Foundations of Statistics and Data Analytics

Introduction

Statistics and data analytics provide a disciplined way to learn from variation, uncertainty, and evidence. Modern organisations collect data from transactions, sensors, surveys, websites, health records, production systems, and social platforms. Data alone, however, does not automatically produce knowledge. Analysts must define what is being studied, determine how observations will be measured, select appropriate summaries and models, and communicate conclusions with suitable caution.

This chapter introduces the conceptual foundations required for later study of probability, statistical inference, regression, forecasting, machine learning, and data-driven decision-making. It distinguishes a population from a sample, a parameter from a statistic, and a variable from an observation. It also explains measurement scales and the four major forms of analytics: descriptive, diagnostic, predictive, and prescriptive.

A central theme is that a sound analysis begins with a well-formulated question. A vague question such as “How can sales be improved?” must be translated into a measurable problem involving a defined outcome, an appropriate population, a time period, relevant explanatory variables, and a decision or action.

Learning Objectives

By the end of this chapter, you should be able to:

1. Distinguish populations, samples, units, variables, observations, parameters, and statistics.
2. Classify variables as categorical or quantitative and as discrete or continuous where appropriate.
3. Explain nominal, ordinal, interval, and ratio measurement scales.
4. Distinguish descriptive, diagnostic, predictive, and prescriptive analytics.
5. Formulate measurable analytical problems from practical business or organisational concerns.
6. Recognise sampling, measurement, data-quality, ethical, and interpretation risks.
7. Select suitable analytical outputs for different professional decisions.

1. The Statistical View of Data

Statistics may be understood in two related ways. In the plural sense, statistics are numerical summaries such as averages, percentages, rates, and measures of variability. In the singular sense, statistics is the discipline concerned with collecting, organising, analysing, interpreting, and communicating data under uncertainty.

Data analysis is the process of converting recorded observations into useful evidence. A typical analytical workflow includes:

1. defining the problem and decision context;
2. identifying the target population and unit of analysis;
3. specifying variables and operational definitions;
4. collecting or obtaining data;
5. checking quality, completeness, and suitability;
6. summarising and visualising the data;
7. analysing patterns or relationships;
8. communicating findings, uncertainty, limitations, and recommended action.

The order is not always strictly linear. Data-quality problems may require revising the question, and exploratory results may suggest additional variables or a better sampling plan. Nevertheless, the workflow protects analysts from beginning with a convenient dataset rather than with a clearly defined problem.

Units, observations, and variables

A statistical unit, or observational unit, is the entity about which data are recorded. It may be a person, household, transaction, machine, hospital, website visit, or country. An observation is the set of recorded values associated with one unit at a particular point or period. A variable is a characteristic that can take different values across units or time.

For example, a customer dataset might contain one row per customer and variables such as customer identifier, age group, annual spending, membership status, number of support contacts, and satisfaction rating. The customer is the unit; each row is an observation; and annual spending is a variable.

An operational definition states exactly how a concept is measured. “Customer loyalty” is an abstract concept. It might be operationalised as the number of purchases in the previous twelve months, the proportion of months with a purchase, or the probability of renewal. Different operational definitions may be reasonable, but they do not measure precisely the same thing.

2. Populations, Samples, Parameters, and Statistics

Population

A population is the complete set of units relevant to a study. The target population is the broader group to which the analyst intends to generalise. The accessible population is the portion that can actually be reached through available records or recruitment procedures.

For example, a company studying employee engagement may define its target population as all current employees worldwide. If the survey system reaches only employees with corporate email accounts, the accessible population may exclude contractors or workers without such accounts. This distinction is important because conclusions may not generalise to units that had no opportunity to be observed.

A population can be finite, such as all invoices issued in 2025, or conceptually infinite, such as all future measurements produced by a stable manufacturing process.

