uncontrollable factors, and decision variables the manager controls) to outputs (profit, cost). Example: Profit = (Price − Variable cost) × Quantity − Fixed cost.

Model Assumptions

Every model rests on assumptions (simplifications), e.g. demand falls as price rises, or costs are linear. If the assumptions are wrong, the result is wrong, so analysts must state and test them.

Uncertainty and Risk

Uncertainty means not knowing what will happen in the future. Risk means the chance of loss or an undesirable outcome, often measured with probabilities. Example: a new product may sell 1,000 or 10,000 units – that is uncertainty; the chance of a loss is risk.

Prescriptive Decision Models

Prescriptive models tell the decision-maker the best course of action. They have an objective function (maximise profit or minimise cost) and constraints (limits on resources). Deterministic models assume all inputs are known; stochastic models include uncertainty.

Likely exam questions

1. (Long, 8/16 marks) What is Business Analytics? Explain its evolution, scope and impacts on business decision-making.
2. (Long, 8/16 marks) What is Big Data? Explain its characteristics. Also explain data reliability and validity with examples.
3. (Short, 4 marks) Distinguish between a data set and a database.
4. (Short, 4 marks) What is a decision model? Give an example.
5. (Short, 4 marks) Distinguish between uncertainty and risk.

Syllabus topics (RTMNU)

• Populations and Samples
• Understanding Statistical Notation
• Measures of Location
• Arithmetic Mean
• Median
• Mode
• Midrange
• Using Measures of Location in Business Decisions
• Measures of Dispersion
• Range
• Interquartile Range
• Variance
• Standard Deviation
• Coefficient of Variation
• Measure of Association
• Covariance
• Correlation
• Statistical Thinking in Business Decision
• Variability in Samples

Populations and Samples

A population is the complete group of all items we want to study (e.g. all 5 crore SBI account holders). A sample is a part of the population selected for study (e.g. 1,000 account holders). A number that describes a population is a parameter; a number from a sample is a statistic.

Understanding Statistical Notation

Σ (sigma, capital) means "sum of". Σx = x₁ + x₂ + … + xₙ.

Measures of Location: Arithmetic Mean, Median, Mode, Midrange

1. Arithmetic mean – sum of values ÷ number of values. x̄ = Σx / n (population: μ = Σx / N). Easy and uses all data, but affected by extreme values.
2. Median – the middle value after arranging data in order. Position = (n + 1)/2. If n is even, it is the average of the two middle values. Not affected by extreme values.
3. Mode – the value that occurs most often. Useful for sizes (shoe size, shirt size).
4. Midrange – (Smallest value + Largest value) / 2. Very quick but depends only on two extreme values.

Using Measures of Location in Business Decisions

• A garment shop stocks the modal size in larger quantity.
• Salary surveys report the median salary because a few very high salaries pull the mean up.
• A restaurant uses the mean daily sales to plan staff and raw material.

Measures of Dispersion: Range, Interquartile Range, Variance, Standard Deviation, Coefficient of Variation

Dispersion means how spread out the data are around the average.

1. Range = Largest − Smallest.
2. Interquartile Range (IQR) = Q₃ − Q₁. Q₁ (first quartile) is at position (n + 1)/4 and Q₃ at 3(n + 1)/4 in ordered data. It covers the middle 50% of values.
3. Variance – average of squared deviations from the mean. Population: σ² = Σ(x − μ)² / N. Sample: s² = Σ(x − x̄)² / (n − 1).
4. Standard deviation (SD) – square root of variance; in the same unit as the data.
5. Coefficient of Variation (CV) = (SD / Mean) × 100. A relative measure used to compare consistency; lower CV = more consistent.

Illustration 1: Daily sales (₹ thousand) of a Nagpur kirana shop for 10 days: 12, 15, 11, 18, 15, 20, 14, 15, 16, 24. Find mean, median, mode, midrange, range, IQR, variance, SD and CV.

Solution: Ordered data: 11, 12, 14, 15, 15, 15, 16, 18, 20, 24 (n = 10).

