Data, Descriptive Statistics and AI Fundamentals

1.1 Course Introduction

This section answers three questions: what the course covers, how it is assessed, and what roles data, models and AI each play in the course.

Course Information

Learning Outcomes (CLO1–CLO7)

Course Outline: Eight Units

Scope of the Course

Unit 1 introduces only the three specialised model families aligned with the course spine:prediction(regression and time series),optimisation(mathematical programming and solvers), and simulation(Monte Carlo). Classification, clustering and similar models are mentioned only in passing and are neither taught nor examined.

Assessment and Assignments

• Assignment 1 one-tailed test for a fuel additive;Assignment 2 MBA mean-age test and a paired t-test of pre- and post-training scores;Assignment 3 A/B experiment design, data analysis and an AI-correction log.
• The open-book examination prohibits AI and internet-connected devices. There is no midterm quiz; that time is devoted to AI-tool labs and the group project.

AI Use Policy (Permissive)

Not required: there is no limit on the proportion of AI-generated content, no mandatory chat log, and no AI-detection screening.

The Decision Path: From Problem to Decision

Four Levels of Analytics

Case: The Efficiency Frontier in US Air Transportation

Place firms in the same industry on one chart: the horizontal axis is input (available seat miles, ASM, a measure of capacity), and the vertical axis is output (revenue passenger miles, RPM, a measure of traffic).envelope This line is the efficiency frontier. For a firm below the frontier, the vertical gap to the frontier measures the additional output achievable with the same inputs, or the input reduction achievable for the same output.

Interactive Demonstration 1

Draw the Efficiency Frontier Yourself

On either chart below,hold down the left mouse button and drag(or use your finger on a touch screen) along the upper edge of the leading firms. Your line is your judgement of the efficiency frontier. You may draw it in several strokes, then explain to a partner why you drew it that way.

Chart 1 · The red line is the frontier you drew

Chart 2

Undo last stroke Clear all lines

• An efficiency frontier places comparable firms in one chart so that performance gaps become visible.
• Firms on the frontier are the most efficient in the current sample; the distance below the frontier represents room for improvement.
• This section focuses on reading the chart and drawing the frontier. Calculating its position belongs to data envelopment analysis (DEA) and is outside this course.
• Terminology note: “efficiency boundary” and “efficiency frontier” refer to the same envelope curve, called an efficiency frontier In Chinese literature,“efficiency frontier” is the more common term, and this course uses it consistently.

Business Applications and Success Stories

1.2 Data and Basic Descriptive Statistics

The goal of this section is not to cover all of statistics, but to help you know what to inspect first, how to compute it, and how to interpret it when you receive a data set. All four orange panels below are interactive: change the numbers and the charts will follow.

Where Data Comes From

• Cross-sectional data observations of different objects at one point in time, such as the average house price in 90 cities.
• Time-series data observations of the same object at different points in time, such as the average daily call volume of a call centre in each quarter.
• Text data unstructured data that must first be converted into labels or numbers before analysis (covered in Unit 4).
• Most classroom data are exported from business systems, so the first step is always to inspect the fields and their definitions.

Variable Types and Data Quality

Check four data-quality issues:missing values,duplicates,inconsistent units,outliers and data-entry errors Definitional issues are the easiest to overlook—for example, whether an amount includes tax and whether a duration is measured in calendar or business days.

The Excel Workbench: Moves to Master

Descriptive Statistics at a Glance

• Mean the sum of all observations divided by the count. It is the most common measure and the most sensitive to extreme values.
• Median the middle value after sorting. It is insensitive to extreme values.
• Mode the most frequent value; useful for identifying the most common amount or category.
• Geometric mean the appropriate average for growth rates, such as the average return over several years.

Measures of Spread: Range and Interquartile Range

• Range = maximum − minimum. It is easy to calculate but uses only two observations.
• Interquartile range (IQR) = third quartile − first quartile. It describes the width of the middle 50% of observations and is unaffected by extreme values.
• Excel: =QUARTILE.INC(range, 1) and =QUARTILE.INC(range, 3).
• Return to the demonstration above: the IQR of the order values is about USD 63, while the range exceeds USD 670—a tenfold difference.

Standard Deviation and Variance

The standard deviation is, on average, how far each observation lies from the mean. It is in the same unit as the data and is therefore easier to interpret than the variance. The variance is the square of the standard deviation and is convenient in regression and portfolio analysis.

The Empirical Rule and Box Plots

• Empirical rule for approximately normal data, about 68% of observations lie within one standard deviation of the mean and about 95% within two.
• For the order data, about 77% lie within one standard deviation—higher than 68% because the distribution is right-skewed.
• Box plot a chart of the minimum, first quartile, median, third quartile and maximum; useful for comparing the centre and spread of several groups.

Descriptive Statistics in Excel

Three Questions for Interpreting Descriptive Statistics

1. Where is the centre? Is there a large gap between the mean and median? A large gap signals extreme values or right skew.
2. How large is the spread? Does the standard deviation or IQR reflect business variation or a data-entry error?
3. What is the shape? Is the distribution symmetric? Does it have a long tail? Are there values that should not exist?

1.3 AI Fundamentals

This section establishes the shared language used in every later unit: how AI families relate, the foundations of machine learning and deep learning, how large language models work (tokens and embeddings), their capability boundaries, how to write prompts and where the limits of agents lie.

The AI Family Map

• Artificial intelligence (AI) the use of machines to perform tasks that require intelligence.
• Machine learning (ML) learning patterns from data rather than hard-coding rules.
• Deep learning (DL) using multi-layer neural networks to learn complex patterns.
• Generative AI generating new text, images and code.
• Large language model (LLM) a branch of generative AI that specialises in language.

