Chapter 1 – Intro to Statistics & Data

Data, Statistics, and Business Analytics

• Data are “facts & figures”—numerical values or qualitative labels—that describe objects, people, events, or transactions.
• Modern reality: datasets are frequently huge (“Big Data”) and stored/processed on computers or in the cloud.
• Statistics is “a way to get information from data.” It involves:
  • Collecting raw observations.
  • Organising & cleaning them.
  • Visualising & summarising them.
  • Extracting insights that support decision-making.
• Practical motivation questions raised in lecture:
  • Effect of advertising investment on subsequent sales.
  • Relationship between shelf location and cereal sales.
  • Delivery/logistics example: UPS tracks weight, destination, cost for every package—massive operational dataset.
• Distinction between data and information:
  • Data = raw, unprocessed input.
  • Information = the “bigger picture” understanding produced after statistical processing.

Business Analytics

• Definition (must memorise / underline):
  • Business analytics is the scientific process of transforming data into insights for making better business decisions.
• Emphasis of course: analytics for business & economic decision-making.
• Links to prior learning:
  • Builds on statistics, computer science, domain knowledge.
  • Ethical importance: data-driven decisions can affect pricing, job allocations, credit, etc.; requires responsible use.

Three Types of Data (Measurement Scales)

1. Nominal
   • Qualitative / categorical; pure labels or names.
   • No arithmetic operations are meaningful (cannot add, multiply, etc.).
   • Examples: gender, product ID, cereal flavour.
2. Ordinal
   • Still categorical but ordered / ranked.
   • Example scale: Excellent > Good > Fair > Poor.
   • Arithmetic still meaningless, yet order conveys preference/intensity.
3. Interval (often called “ratio” or “quantitative” in some texts)
   • Numeric, equal intervals between points; full arithmetic operations are valid.
   • Can compute means, differences, ratios, etc.
   • Examples: age, income, weight, price.

Branches of Statistics

• Descriptive Statistics
  • Summarise important aspects of a dataset (centre, spread, shape, patterns).
  • Tools include frequency tables, charts, measures such as mean $\bar{x}$, median, mode, variance $s^2$.
  • Focus for first chapters/weeks.
• Inferential Statistics
  • Go beyond available data to draw conclusions about a population.
  • Use probability theory, confidence intervals, hypothesis tests.
  • Example hypothesis from lecture: “Average American Idol viewer age $=23$.” Test $H<em>0: \mu=23$ vs HA: \mu>23 using sample $n=500$.

Core Terminology

• Population
  • Entire set of items/individuals of interest (e.g.
    all California residents, all American Idol viewers).
• Parameter
  • Numerical characteristic of a population (e.g.
    true mean age $\mu$, true proportion $p$ supporting an issue).
• Sample
  • Subset of the population selected for analysis (e.g.
    5,000 California residents surveyed).
• Statistic
  • Numerical measure computed from a sample (e.g.
    sample mean $\bar{x}$, sample proportion $\hat{p}$).
• Relationship mnemonic:
  • “Statistic is to Sample as Parameter is to Population.”

Example Analyses Discussed

Example 1: California Economy Sentiment

• Sample: 5,000 California residents (randomly selected).
• Reported result: >55\% have positive view.
• Because researcher generalises to all Californians, this is inferential statistics.

Example 2: CSUF Students & Statistics Enthusiasm

• Sample: 5,000 CSUF students; 80 % excited about statistics.
• Statement limited to sample—no population claim—thus descriptive statistics.

Example 3: American Idol Viewer Age

• Population: All viewers of American Idol.
• Variable: Age (interval/quantitative).
• Sample: 500 viewers.
• Statistic: Sample mean age $\bar{x}_{sample}$.
• Inference goal: Decide whether population mean age $\mu$ differs from $23$ (producer’s hypothesis \mu>23).
• Hypothesis test form once course completed:
  • $H<em>0: \mu=23$; $H</em>A: \mu \neq 23$ (or >23).
  • Decision at $\alpha=0.05$ ("5 % level of risk").

Goals & Best Practices in Data Collection

• Main goal: Obtain a representative sample mirroring population characteristics.
• Most common method: Simple Random Sampling (SRS)—every experimental unit has equal selection probability.
• Pitfalls/ethical notes:
  • Bias if sampling frame incomplete or response rates differ.
  • Privacy and informed consent when gathering personal data.

Road-Map of the Course (as highlighted)

1. Intro & foundational definitions (this lecture).
2. Descriptive statistics: tables, charts, numerical summaries.
3. Inferential statistics: estimation & hypothesis testing.
4. Business applications / analytics cases.

Key Take-aways for Exams & Practice

• Memorise core definitions (population, parameter, sample, statistic, business analytics).
• Be able to classify data scales (nominal, ordinal, interval).
• Distinguish descriptive vs inferential tasks given a scenario.
• Remember mnemonic: $Statistic \rightarrow Sample,\ Parameter \rightarrow Population$.
• Understand role of randomness in producing representative samples.
• Recognise real-world relevance: advertising ROI, shelf placement, logistics optimisation.