0.2 Appendix b: mathematical phrases, symbols, and formulas

Introductory statistics Page 1 / 1

English phrases written mathematically

When the English says:	Interpret this as:
X is at least 4.	X ≥ 4
The minimum of X is 4.	X ≥ 4
X is no less than 4.	X ≥ 4
X is greater than or equal to 4.	X ≥ 4
X is at most 4.	X ≤ 4
The maximum of X is 4.	X ≤ 4
X is no more than 4.	X ≤ 4
X is less than or equal to 4.	X ≤ 4
X does not exceed 4.	X ≤ 4
X is greater than 4.	X >4
X is more than 4.	X >4
X exceeds 4.	X >4
X is less than 4.	X <4
There are fewer X than 4.	X <4
X is 4.	X = 4
X is equal to 4.	X = 4
X is the same as 4.	X = 4
X is not 4.	X ≠ 4
X is not equal to 4.	X ≠ 4
X is not the same as 4.	X ≠ 4
X is different than 4.	X ≠ 4

Formulas

Formula 1: factorial

n! = n (n - 1) (n - 2) . . . (1)

$0! = 1$

Formula 2: combinations

(\begin{array}{l} n \\ r \end{array}) = \frac{n!}{(n - r)! r!}

Formula 3: binomial distribution

X ~ B (n, p)

$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x}$ , for $x = 0, 1, 2, . . ., n$

Formula 4: geometric distribution

X ~ G (p)

$P (X = x) = q^{x - 1} p$ , for $x = 1, 2, 3, . . .$

Formula 5: hypergeometric distribution

X ~ H (r, b, n)

$P (X = x) = (\frac{(\binom{r}{x}) (\binom{b}{n - x})}{(\binom{r + b}{n})})$

Formula 6: poisson distribution

X ~ P (μ)

$P (X = x) = \frac{μ^{x} e^{- μ}}{x!}$

Formula 7: uniform distribution

X ~ U (a, b)

$f (X) = \frac{1}{b - a}$ , $a < x < b$

Formula 8: exponential distribution

X ~ E x p (m)

$f (x) = m e^{- m x} m > 0, x \geq 0$

Formula 9: normal distribution

X ~ N (μ, σ^{2})

$f (x) = \frac{1}{σ \sqrt{2 π}} e^{\frac{{- (x - μ)}^{2}}{{2 σ}^{2}}}$ , $- \infty < x < \infty$

Symbols and their meanings

Symbols and their meanings
Chapter (1st used)	Symbol	Spoken	Meaning
Sampling and Data	$\sqrt{\begin{matrix} \end{matrix}}$	The square root of	same
Sampling and Data	$π$	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	$\bar{x}$	x-bar	sample mean
Descriptive Statistics	$μ$	mu	population mean
Descriptive Statistics	s	s	sample standard deviation
Descriptive Statistics	$s^{2}$	s squared	sample variance
Descriptive Statistics	$σ$	sigma	population standard deviation
Descriptive Statistics	$σ^{2}$	sigma squared	population variance
Descriptive Statistics	$Σ$	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 ′	A-prime, complement of A	complement of A, not A
Probability Topics	P ( A ')	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 ~	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	≠	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	$\bar{X}$	X -bar	the random variable X -bar
The Central Limit Theorem	$μ_{\bar{x}}$	mean of X -bars	the average of X -bars
The Central Limit Theorem	$σ_{\bar{x}}$	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	$t_{\frac{α}{2}}$	student t with α /2 area in right tail	same
Confidence Intervals	$p'$	p -prime	sample proportion of success
Confidence Intervals	$q'$	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	$α$	alpha	probability of Type I error
Hypothesis Testing	$β$	beta	probability of Type II error
Hypothesis Testing	$\bar{X 1} - \bar{X 2}$	X 1-bar minus X 2-bar	difference in sample means
Hypothesis Testing	$μ_{1} - μ_{2}$	mu -1 minus mu -2	difference in population means
Hypothesis Testing	${P^{'}}_{1} - {P^{'}}_{2}$	P 1-prime minus P 2-prime	difference in sample proportions
Hypothesis Testing	$p_{1} - p_{2}$	p 1 minus p 2	difference in population proportions
Chi-Square Distribution	$Χ^{2}$	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	$ε$	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

Please click the link below to download the additional formula sheet needed for this class.

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Source: OpenStax, Introductory statistics. OpenStax CNX. Aug 09, 2016 Download for free at http://legacy.cnx.org/content/col11776/1.26

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