2.5: Chapter 2 - Key Terms and Symbols
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Glossary of Key Terms and Symbols
Key Terms
Bar graph: a chart that uses rectangular bars to show the size or amount of different categories. The length or height of each bar represents the value or frequency of that category, making it easy to compare different groups.
Dot plot: a graph that uses dots to represent individual data values along a number line. Each dot represents one occurrence of a value. If a value appears more than once, the dots are stacked vertically above that number.
Frequency polygon: a line graph that shows the distribution of a dataset. It is created by plotting points at the midpoints of each class interval and connecting them with straight lines. This graph helps to visualize the shape of the data.
Histogram: a type of bar graph that shows how data is grouped into intervals. Each bar represents the frequency of data within a specific range, and the bars touch each other to show that the data is continuous.
Ogive: a line graph of the cumulative frequency distribution.
Outlier: a data value far from the rest of the values.
Pareto chart: a bar graph combined with a line graph that represents categorical data in descending order of frequency or impact.
Pie chart: a circle divided into sections according to the percentage of frequencies in each category. The formula for these percentages is P = f / n * 100%. Where P stands for percent, f for the frequency of each class, and n for the sum of all the frequencies. To draw each section, use the percentages (recall that a quarter of the circle equals 25%).
Relative frequency: the proportion of times a value or category occurs compared to the total number of observations.
Scatter plot: a graph used in statistics to display the relationship between two numerical variables.
Skewness: describes the direction in which the data tails off. A distribution is skewed right (positively skewed) if it has a long tail on the right side, and skewed left (negatively skewed) if it has a long tail on the left.
Stem-and-leaf plot: a type of graph where each number is split into a "stem" (the leading digit or digits) and a "leaf" (the last digit). The stems are listed in a vertical column, and the leaves that correspond to each stem are listed in rows to the right.
Symmetry: a balanced shape where the left and right sides of the distribution are mirror images. A perfectly symmetrical distribution, like the normal distribution, has values evenly distributed around the center.
Key Symbols
\( f \) - frequency (the count of how often a value appears).
\( n \) - total number of observations (sum of all frequencies).
\( \% \) - percent (used to express a part out of 100).
\( \frac{f}{n} \times 100 \) - formula to calculate percent.
\( \theta \) - degrees (angle measure for a pie chart).
\( \frac{f}{n} \times 360^\circ \) - formula to convert frequency to degrees in a pie chart.
\( \frac{f}{n} \) - formula for relative frequency.
\( \sum \) - summation symbol (used to indicate the sum of frequencies or other values).
Authors
"2.5: Chapter 2 - Key Terms and Symbols" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY 4.0