Sample

A sample is a subset of the population that is actually observed. A census attempts to observe every unit in the defined population, whereas a sample study observes only some units. A census can reduce sampling uncertainty but does not eliminate non-response, inaccurate measurement, missing data, processing errors, or coverage bias.

Sampling is often necessary because a population may be large, geographically dispersed, changing over time, expensive to measure, or destructive to test. The value of a sample depends not simply on its size but also on how it was selected and measured.

Parameter and statistic

A parameter is a numerical characteristic of a population. A statistic is a numerical characteristic calculated from a sample. Parameters are usually unknown in practical studies; statistics are used to estimate or describe them.

For a population of N units with values x₁, x₂, …, x_N, the population mean is:

Here, μ is the population mean, N is the population size, and xᵢ is the value for unit i. The formula applies when the variable is quantitative and the arithmetic mean is meaningful.

For a sample of n observations, the sample mean is:

Here, x̄ is the sample mean, n is the sample size, and xᵢ is the observed value for sample unit i. Both μ and x̄ have the same units as the measured variable.

The distinction between parameter and statistic is conceptual rather than a difference in formula. A population mean and a sample mean are calculated similarly, but they refer to different sets of units. Confusing them can lead to unjustified claims about a wider population.

Sampling error and bias

Sampling error is the natural difference between a sample result and the corresponding population value caused by observing only part of the population. It can often be quantified using inferential methods.

Bias is systematic error that causes results to be consistently unrepresentative. Examples include:

• coverage bias, when some population groups cannot be selected;
• non-response bias, when respondents differ meaningfully from non-respondents;
• selection bias, when inclusion depends on characteristics related to the outcome;
• measurement bias, when the recording process systematically distorts values.

A larger biased sample can be less useful than a smaller, well-designed sample. Random selection can reduce selection bias, but it does not correct a poorly defined variable or a defective measurement instrument.

3. Variables and Their Classification

Variables can be classified in several ways, and the correct classification depends on the analytical purpose.

Categorical and quantitative variables

A categorical variable places units into groups or categories. Examples include payment method, department, product type, and complaint category. Categories should be mutually exclusive where possible, and collectively exhaustive for the intended population. An “other” or “unknown” category may be necessary, but it should not conceal substantial data-quality problems.

A quantitative variable records numerical amounts for which arithmetic operations have meaningful interpretation. Examples include income, distance, processing time, temperature, and number of purchases.

Binary variables have two categories, such as paid/unpaid or defective/non-defective. They may be stored numerically as 0 and 1, but the numerical coding does not automatically make them quantitative in the ordinary measurement sense.

Discrete and continuous variables

A discrete variable takes separate, countable values, often whole numbers. The number of defects in a batch is discrete. A continuous variable can, in principle, take any value within an interval. Weight, duration, and voltage are commonly treated as continuous, although instruments record them to finite precision.

The distinction affects modelling and visualisation. Counts may be analysed using count-based methods, while measurements such as duration may require methods suited to continuous distributions. In practice, recorded precision and the decision context must also be considered.

Explanatory and response variables

In an analytical study, the response variable is the outcome being explained, predicted, or managed. Explanatory variables are characteristics used to understand or predict variation in the response. In a customer-retention study, renewal status may be the response, while tenure, service usage, price, and support contacts may be explanatory variables.

The labels do not prove causality. Calling a variable “explanatory” means that it is used in the analysis, not that changing it will necessarily change the outcome.

Identifiers and derived variables

An identifier, such as an employee number or transaction ID, distinguishes records but usually has no substantive numerical meaning. Treating an identifier as a continuous predictor can produce meaningless results.

A derived variable is calculated from one or more recorded fields. Examples include profit margin, age calculated from date of birth, and average handling time. Derived variables should have documented definitions, units, inclusion rules, and treatment of missing values.

4. Measurement Scales

Measurement scale determines what comparisons and mathematical operations are defensible. Four traditional scales are nominal, ordinal, interval, and ratio.