• Mean x̄ = 160 / 10 = 16 (₹16,000).
• Median: position (10 + 1)/2 = 5.5th → (15 + 15)/2 = 15.
• Mode = 15 (occurs 3 times).
• Midrange = (11 + 24)/2 = 17.5.
• Range = 24 − 11 = 13.
• Q₁: position 11/4 = 2.75th → 12 + 0.75(14 − 12) = 13.5. Q₃: position 8.25th → 18 + 0.25(20 − 18) = 18.5. IQR = 18.5 − 13.5 = 5.
• Population variance σ² = 132 / 10 = 13.2; SD σ = √13.2 = 3.63.
  (Sample variance s² = 132 / 9 = 14.67; s = 3.83.)
• CV = (3.63 / 16) × 100 = 22.7%.

Illustration 2 (CV comparison): Monthly sales (units) of Branch A: 50, 55, 45, 60, 40; Branch B: 48, 52, 50, 51, 49. Both means = 50. σ_A = √50 = 7.07, CV_A = 14.14%. σ_B = √2 = 1.41, CV_B = 2.83%. Branch B is more consistent.

Measure of Association: Covariance and Correlation

Covariance shows the direction in which two variables move together. Population covariance = Σ(x − x̄)(y − ȳ) / N (sample: divide by n − 1). Positive → move together; negative → move opposite. Its value depends on units, so its size is hard to judge.

Correlation coefficient (Karl Pearson's r) = Σ(x − x̄)(y − ȳ) / √[Σ(x − x̄)² × Σ(y − ȳ)²]. It is unit-free and lies between −1 and +1. r = +1 perfect positive, 0 no linear relation, −1 perfect negative.

Illustration 3: Advertising (x) and sales (y), ₹ lakh, for 5 months: (2, 10), (4, 14), (5, 15), (6, 19), (8, 22). Find covariance and r.

x̄ = 25/5 = 5, ȳ = 80/5 = 16.

• Covariance (population) = 41 / 5 = 8.2 (sample: 41 / 4 = 10.25).
• r = 41 / √(20 × 86) = 41 / √1720 = 41 / 41.47 = 0.989 → very high positive correlation; more advertising goes with more sales.

Statistical Thinking in Business Decision

Statistical thinking means understanding that all work is a process, all processes have variation, and decisions should be based on data that measure and reduce that variation. A manager should ask: Is this change real or just normal variation?

Variability in Samples

Different samples from the same population give different means and SDs. This is called sampling variability. Larger samples give more stable results. So a sample result is an estimate, not the exact population value.

Likely exam questions

1. (Long, 8/16 marks) Explain measures of dispersion: range, interquartile range, variance, standard deviation and coefficient of variation. Daily sales (₹ thousand) of a shop are 12, 15, 11, 18, 15, 20, 14, 15, 16, 24. Calculate the mean, standard deviation and coefficient of variation.
2. (Long, 8/16 marks) What are covariance and correlation? From the following data find Karl Pearson's coefficient of correlation: Advertising (₹ lakh) 2, 4, 5, 6, 8; Sales (₹ lakh) 10, 14, 15, 19, 22.
3. (Short, 4 marks) Distinguish between population and sample, and between parameter and statistic.
4. (Short, 4 marks) Find the median, mode and midrange of 11, 12, 14, 15, 15, 15, 16, 18, 20, 24.
5. (Short, 4 marks) What is statistical thinking? Explain variability in samples.

Syllabus topics (RTMNU)

• Introduction to Data Mining
• The Scope of Data Mining
• Data Exploration and Reduction
• Sampling
• Data Visualization
• Dirty Data
• Cluster Analysis
• Classification
• An Intuitive Explanation of Classification
• Measuring Classification Performance
• Using Training and Validation Data
• Classifying New Data
• Classification Techniques
• k-Nearest Neighbors (k-NN)
• Discriminant Analysis
• Logistic Regression
• Association Rule Mining
• Cause-and-Effect Modeling

Introduction to Data Mining and the Scope of Data Mining

Data mining is the process of finding hidden patterns, relationships and trends in large data sets using statistics, mathematics and computer methods, so that future outcomes can be predicted. It is the main tool of predictive analytics.

