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

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.

Kate Reply

To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.

Muhammed

What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?

Kate Reply

what is the change in momentum of a body?

Eunice Reply

what is a capacitor?

Raymond Reply

Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.

Gautam

A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate

Maria Reply

please solve

Sharon

8m/s²

Aishat

What is Thermodynamics

Muordit

velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.

Mehmet

A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat

Saheed Reply

50 m/s due south east

Someone

which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer

Ramon Reply

I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.

Someone

Scratch that

Someone

temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....

Someone

about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle

Someone

definitely of physics

Haryormhidey Reply

how many start and codon

Esrael Reply

what is field

Felix Reply

physics, biology and chemistry this is my Field

ALIYU

field is a region of space under the influence of some physical properties

Collete

what is ogarnic chemistry

WISDOM Reply

determine the slope giving that 3y+ 2x-14=0

WISDOM

Another formula for Acceleration

Belty Reply

a=v/t. a=f/m a

IHUMA

innocent

Adah

pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?

Nassze Reply

how do lnternal energy measures

Esrael

Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.

JALLAH Reply

No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.

Dlovan

Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?

Robert

like charges repel while unlike charges atttact

Raymond

What is specific heat capacity

Destiny Reply

Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).

AI-Robot

specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin

ROKEEB

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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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