Machine Learning and Deep Learning in Plain Language

Machine learning A different approach: rather than hand-coding rules one by one, we give an algorithm many “input–answer” examples and let it discover the pattern. Spam detection is one example—instead of writing every rule, we give the model 100,000 labelled emails.

• Supervised learning uses labelled examples to learn a classification or prediction rule. The regression and time-series prediction in this course follow this logic.
• Unsupervised learning provides only data, without labels, so the algorithm discovers structure such as groups or lower-dimensional representations.
• Reinforcement learning adjusts a policy through trial and error based on rewards, as in games or robot scheduling.
• Deep learning uses multi-layer neural networks to transform raw data into increasingly abstract features.

Tokens and Embeddings: How Models “Read” Text

• token Models do not process text as whole characters or words. They first split text into tokens, which may be a Chinese character, part of an English word, or a punctuation mark. Context-window length and API billing are also measured in tokens.
• embedding Each token is mapped to a string of numbers, often a vector with hundreds or thousands of dimensions. Words with similar meanings have similar vectors, so comparing meaning becomes comparing distance.

A sentence therefore moves through the model as follows:text → tokens → embeddings → layer-by-layer computation in a multi-layer network (attention determines which earlier positions the current word should emphasise) → a probability distribution over the next token. Repeating the choice of “pick one token and append it” produces the complete response.

How a Large Language Model Works

Continue through the process: the model has read an enormous body of text and learned which words co-occur; when generating, it repeatedly estimates the most likely next token. Its output is therefore the most plausible-sounding continuation not a verified fact—which is why it can explain a concept fluently and still invent a non-existent number.

• Asking the same question twice can produce different answers, and rephrasing the question can change the conclusion.
• For details absent from its training data, the model may fill in a plausible version; specific dates, numbers and citations are especially prone to error.
• Countermeasure: request sources and derivations, and verify against Excel and the original material.

Capability Boundaries of LLMs

Three Specialised AI Model Families Along the Course Spine

Classification, clustering, neural networks and similar models are common in industry but outside this course. The modelling content here is limited to regression, time series and mathematical programming, plus uncertainty and simulation in Unit 7.

Prompt Engineering: Five Components

Useful Prompt Patterns and Failure Modes

• Provide an example give one sample of the expected output and ask the model to follow it.
• Request step-by-step work ask for an outline before expansion so you can intervene early.
• Specify a table define the column names and order so the result can be pasted directly into Excel.
• Failure modes: fabricated data, ignored constraints, overconfidence and answering a different question. When these occur, narrow the task, provide more data, and require item-by-item verification.

AI Agents

Agent = objective + tool use + multi-step execution + memory. Unlike a conversational model, an agent can retrieve data, call tools and iterate. Management applications include automated data retrieval and weekly reporting, model-draft generation and automated sensitivity scans.

• Reliability an error at any intermediate step may propagate to the final output.
• Access boundaries the data an agent may access must be defined in advance.
• Auditability and responsibility who approves, reviews and remains accountable? In this course, an agent may generate a draft, but a person must verify and sign off on the conclusion.

Data Security and AI-Use Disclosure

• Permitted inputs: course-provided classroom data, public data and synthetic data you create yourself.
• Prohibited inputs: unpublished operating data, customer personal information, contracts and personnel materials.
• Sample disclosure: “In this assignment, I used Doubao to explain the regression coefficients; I recomputed every numerical conclusion in Excel.”

Live Comparison: Doubao and DeepSeek

Ask two models the same question and compare three things: whether the conclusions agree, whether the explanations are specific, and whether either model invents numbers. Platform differences are themselves teaching material.

The chat interface above is illustrative; the tools you use will look slightly different.

Checkpoint: do Model B’s claims of “approximately normal” and “108.5” hold? Use the distribution explorer in Section 1.2: the mean is 102.84, the median is 91.02, and the distribution is right-skewed.

1.4 First Hands-On AI Activity

Apply the capability boundaries and prompting method you have just learned: ask AI to perform descriptive analysis on real order data, then verify every item.

1. Upload S1_online_orders.xlsx to Doubao or DeepSeek and ask for a set of descriptive statistics with an interpretation.
2. Write the prompt using all five components: role, task, data, output format and constraints. You may generate it with the builder above.
3. Require at least the sample size, mean, median, maximum and minimum.
4. Add a follow-up: is the order-value distribution right-skewed, and should the report use the mean or the median?
5. Recompute every value in Excel and record every discrepancy.

1.5 Unit Summary and Next Steps

• Descriptive statistics answer three questions: where the centre is, how large the spread is, and what the shape is.
• With extreme values, the median represents a typical observation better than the mean; reports for right-skewed data should present both.
• AI is strong in language and framing but weak in facts and calculation, so conclusions must be verified; the five prompt components make a request actionable.
• This unit does not cover statistical inference—the normal distribution, sampling, hypothesis testing and A/B testing are covered in Unit 2.

Appendix: Interactive Demonstrations and Classroom Exercises

Data sources: S1_online_orders.xlsx (11,121 order values) and S1_Height and Weight.xlsx (1,587 athletes). All reference values in the exercises and demonstrations are computed in real time from data embedded in the page.

The diagrams on this page—the textbook cover, four levels of analytics, AI family, traditional programming versus machine learning, deep-learning layers, tokenisation, embedding space, next-token prediction, agent workflow and chat window—are drawn as vectors and remain sharp when enlarged.

Unit Glossary (English–Chinese)