Scope (uses): market basket analysis in supermarkets, customer segmentation, credit scoring and loan approval in banks, fraud detection in UPI/credit cards, customer churn prediction in telecom (Jio, Airtel), product recommendations on Flipkart and Amazon, and insurance claim analysis.

Data Exploration and Reduction

Data exploration means looking at the data first – summaries, charts, missing values – to understand it. Data reduction means making the data smaller but still useful: selecting only important variables, grouping similar items, or taking a sample.

Sampling

In data mining, a random sample of a very large database is often analysed to save time. The sample must represent the whole data. Data are also split into training and validation parts (see below).

Data Visualization

Showing data as pictures – bar charts, histograms, scatter plots, heat maps, dashboards – so patterns are seen quickly. Tools: Excel, Tableau, Power BI.

Dirty Data

Dirty data are data with errors: missing values, duplicate records, wrong entries (age = 250), inconsistent formats ("Nagpur", "NGP"). Data cleaning removes or corrects these: delete duplicates, fill missing values with mean/median, correct spellings. Rule: "garbage in, garbage out".

Cluster Analysis

Cluster analysis groups objects so that items in the same group (cluster) are similar and items in different groups are different. It is unsupervised – groups are not known in advance. Similarity is measured by distance (Euclidean distance). Methods: hierarchical clustering (tree/dendrogram) and k-means clustering. Use: dividing customers into "budget", "regular" and "premium" segments.

Classification and An Intuitive Explanation of Classification

Classification assigns a new record to one of the already known groups (classes) using past data where the class is known. It is supervised learning. Intuition: a bank officer looks at past borrowers – those with low income and many loans often defaulted. So a new applicant with a similar profile is placed in the "risky" class.

Measuring Classification Performance

A confusion matrix compares actual and predicted classes.

Illustration 1: A model checked 100 loan applicants. Actual defaulters = 50: model caught 40 (True Positive), missed 10 (False Negative). Actual good = 50: 45 correctly predicted good (True Negative), 5 wrongly called defaulters (False Positive).

• Accuracy = (TP + TN)/Total = 85/100 = 85%; error rate = 15%.
• Precision = TP/(TP + FP) = 40/45 = 0.889.
• Recall (sensitivity) = TP/(TP + FN) = 40/50 = 0.80.
• Specificity = TN/(TN + FP) = 45/50 = 0.90.

Using Training and Validation Data

The data are divided into a training set (e.g. 60–70%) used to build the model and a validation set (30–40%) used to test it on data it has not seen. This avoids over-fitting (a model that fits old data perfectly but predicts new data badly).

Classifying New Data

After validation, the model is applied to new records whose class is unknown, e.g. new loan applications or new customers.

Classification Techniques: k-Nearest Neighbors (k-NN)

k-NN classifies a new record by finding the k most similar (nearest) records in the training data and taking the majority class among them. Distance: d = √[(x₁ − x₂)² + (y₁ − y₂)²].

Illustration 2: A showroom has data on 6 visitors. Classify a new visitor aged 40 with income ₹60 thousand, using k = 3.

The 3 nearest are B, F and one of C/E (tied at 20.62). B and F are "Yes", so whichever tied record is taken, the majority (at least 2 of 3) is "Yes". New visitor is classified as a likely buyer. (In practice, variables are first scaled so that one with large numbers does not dominate.)

Discriminant Analysis

Discriminant analysis builds a linear equation (discriminant function) D = b₀ + b₁X₁ + b₂X₂ + … from known groups. A new record's D score is compared with a cut-off value to place it in a group. Example: classifying firms as "healthy" or "sick" using financial ratios.

Logistic Regression

Logistic regression predicts the probability of a yes/no outcome. p = 1 / (1 + e^{−(b₀ + b₁X)}), so p always lies between 0 and 1. If p ≥ 0.5 (cut-off), the record is classed "yes".

Example: b₀ = −4, b₁ = 0.1, income X = 50 → z = −4 + 5 = 1 → p = 1/(1 + e⁻¹) = 0.731 → likely buyer.

