3.6: Vocabulary (Chapter 3)
- Page ID
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter 3 Vocabulary
Here is a list of key terms introduced throughout Chapter 3. These concepts help you visualize distributions, compare variables, and describe how data changes over time. Strong visualization skills will help you better analyze patterns, spot outliers, and prepare your data for deeper exploration in Chapters 4 and beyond.
- Bar Chart
- A graph that uses rectangular bars to represent the frequencies or proportions of different categories. The height (or length) of each bar corresponds to its value. Often used with categorical data. Bars do not touch.
- Pie Chart
- A circular chart divided into slices to represent parts of a whole. Each slice shows the proportion of a category relative to the total dataset. Best used with a small number of categories.
- Histogram
- A graph that displays the distribution of quantitative data by grouping values into equal-width intervals (bins). The height of each bar represents the frequency within each interval. Bars touch to show continuity.
- Bin
- An interval used when grouping numerical data for a histogram. Each bin includes a fixed range of values (e.g., 60–70), and all bins should be of equal width unless otherwise noted.
- Dot Plot
- A simple graph where each data point is shown as a dot placed above a number line. Repeated values are stacked vertically. Ideal for small datasets.
- Stem-and-Leaf Plot
- A tabular display where quantitative values are split into stems (typically the leading digits) and leaves (the final digit). This chart preserves the original dataset while showing distribution shape.
- Frequency
- The number of times a specific value or interval appears in a dataset. Frequencies are often shown in tables or bar charts to summarize distributions.
- Relative Frequency
- The proportion or percentage of total values that fall in a particular category or bin. Calculated as: frequency ÷ total sample size.
- Distribution
- The way data values are spread or clustered across a range. A distribution can be described by its center, spread, shape, and presence of outliers.
- Symmetric Distribution
- A distribution where the left and right sides are mirror images of each other. Often has a single peak near the center.
- Skewed Distribution
- Asymmetry in a dataset's shape. If the right tail (larger values) is longer, it’s right-skewed; if the left tail (smaller values) is longer, it’s left-skewed.
- Uniform Distribution
- A distribution where all values (or ranges) are approximately equally frequent. Appears flat with no clear peak.
- Bimodal Distribution
- A distribution with two clear peaks (modes) in different parts of the data. May suggest the combination of two separate groups.
- Time Plot
- A graph that shows how a numeric variable changes over time. Time is placed on the x-axis, and values are plotted on the y-axis, often with points connected by a line.
- Scatter Plot
- A graph that uses points to show the relationship between two numerical variables. Used in time plots (with time on the x-axis) or to display general associations between variables. Lines may or may not be included.
- Axis (Plural: Axes)
- The reference lines in a graph. The x-axis runs horizontally (typically showing categories or time), and the y-axis runs vertically (often showing numerical values or frequency).
Tip: You're now equipped with a whole toolkit of visualization types. Use these techniques to make your project data more clear, meaningful, and ready to analyze in Chapter 4 and beyond.