Nominal scale

Nominal values identify categories without inherent order. If a dataset codes region as 1 = North, 2 = South, and 3 = West, the numbers are labels. A mean region code is not meaningful. Analysts may calculate category counts, percentages, or the most frequent category.

Ordinal scale

Ordinal values have an order, but the distance between adjacent categories may not be equal. “Poor,” “fair,” “good,” and “excellent” can be ranked, but the difference between poor and fair is not necessarily the same as the difference between good and excellent. Medians, percentiles, and rank-based summaries are often appropriate. A numerical average may sometimes be used for a multi-item scale under explicit methodological justification, but it should not be treated as automatically valid.

Interval scale

Interval measurements have equal numerical differences but no meaningful absolute zero. A temperature of 20 °C is 10 °C warmer than 10 °C, but it is not correct to say it is twice as warm. Differences and averages can be meaningful, while ratio statements require a scale with a true zero.

Ratio scale

Ratio measurements have equal intervals and a meaningful zero representing absence of the measured quantity. A duration of 20 minutes is twice a duration of 10 minutes. Income, length, mass, and elapsed time are common examples, although the measurement process and context must still be checked.

Measurement scale is not the only consideration. A variable may be recorded numerically but still be categorical, and a mathematically permissible operation may not be substantively meaningful. Good analysis combines scale information with domain knowledge.

5. Describing Data: Basic Statistical Language

Descriptive statistics organise and summarise observed data without, by themselves, generalising beyond those data.

For a quantitative dataset, common measures include:

• centre: mean, median, and mode;
• spread: range, interquartile range, variance, and standard deviation;
• position: percentiles and quartiles;
• shape: skewness, concentration, and unusual observations.

For sample observations, the sample variance is commonly defined as:

The sample standard deviation is:

Here, s² is sample variance, s is sample standard deviation, n is sample size, xᵢ is observation i, and x̄ is the sample mean. The n − 1 denominator is used in the conventional unbiased estimator of population variance under random-sampling assumptions; it is not a universal rule for every descriptive calculation. The variance has squared units, while the standard deviation has the original units.

The mean is sensitive to extreme values, whereas the median is generally more resistant. For income data, where a small number of very large values may create right skew, the median can better represent a typical individual. Analysts should report the measure that fits the distribution and decision context rather than relying automatically on the mean.

Descriptive analysis often uses frequency tables, bar charts, histograms, box plots, line charts, and scatterplots. A chart should identify units, time period, denominator, source, and relevant exclusions. Percentages without denominators can be misleading: “complaints increased by 50%” has different implications if complaints rose from 2 to 3 or from 2,000 to 3,000.

6. Four Major Types of Analytics

Analytics is commonly organised into four complementary categories. They are not isolated departments; a single project may use all four.

Descriptive analytics: What happened?

Descriptive analytics summarises historical or current data. It addresses questions such as:

• How many units were sold last quarter?
• What was the average delivery time?
• Which products generated the greatest revenue?
• How did website traffic vary by week?

Typical outputs include dashboards, reports, frequency distributions, summary statistics, and trend charts. Descriptive analysis should establish the facts before explanations or predictions are attempted.

Diagnostic analytics: Why did it happen?

Diagnostic analytics investigates patterns, differences, and possible contributing factors. It may involve segmentation, drill-down analysis, comparison across groups, correlation analysis, process investigation, or root-cause methods.

A diagnostic result should distinguish association from causation. If customers who receive more support contacts are more likely to cancel, this does not prove that support contacts cause cancellation. Customers experiencing severe problems may both contact support more often and be more likely to cancel. Confounding, reverse causality, selection effects, and measurement problems must be considered.

Predictive analytics: What is likely to happen?

Predictive analytics estimates future or unobserved outcomes using historical data, statistical models, or machine-learning methods. Examples include forecasting demand, estimating default risk, predicting equipment failure, and identifying customers at risk of leaving.

