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

what does preconceived mean

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.

effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.

it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.

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

Wekolamo Reply

please i need answer

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).

Manix Reply

Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!

ARC

A child is a member of community not society elucidate ?

JESSY Reply

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?

Simon Reply

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

namakula Reply

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

war

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

Amesalu Reply

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.

Samuel

I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills

Zyryn Reply

good👍

Jonathan

and having a good philosophy of the world is like a sandwich and a peanut butter 👍

Jonathan

generally amnesi how long yrs memory loss

Kelu Reply

interpersonal relationships

Abdulfatai Reply

What would be the best educational aid(s) for gifted kids/savants?

Heidi Reply

treat them normal, if they want help then give them. that will make everyone happy

Saurabh

What are the treatment for autism?

Magret Reply

hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these

Jharna

continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child

Jharna

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Jharna

results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.

Jharna

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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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