0.6 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})

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

Formula 10: gamma function

Γ (z) = {\int^{​}}_{\infty}^{0} x^{z - 1} e^{- x} d x

z > 0

$Γ (\frac{1}{2}) = \sqrt{π}$

$Γ (m + 1) = m!$ for $m$ , a nonnegative integer

otherwise: $Γ (a + 1) = a Γ (a)$

Formula 11: student's t -distribution

X ~ t_{d f}

$f (x) = \frac{{(1 + \frac{x^{2}}{n})}^{\frac{- (n + 1)}{2}} Γ (\frac{n + 1}{2})}{\sqrt{nπ} Γ (\frac{n}{2})}$

$X = \frac{Z}{\sqrt{\frac{Y}{n}}}$

$Z ~ N (0, 1), Y ~ Χ_{d f}^{2}$ , $n$ = degrees of freedom

Formula 12: chi-square distribution

X ~ Χ_{d f}^{2}

$f (x) = \frac{x^{\frac{n - 2}{2}} e^{\frac{- x}{2}}}{2^{\frac{n}{2}} Γ (\frac{n}{2})}$ , $x > 0$ , $n$ = positive integer and degrees of freedom

Formula 13: f distribution

X ~ F_{d f (n), d f (d)}

$d f (n) =$ degrees of freedom for the numerator

$d f (d) =$ degrees of freedom for the denominator

$f (x) = \frac{Γ (\frac{u + v}{2})}{Γ (\frac{u}{2}) Γ (\frac{v}{2})} {(\frac{u}{v})}^{\frac{u}{2}} x^{(\frac{u}{2} - 1)} [1 + (\frac{u}{v}) x^{- 0.5 (u + v)}]$

$X = \frac{Y_{u}}{W_{v}}$ , $Y$ , $W$ are chi-square

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 _x sx	s	sample standard deviation
Descriptive Statistics	$s^{2}$ $s_{x}^{2}$	s squared	sample variance
Descriptive Statistics	$σ$ $σ_{x}$ σx	sigma	population standard deviation
Descriptive Statistics	$σ^{2}$ $σ_{x}^{2}$	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	$P (A OR B)$	prob. of A or B	prob. of A or B or both occurring
Probability Topics	$P (A AND B)$	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. distribution function	same
Discrete Random Variables	X	X	the random variable X
Discrete Random Variables	X ~	the distribution of X	same
Discrete Random Variables	B	binomial distribution	same
Discrete Random Variables	G	geometric distribution	same
Discrete Random Variables	H	hypergeometric dist.	same
Discrete Random Variables	P	Poisson dist.	same
Discrete Random Variables	$λ$	Lambda	average of Poisson distribution
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	k	k	critical value
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	CLT	Central Limit Theorem	same
The Central Limit Theorem	$\bar{X}$	X -bar	the random variable X -bar
The Central Limit Theorem	$μ_{x}$	mean of X	the average of X
The Central Limit Theorem	$μ_{\bar{x}}$	mean of X -bar	the average of X -bar
The Central Limit Theorem	$σ_{x}$	standard deviation of X	same
The Central Limit Theorem	$σ_{\bar{x}}$	standard deviation of X -bar	same
The Central Limit Theorem	$Σ X$	sum of X	same
The Central Limit Theorem	$Σ x$	sum of x	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 a /2 area in right tail	same
Confidence Intervals	$p'$ ; $\hat{p}$	p -prime; p -hat	sample proportion of success
Confidence Intervals	$q'$ ; $\hat{q}$	q -prime; q -hat	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 line
Linear Regression and Correlation	$\hat{y}$	y -hat	estimated value of y
Linear Regression and Correlation	$r$	correlation coefficient	same
Linear Regression and Correlation	$ε$	error	same
Linear Regression and Correlation	SSE	Sum of Squared Errors	same
Linear Regression and Correlation	1.9 s	1.9 times s	cut-off value for outliers
F -Distribution and ANOVA	F	F -ratio	F -ratio

Questions & Answers

I'm interested in biological psychology and cognitive psychology

Tanya Reply

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sammie Reply

physiological Psychology

Nwosu Reply

How can I develope my cognitive domain

Amanyire Reply

why is communication effective

Dakolo Reply

Communication is effective because it allows individuals to share ideas, thoughts, and information with others.

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miss

Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment

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Wekolamo

because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).

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ARC

A child is a member of community not society elucidate ?

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Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?

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compare and contrast skinner's perspective on personality development on freud

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Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning

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explain how nature and nurture affect the development and later the productivity of an individual.

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nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.

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Source: OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18

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