A prediction is not a certainty and need not establish causation. Predictive performance must be evaluated on data that were not used to fit the model, ideally reflecting the future deployment environment. Relevant measures depend on the outcome: mean absolute error for some numerical forecasts, and accuracy, precision, recall, or area under a receiver operating characteristic curve for classification tasks. Metrics should be selected according to the costs of false positives and false negatives.

Prescriptive analytics: What should be done?

Prescriptive analytics recommends actions by combining predictions, objectives, constraints, and possible interventions. Examples include setting delivery routes, allocating staff, choosing inventory levels, or determining which customer offers to present.

Prescriptive analysis requires an explicit decision structure. A recommendation that maximises predicted revenue may violate budget, capacity, fairness, safety, or legal constraints. Optimisation models often represent an objective function subject to constraints. In a general form:

Here, a represents possible actions, f(a) is the objective to maximise or minimise, gⱼ(a) are constraint functions, bⱼ are constraint limits, and m is the number of constraints. The formula is a general framework, not a claim that every decision problem is linear or easily optimised.

The progression from descriptive to prescriptive is not automatically a progression from “simple” to “advanced.” A carefully designed descriptive measure may be more useful than an unreliable predictive model, and a prescriptive recommendation is only as sound as its assumptions and constraints.

7. Formulating Measurable Analytical Problems

A professional analytical problem should connect a decision with evidence. A useful formulation identifies:

1. the decision-maker or organisational context;
2. the unit of analysis;
3. the target population;
4. the response or outcome variable;
5. the explanatory variables or action variables;
6. the time period and prediction horizon;
7. the desired level of aggregation;
8. the success metric;
9. constraints, ethical boundaries, and risks.

A weak formulation is: “Why are customers unhappy?” It is unclear who counts as a customer, how unhappiness is measured, which period is relevant, and what action would follow.

A stronger formulation is: “Among customers who completed a support interaction between January and June, which measurable service characteristics are associated with a satisfaction rating below 3 on a five-point survey, and which operational changes could reduce the rate of low ratings during the next quarter?”

This formulation still requires refinement. The analyst must specify whether the unit is an interaction or a customer, whether repeated interactions are allowed, how missing ratings are treated, and whether the purpose is diagnosis or causal evaluation.

From broad concern to analytical specification

Consider the concern: “Delivery performance needs to improve.” A measurable specification could be:

• population: all domestic deliveries completed during the next quarter;
• unit: one delivery order;
• response: delivery delay in minutes beyond the promised time;
• explanatory variables: route, distance, dispatch time, weather category, warehouse, carrier, and package class;
• descriptive question: What proportion of deliveries were late by region and carrier?
• diagnostic question: Which observable process conditions are associated with delay?
• predictive question: Which scheduled deliveries have a high probability of being late?
• prescriptive question: How should staffing or routing be adjusted subject to available drivers and service commitments?
• success metric: reduction in the late-delivery rate without increasing cost beyond an agreed limit.

The same domain can therefore produce different analytical questions. The question type determines the data, methods, validation, and communication required.

Causal versus predictive questions

“Does an extra training session reduce processing errors?” is causal. “Which employees are likely to make a processing error next month?” is predictive. A causal question requires a credible comparison of what happened under an intervention with what would have happened without it. A predictive question requires accurate generalisation to future or unseen cases. A variable can be useful for prediction without being suitable as an intervention target.

SMART and testable questions

Analytical questions benefit from being specific, measurable, relevant, and time-bounded. They should also be feasible with available data and sufficiently precise to support a decision. “Improve service” is not testable until service, improvement, population, time horizon, and target are defined.

8. Worked Example: A Sample Survey

A university wants to estimate the proportion of enrolled students who use the library at least once per week. It surveys 200 students selected from the enrolment register. Of these, 86 report weekly use.

The target population is all enrolled students in the defined semester. The sample is the 200 selected students. The variable is weekly library use, a binary categorical variable. The population proportion is a parameter, while the observed proportion is a statistic.

