2.5: Vocabulary (Chapter 2)
- Page ID
- 59002
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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 2 Vocabulary
Here is a list of key terms introduced throughout Chapter 2. These concepts help you describe data numerically and visually — forming the bridge between raw values and interpretation.
- Measure of Center
- A single number that represents the “typical” or central value in a dataset. Includes the mean, median, and mode.
- Mean (Arithmetic Average)
- The sum of all values divided by the number of values. Sensitive to outliers. Symbol: \( \bar{x} \)
- Median
- The middle value when the data are sorted. If there’s an even number of values, it’s the average of the two middle ones. Resistant to outliers.
- Mode
- The value (or values) that occur most often in a dataset. There can be no mode, one mode, or multiple modes.
- Measure of Spread
- A statistic that describes how much the values vary around the center. Includes range, IQR, and standard deviation.
- Range
- The difference between the maximum and minimum values in a dataset. Sensitive to outliers.
- Interquartile Range (IQR)
- The range of the middle 50% of values. Calculated as \( Q3 - Q1 \); resistant to extreme values.
- Standard Deviation
- The average distance from each data point to the mean. Uses all values in the dataset and is sensitive to outliers.
- Variance
- The squared average distance from the mean. Used as an intermediate step when calculating standard deviation.
- Percentile
- A value that separates a certain percent of the data. For example, the 80th percentile is the value that 80% of the dataset lies below.
- Quartiles
- Special percentiles that divide the data into quarters:
- Q1: 25th percentile
- Q2: 50th percentile / median
- Q3: 75th percentile
- Five-Number Summary
- A descriptive summary of a dataset using five values: minimum, Q1, median, Q3, and maximum.
- Outlier
- A data point that is unusually far from the others. Often flagged if it lies beyond 1.5 × IQR below Q1 or above Q3.
- Bessel’s Correction
- The practice of dividing by \( n - 1 \) instead of \( n \) when calculating the sample variance or standard deviation. Helps make estimates less biased when working with sample data.
- Box-and-Whisker Plot (Boxplot)
- A standardized graph that displays the five-number summary. Visually shows a dataset’s spread, skew, and potential outliers.
- Whiskers
- Lines on a boxplot that extend from Q1 to the minimum and from Q3 to the maximum — unless outliers are present, in which case they stop at the nearest non-outlier.
- Skew (in a boxplot)
- Asymmetry in the distribution. A longer whisker on one side suggests skew in that direction.
Tip: As you work on your semester project, you can refer back to these definitions to describe your data clearly and efficiently.