14.1.1: Symbols and Their Meanings
- Page ID
- 46166
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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 (1st used) | Symbol | Spoken | Meaning |
|---|---|---|---|
| Sampling and Data | \(\sqrt{ } \) | The square root of | same |
| Sampling and Data | \(\pi\) | Pi | 3.14159… (a specific number) |
| Descriptive Statistics | \(Q_1\) | Quartile one | the first quartile |
| Descriptive Statistics | \(Q_2\) | Quartile two | the second quartile |
| Descriptive Statistics | \(Q_3\) | Quartile three | the third quartile |
| Descriptive Statistics | \(IQR\) | interquartile range | \(Q_3 – Q_1 = IQR\) |
| Descriptive Statistics | \(\overline X\) | \(x\)-bar | sample mean |
| Descriptive Statistics | \(\mu\) | mu | population mean |
| Descriptive Statistics | \(s\) | s | sample standard deviation |
| Descriptive Statistics | \(s^2\) | \(s\) squared | sample variance |
| Descriptive Statistics | \(\sigma\) | sigma | population standard deviation |
| Descriptive Statistics | \(\sigma^2\) | sigma squared | population variance |
| Descriptive Statistics | \(\Sigma\) | capital sigma | sum |
| Probability Topics | \(\{ \}\) | brackets | set notation |
| Probability Topics | \(S\) | S | sample space |
| Probability Topics | \(A\) | Event A | event A |
| Probability Topics | \(P(A)\) | probability of A | probability of A occurring |
| Probability Topics | \(P(A|B)\) | probability of A given B | prob. of A occurring given B has occurred |
| Probability Topics | \(P(A\cup B)\) | prob. of A or B | prob. of A or B or both occurring |
| Probability Topics | \(P(A\cap B)\) | prob. of A and B | prob. of both A and B occurring (same time) |
| Probability Topics | \(A^{\prime}\) | A-prime, complement of A | complement of A, not A |
| Probability Topics | \(P(A^{\prime})\) | prob. of complement of A | same |
| Probability Topics | \(G_1\) | green on first pick | same |
| Probability Topics | \(P(G_1)\) | prob. of green on first pick | same |
| Discrete Random Variables | \(PDF\) | prob. density function | same |
| Discrete Random Variables | \(X\) | X | the random variable X |
| Discrete Random Variables | \(X \sim\) | the distribution of X | same |
| Discrete Random Variables | \(\geq\) | greater than or equal to | same |
| Discrete Random Variables | \(\leq\) | less than or equal to | same |
| Discrete Random Variables | \(=\) | equal to | same |
| Discrete Random Variables | \(\neq\) | not equal to | same |
| Continuous Random Variables | \(f(x)\) | f of x | function of x |
| Continuous Random Variables | \(pdf\) | prob. density function | same |
| Continuous Random Variables | \(U\) | uniform distribution | same |
| Continuous Random Variables | \(Exp\) | exponential distribution | same |
| Continuous Random Variables | \(f(x) =\) | f of \(X\) equals | same |
| Continuous Random Variables | \(m\) | m | decay rate (for exp. dist.) |
| The Normal Distribution | \(N\) | normal distribution | same |
| The Normal Distribution | \(z\) | z-score | same |
| The Normal Distribution | \(Z\) | standard normal dist. | same |
| The Central Limit Theorem | \(\overline X\) | X-bar | the random variable X-bar |
| The Central Limit Theorem | \(\mu_{\overline{x}}\) | mean of X-bars | the average of X-bars |
| The Central Limit Theorem | \(\sigma_{\overline{x}}\) | standard deviation of X-bars | same |
| Confidence Intervals | \(CL\) | confidence level | same |
| Confidence Intervals | \(CI\) | confidence interval | same |
| Confidence Intervals | \(EBM\) | error bound for a mean | same |
| Confidence Intervals | \(EBP\) | error bound for a proportion | same |
| Confidence Intervals | \(t\) | Student's t-distribution | same |
| Confidence Intervals | \(df\) | degrees of freedom | same |
| Confidence Intervals | \(t_{\frac{\alpha}{2}}\) | student t with α/2 area in right tail | same |
| Confidence Intervals | \(p^{\prime}\) | p-prime | sample proportion of success |
| Confidence Intervals | \(q^{\prime}\) | q-prime | sample proportion of failure |
| Hypothesis Testing | \(H_0\) | H-naught, H-sub 0 | null hypothesis |
| Hypothesis Testing | \(H_a\) | H-a, H-sub a | alternate hypothesis |
| Hypothesis Testing | \(H_1\) | H-1, H-sub 1 | alternate hypothesis |
| Hypothesis Testing | \(\alpha\) | alpha | probability of Type I error |
| Hypothesis Testing | \(\beta\) | beta | probability of Type II error |
| Hypothesis Testing | \(\overline{X 1}-\overline{X 2}\) | X1-bar minus X2-bar | difference in sample means |
| Hypothesis Testing | \(\mu_{1}-\mu_{2}\) | mu-1 minus mu-2 | difference in population means |
| Hypothesis Testing | \(P_{1}^{\prime}-P_{2}^{\prime}\) | P1-prime minus P2-prime | difference in sample proportions |
| Hypothesis Testing | \(p_{1}-p_{2}\) | p1 minus p2 | difference in population proportions |
| Chi-Square Distribution | \(X^2\) | Ky-square | Chi-square |
| Chi-Square Distribution | \(O\) | Observed | Observed frequency |
| Chi-Square Distribution | \(E\) | Expected | Expected frequency |
| Linear Regression and Correlation | \(y = a + bx\) | y equals a plus b-x | equation of a straight line |
| Linear Regression and Correlation | \(\hat y\) | y-hat | estimated value of y |
| Linear Regression and Correlation | \(r\) | sample correlation coefficient | same |
| Linear Regression and Correlation | \(\varepsilon\) | error term for a regression line | same |
| Linear Regression and Correlation | \(SSE\) | Sum of Squared Errors | same |
| F-Distribution and ANOVA | \(F\) | F-ratio | F-ratio |