The sample proportion is:

Thus, 43% of sampled students reported weekly use. The result is not automatically the exact percentage for all students. Its usefulness depends on selection, response, question wording, and data quality. If students who use the library were more likely to respond, the observed percentage could overestimate population use. A margin of error or confidence interval would require additional inferential assumptions and is not justified merely by calculating 43%.

9. Applied Case: Reducing Customer Churn

Background

This illustrative case concerns a subscription-based digital service. Management reports that monthly cancellations have increased and asks the data team to “find the customers who will leave.”

Problem definition

The team defines one customer-month as the unit of analysis. The response variable is cancellation during the following 30 days. The target population is active individual subscribers during the study period. Candidate variables include tenure, plan type, recent usage, payment failures, support contacts, price changes, and service interruptions.

This definition is superior to using one row per customer without a reference date because customer behaviour changes over time. It also prevents information from the future from being accidentally used to predict the past.

Analysis

Descriptive analysis first reports cancellation rates by plan, tenure band, and recent usage. Diagnostic analysis investigates whether cancellations are associated with payment failures, outages, or declining usage. The team checks whether these variables are recorded consistently and whether some customer groups are absent from the data.

For predictive analysis, the team creates training and evaluation periods separated by time. This is preferable to a purely random split when the operational task is future prediction and customer behaviour may change. The model produces a risk score for each active customer-month. Evaluation considers recall among high-risk customers, false-positive cost, and whether intervention capacity is limited.

The team avoids using “cancellation date” or a support outcome recorded after cancellation because these variables would create target leakage. It also examines performance across customer segments rather than relying only on an overall metric.

Approach and solution

The business does not automatically cancel or penalise high-risk customers. Instead, it tests a retention intervention, such as a service check or targeted support offer, using a controlled evaluation where feasible. Predictive risk identifies candidates; a causal test is needed to estimate whether the intervention changes cancellation behaviour.

A prescriptive decision rule could consider predicted risk, intervention cost, expected benefit, service capacity, and fairness constraints. Customers may also be excluded from automated decisions where legal or ethical requirements demand human review.

Outcome

Suppose the pilot reduces cancellations among contacted customers but increases support workload. Management must evaluate the net benefit, not merely the model’s prediction accuracy. It should compare intervention cost, retained revenue, customer experience, staff capacity, and differences across groups.

Learning points

1. A business request must be converted into a unit, outcome, time horizon, and decision.
2. Predictive accuracy does not establish that a proposed intervention will work.
3. Time-aware validation helps prevent unrealistic performance estimates.
4. Data leakage can make a model appear effective while being unusable in practice.
5. Fairness, privacy, explainability, and operational capacity are part of analytical quality.

10. Data Ethics, Governance, and Professional Practice

Statistics and analytics can affect access to credit, employment, education, healthcare, insurance, and public services. Analysts therefore have responsibilities beyond technical accuracy.

Important principles include:

• purpose limitation: collect and use data for a defined legitimate purpose;
• data minimisation: avoid collecting information that is not needed;
• transparency: explain what is measured, how it is used, and what limitations apply;
• privacy and security: control access, protect identifiers, and retain data only as justified;
• fairness: investigate whether data or models produce unjustified disparate outcomes;
• accountability: document definitions, transformations, assumptions, and decisions;
• human oversight: provide review for high-impact or uncertain decisions.

Anonymisation is not always absolute protection. Combinations of fields can permit re-identification, especially when linked with external datasets. Sensitive variables may be necessary for fairness auditing even when they should not be used directly for decision-making; governance must specify who can access them and why.

Analysts should distinguish statistical significance from practical importance, avoid selective reporting, disclose missing data and exclusions, and avoid causal language when the design supports only association. Reproducible workflows, versioned code, data dictionaries, validation checks, and clear provenance improve reliability.