Association Rule Mining

Finds "if–then" rules about items that occur together, e.g. "If a customer buys bread, he also buys butter" (market basket analysis).

• Support = transactions with both A and B ÷ total transactions.
• Confidence (A → B) = transactions with A and B ÷ transactions with A.
• Lift = Confidence ÷ Support of B. Lift > 1 means A and B are bought together more than by chance.

Illustration 3: Out of 100 bills, 40 have bread, 30 have butter, 20 have both. Support = 20/100 = 0.20; Confidence (bread → butter) = 20/40 = 0.50; Lift = 0.50/0.30 = 1.67 → keep butter near bread.

Cause-and-Effect Modeling

Data mining finds association, but managers want to know causes. Cause-and-effect modeling links an outcome (e.g. customer satisfaction) to its possible causes (price, service, quality) using correlation, regression and tools like the fishbone (Ishikawa) diagram. A cause should come before the effect, and other explanations must be ruled out.

Likely exam questions

1. (Long, 8/16 marks) What is data mining? Explain its scope, data exploration and reduction, and the problem of dirty data.
2. (Long, 8/16 marks) What is classification? Explain the k-Nearest Neighbors technique and how classification performance is measured using a confusion matrix (TP = 40, FN = 10, FP = 5, TN = 45).
3. (Short, 4 marks) Distinguish between cluster analysis and classification.
4. (Short, 4 marks) Explain support, confidence and lift in association rule mining.
5. (Short, 4 marks) Why are training and validation data used in data mining?

Syllabus topics (RTMNU)

• Linear Optimization
• Building Linear Optimization Models
• Identifying Elements for an Optimization Model
• Translating Model Information into Mathematical Expressions
• More about Constraints
• Characteristics of Linear Optimization
• Decision Analysis
• Formulating Decision Problems
• Decision Strategies without Outcome Probabilities
• Decision Strategies for a Minimize / Maximize Objective
• Decision Strategies with Outcome Probabilities
• Average Payoff Strategy
• Expected Value Strategy
• Evaluating Risk
• Decision Trees and Monte Carlo Simulation

Linear Optimization – Building Linear Optimization Models

Linear optimization (Linear Programming, LP) is a mathematical method to find the best (maximum profit or minimum cost) way to use limited resources, when the objective and all constraints are linear (straight-line) relationships.

Steps to build a model: (1) understand the problem, (2) define decision variables, (3) write the objective function, (4) write the constraints, (5) add non-negativity, (6) solve (graph or Excel Solver) and interpret.

Identifying Elements for an Optimization Model

1. Decision variables – quantities the manager controls (units of each product to make).
2. Objective function – what is to be maximised or minimised (profit, cost, time).
3. Constraints – limits on resources (machine hours, labour, raw material, budget, demand).
4. Parameters – fixed known numbers (profit per unit, hours per unit).

Translating Model Information into Mathematical Expressions

Illustration 1: A Nagpur furniture unit makes tables and chairs. Profit: ₹500 per table, ₹300 per chair. A table needs 4 carpentry hours and 2 painting hours; a chair needs 2 and 2 hours. Available: 100 carpentry hours and 60 painting hours per week. Formulate and solve.

Let x = tables, y = chairs.
Maximise Z = 500x + 300y
Subject to: 4x + 2y ≤ 100 (carpentry); 2x + 2y ≤ 60 (painting); x ≥ 0, y ≥ 0.

Corner points of the feasible region (graphical method): the two lines meet where 4x + 2y = 100 and 2x + 2y = 60 → subtracting, 2x = 40, x = 20, y = 10.

Optimal: make 20 tables and 10 chairs; maximum profit ₹13,000 per week. Both constraints are fully used (binding).

More about Constraints

• Types: ≤ (limit, e.g. hours available), ≥ (requirement, e.g. minimum order of 50 units), = (exact, e.g. total budget fully spent).
• Binding constraint – fully used at the optimum; non-binding – has slack (unused resource).
• Non-negativity – production cannot be negative.
• Bounds, ratio constraints (chairs at least twice tables: y ≥ 2x → y − 2x ≥ 0) and proportion constraints are also possible.

