1.7: Vocabulary (Chapter 1)
- Page ID
- 58997
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter 1 Vocabulary
Below is a list of key vocabulary terms introduced in Chapter 1. These words form the foundation of your statistical thinking and will appear throughout the rest of the course. Keep this glossary handy as a reference!
- Data
- Information collected about individuals, objects, events, or conditions. Each data point represents an observation.
- Observation
- A single row or record in a dataset; one instance of data collected from an individual or object.
- Dataset
- A structured collection of data, typically organized in rows (observations) and columns (variables).
- Variable
- A characteristic that is recorded about each observation and can vary from one observation to another.
- Statistics
- The science of collecting, analyzing, interpreting, and communicating data in the presence of variability.
- Variability
- The tendency for data values to differ from one another; natural differences observed in real-world data.
- Categorical Variable
- A variable that places observations into non-numeric groups or categories.
- Numerical Variable
- A variable that represents quantifiable amounts or measurements; values are numeric and meaningful.
- Nominal Variable
- A categorical variable with no natural order (e.g., color, gender, blood type).
- Ordinal Variable
- A categorical variable with a meaningful order but inconsistent spacing between values (e.g., satisfaction level, fitness difficulty).
- Discrete Variable
- A numerical variable based on counts; values are whole numbers (e.g., number of pets, number of bedrooms).
- Continuous Variable
- A numerical variable based on measurements; values can include decimals and fall along an interval (e.g., height, income, temperature).
- Population
- The entire group of individuals or observations that you're interested in studying or learning about.
- Sample
- A subset of the population that is actually studied or measured. Used to make inferences about the population.
- Sampling
- The process of selecting individuals or units from a population to create a sample.
- Representative Sample
- A sample that accurately reflects the characteristics of the population.
- Simple Random Sample (SRS)
- A sample in which every member of the population has an equal chance of being selected.
- Stratified Sample
- A sample created by dividing the population into subgroups (strata) and randomly sampling from each subgroup.
- Cluster Sample
- A sample created by dividing the population into groups (clusters), then randomly selecting entire clusters.
- Systematic Sample
- A sample chosen by selecting every nth individual from a list or process.
- Convenience Sample
- A non-random sample chosen based on ease of access, often leading to bias.
- Bias
- Systematic error in the way a sample is collected or data is measured, leading to results that do not accurately reflect the population.
- Sampling Bias
- A specific type of bias introduced when some members of the population are less likely to be included in the sample than others.
- Convenience Bias
- Bias introduced when individuals are selected simply because they are easy to reach.
- Nonresponse Bias
- Bias that occurs when individuals selected for a survey do not respond, and their views differ from those who did respond.
- Undercoverage Bias
- Bias caused by systematically missing part of the population during sampling.
- Voluntary Response Bias
- Bias that occurs when participants choose to respond — often those with strong opinions are overrepresented.
- Random Sampling
- A method of sampling where each member of the population has a known and typically equal chance of being selected.
- Statistical Question
- A question that can be answered using data and involves variability in the answers.
- Observational Study
- A study in which researchers observe and measure variables without affecting or influencing subjects.
- Survey
- A method of collecting information from individuals by asking structured questions.
- Experiment
- A study in which researchers deliberately apply a treatment and observe the outcomes, often using random assignment.
- Treatment Group
- The group that receives the experimental condition or change in an experiment.
- Control Group
- The group in an experiment that does not receive the treatment; used as a baseline comparison.
- Confounding Variable
- An outside factor that affects both the explanatory and response variable, potentially obscuring results.
- Random Assignment
- Assigning individuals to groups in an experiment by chance to ensure fairness and reduce bias.
- Blinding
- A method used in experiments to prevent subjects or researchers from knowing which treatment was given, to reduce bias.
- Statistical Process
- A step-by-step approach to answering questions with data: ask a question, collect data, organize/summarize, analyze, interpret, communicate.
- Data Collection Plan
- A plan that outlines what data will be gathered, how it will be obtained, and what variables will be included.
- Variable of Interest
- A specific characteristic or measurement that is central to a particular study or research question.
- Semester Project
- A long-term project where students apply the full statistical process to a real-world topic — in this case, housing affordability.
Tip: Don’t try to memorize everything! Instead, refer back to these terms as we dive deeper. You’ll become familiar with each one as we use it in real examples, calculations, and discussions.