11. Challenges and Limitations

Foundational analytical work faces recurring difficulties:

• Ambiguous concepts: abstract ideas such as engagement or wellbeing require defensible operational definitions.
• Missing data: missingness may be related to the outcome and therefore may not be harmless.
• Changing populations: a model trained on past customers may perform poorly after a policy or market change.
• Confounding: observed relationships may reflect unmeasured common causes.
• Measurement error: inaccurate or inconsistent recording weakens conclusions.
• Data integration: different systems may use incompatible identifiers, units, dates, or category definitions.
• Overfitting: a complex model may fit historical noise rather than general patterns.
• Base-rate neglect: a high accuracy rate can be misleading when the event of interest is rare.
• Visual and communication bias: truncated axes, unclear denominators, or selective time periods can distort interpretation.

These limitations do not make analytics futile. They indicate why study design, documentation, validation, and cautious communication are essential.

12. Contemporary Developments

Cloud platforms, automated data pipelines, real-time dashboards, and generative artificial intelligence have expanded the speed and scale of analytics. However, automation does not remove the need for statistical reasoning. An AI system can produce a fluent explanation from poorly defined or biased data. Analysts should validate generated code, inspect sources, test calculations, protect confidential information, and retain human responsibility for consequential conclusions.

Modern practice increasingly combines statistical methods with machine learning, causal inference, experimentation, and optimisation. The choice should be driven by the question. A transparent descriptive report may be appropriate for monitoring; an experiment may be required for a causal claim; a calibrated predictive model may support prioritisation; and an optimisation model may be required when resources are constrained.

Chapter Summary

Statistics and data analytics transform observations into evidence for decisions. A population is the complete set of relevant units, while a sample is the observed subset. A parameter describes a population; a statistic describes a sample and may estimate a parameter. Units, observations, variables, identifiers, and derived measures must be distinguished clearly.

Variables may be categorical or quantitative, discrete or continuous, and may serve as response or explanatory variables. Measurement scales—nominal, ordinal, interval, and ratio—determine which comparisons and calculations are meaningful. Descriptive statistics summarise observed data, but sampling bias, measurement error, and non-response can limit generalisation.

Descriptive analytics asks what happened, diagnostic analytics investigates why it happened, predictive analytics estimates what is likely to happen, and prescriptive analytics addresses what should be done under objectives and constraints. A measurable analytical problem specifies the population, unit, outcome, variables, time period, success metric, and decision context. Ethical practice requires privacy, fairness, transparency, accountability, and appropriate human oversight.

Key Terms

Population: The complete set of units relevant to a study.

Target population: The population to which the analyst intends to generalise.

Accessible population: The portion of the target population that can be reached or observed.

Sample: A subset of a population that is actually observed.

Unit of analysis: The entity represented by one analytical observation.

Observation: A recorded set of values for one unit.

Variable: A characteristic that can take different values.

Parameter: A numerical characteristic of a population.

Statistic: A numerical characteristic calculated from a sample.

Sampling error: Difference caused by observing a sample rather than the full population.

Bias: Systematic error that produces unrepresentative results.

Categorical variable: A variable containing groups or labels.

Quantitative variable: A variable representing numerical amounts.

Nominal scale: A scale containing categories without order.

Ordinal scale: An ordered scale without guaranteed equal spacing.

Interval scale: A scale with equal differences but no meaningful absolute zero.

Ratio scale: A scale with equal differences and a meaningful zero.

Descriptive analytics: Analysis of what has happened or what is currently observed.

Diagnostic analytics: Analysis of possible reasons or contributing factors.

Predictive analytics: Estimation of future or unobserved outcomes.

Prescriptive analytics: Recommendation of actions under objectives and constraints.

Review Questions

Short Answer Questions

1. What is the difference between a population and a sample?
2. Distinguish a parameter from a statistic.
3. Why is a numerical code for a nominal category not necessarily quantitative?
4. State the central question addressed by predictive analytics.
5. Give one example of measurement bias.