Characteristics of Linear Optimization

1. Linearity/Proportionality – profit and resource use rise in direct proportion.
2. Additivity – total = sum of parts.
3. Divisibility – variables may take fractional values.
4. Certainty – all parameters are known and fixed.
5. Non-negativity and finite choices with limited resources.

Possible outcomes: unique optimal solution, alternative optima, unbounded solution, or infeasible (no solution).

Decision Analysis – Formulating Decision Problems

Decision analysis helps choose the best alternative when the future is uncertain. Elements: (1) decision alternatives (choices), (2) outcomes / states of nature (events not in our control, e.g. demand high/low), (3) payoffs (profit or cost of each combination), shown in a payoff table.

Illustration 2: A company must choose plant size. Payoff (₹ lakh):

Probabilities of demand: High 0.3, Medium 0.5, Low 0.2.

Decision Strategies without Outcome Probabilities

1. Maximax (optimistic / aggressive) – pick the best of the best payoffs.
2. Maximin (pessimistic / conservative) – pick the best of the worst payoffs.
3. Minimax regret (opportunity loss) – regret = best payoff in that column − actual payoff; pick the alternative whose maximum regret is smallest.

Regret table (column best: 200, 80, 10):

Decision Strategies for a Minimize / Maximize Objective

For a maximize objective (profit) use maximax, maximin and regret as above. For a minimize objective (cost): aggressive = minimin (smallest of the smallest costs), conservative = minimax (smallest of the largest costs), and regret = actual cost − lowest cost in that column, then choose the smallest maximum regret.

Decision Strategies with Outcome Probabilities: Average Payoff Strategy and Expected Value Strategy

• Average payoff – assumes all outcomes equally likely; average of each row.
• Expected Value (EV) = Σ (payoff × probability). Choose highest EV (lowest for cost).

EV(Large) = 200(0.3) + 50(0.5) + (−120)(0.2) = 60 + 25 − 24 = 61. EV(Medium) = 30 + 40 − 4 = 66. EV(Small) = 12 + 15 + 2 = 29.

Decisions: Maximax → Large plant; Maximin → Small plant; Minimax regret → Medium plant; Average payoff → Medium plant (53.33); Expected value → Medium plant (₹66 lakh).

Evaluating Risk

EV alone ignores risk. Risk is measured by the standard deviation of payoffs: σ = √Σ p(x − EV)². σ(Large) = √12,409 = 111.40; σ(Medium) = √1,924 = 43.86; σ(Small) = √109 = 10.44. Medium plant has the highest EV with moderate risk, so it is a sound choice. A risk-averse manager may prefer the small plant.

Decision Trees and Monte Carlo Simulation

A decision tree is a diagram of decisions and outcomes in sequence: a square (□) is a decision node, a circle (○) is a chance node with probabilities on branches, and payoffs are at the end. It is solved by "rolling back" – computing EVs from right to left and choosing the best branch at each decision node.

Monte Carlo simulation uses random numbers to generate many possible values of uncertain inputs (demand, cost) from their probability distributions, calculates the outcome each time (e.g. 1,000 trials in Excel with RAND()), and studies the distribution of results – average profit, chance of loss, etc.

Likely exam questions

1. (Long, 8/16 marks) What is linear optimization? Explain its elements and characteristics. A firm earns ₹500 per table and ₹300 per chair; a table needs 4 carpentry and 2 painting hours, a chair 2 and 2 hours; 100 carpentry and 60 painting hours are available. Formulate the model and find the optimal product mix.
2. (Long, 8/16 marks) Explain decision strategies with and without outcome probabilities. Payoffs (₹ lakh) for Large, Medium and Small plants under High/Medium/Low demand are (200, 50, −120), (100, 80, −20) and (40, 30, 10); probabilities 0.3, 0.5, 0.2. Find the decision under maximax, maximin, minimax regret and expected value.
3. (Short, 4 marks) State any four characteristics of linear optimization.
4. (Short, 4 marks) What is a decision tree? Explain its nodes.
5. (Short, 4 marks) Explain Monte Carlo simulation in brief.