Long Answer Questions

1. Explain nominal, ordinal, interval, and ratio measurement scales, giving one example and one analytical implication for each.
2. Discuss why a large sample can still produce misleading conclusions.
3. Explain the differences among descriptive, diagnostic, predictive, and prescriptive analytics.
4. Describe the steps required to convert a broad organisational concern into a measurable analytical problem.
5. Explain why predictive association does not establish causation, using the customer-churn case as an example.

Analytical / Application Questions

1. A hospital wants to reduce missed appointments. Define a suitable unit of analysis, response variable, target population, time horizon, and one descriptive, one diagnostic, one predictive, and one prescriptive question.
2. A survey of 500 employees finds that 72% of respondents are satisfied with remote working. Identify at least three issues that must be assessed before generalising this percentage to all employees.
3. A retailer wants to use an AI model to identify customers for special offers. Propose a validation and governance plan that addresses data leakage, fairness, privacy, intervention effectiveness, and operational capacity.

Multiple Choice Questions with Answers

Question 1

Which statement correctly distinguishes a parameter from a statistic?

A. A parameter describes a sample, while a statistic describes a population.

B. A parameter describes a population, while a statistic is calculated from a sample.

C. A parameter is always categorical, while a statistic is always quantitative.

D. A parameter is an observation, while a statistic is a variable.

Correct Answer: B. A parameter describes a population, while a statistic is calculated from a sample.

Question 2

A customer’s payment method recorded as cash, card, or transfer is primarily which type of variable?

A. Nominal categorical

B. Ordinal categorical

C. Continuous quantitative

D. Ratio quantitative

Correct Answer: A. Nominal categorical

Question 3

Which question is diagnostic?

A. How many orders were delivered last month?

B. Which orders are likely to be late next week?

C. Why did late deliveries increase in the eastern region?

D. How should delivery routes be assigned?

Correct Answer: C. Why did late deliveries increase in the eastern region?

Question 4

A temperature measured in degrees Celsius is generally classified as which measurement scale?

A. Nominal

B. Ordinal

C. Interval

D. Ratio

Correct Answer: C. Interval

Question 5

A sample contains 80 successful outcomes out of 200 observations. What is the sample proportion?

A. 0.20

B. 0.40

C. 0.60

D. 2.50

Correct Answer: B. 0.40

Question 6

Which situation is an example of non-response bias?

A. A scale rounds weights to the nearest kilogram.

B. Some selected survey participants do not respond, and their views differ from respondents.

C. A dataset contains a calculated profit-margin variable.

D. A researcher observes every unit in the population.

Correct Answer: B. Some selected survey participants do not respond, and their views differ from respondents.

Question 7

Which statement about an identifier is most accurate?

A. It should always be used as a continuous predictor.

B. It is a label for distinguishing records and usually has no substantive numerical meaning.

C. It is always an ordinal variable.

D. It must be measured on a ratio scale.

Correct Answer: B. It is a label for distinguishing records and usually has no substantive numerical meaning.

Question 8

Which activity is most characteristic of prescriptive analytics?

A. Summarising last quarter’s revenue by region

B. Estimating the probability that a machine will fail

C. Investigating why a complaint rate increased

D. Selecting staff schedules subject to coverage and budget constraints

Correct Answer: D. Selecting staff schedules subject to coverage and budget constraints

Question 9

Why can a model using information recorded after a customer cancels be invalid for pre-cancellation prediction?

A. It creates target leakage.

B. It converts the response into a nominal variable.

C. It guarantees underfitting.

D. It removes all sampling error.

Correct Answer: A. It creates target leakage.

Question 10

Which statement is correct about association?

A. An observed association always proves that one variable causes another.

B. Association is irrelevant in predictive analytics.

C. An association may be due to confounding, reverse causality, or selection effects.

D. Association can be assessed only for nominal variables.

Correct Answer: C. An association may be due to confounding, reverse causality, or selection effects.