13.2: Appendix F | Mathematical Phrases, Symbols, and Formulas

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

Table F1

Symbols and Their Meanings

Chapter (1st used)	Symbol	Spoken	Meaning
Sampling and Data	−−−−√	The square root of	same
Sampling and Data	ππ	Pi	3.14159… (a specific number)
Descriptive Statistics	Q1	Quartile one	the first quartile
Descriptive Statistics	Q2	Quartile two	the second quartile
Descriptive Statistics	Q3	Quartile three	the third quartile
Descriptive Statistics	IQR	interquartile range	Q3 – Q1 = IQR
Descriptive Statistics	x–x–	x-bar	sample mean
Descriptive Statistics	μμ	mu	population mean
Descriptive Statistics	s	s	sample standard deviation
Descriptive Statistics	s2s2	s squared	sample variance
Descriptive Statistics	σσ	sigma	population standard deviation
Descriptive Statistics	σ2σ2	sigma squared	population variance
Descriptive Statistics	ΣΣ	capital sigma	sum
Probability Topics	{}{}	brackets	set notation
Probability Topics	SS	S	sample space
Probability Topics	AA	Event A	event A
Probability Topics	P(A)P(A)	probability of A	probability of A occurring
Probability Topics	P(A|B)P(A|B)	probability of A given B	prob. of A occurring given B has occurred
Probability Topics	P(A∪B)P(A∪B)	prob. of A or B	prob. of A or B or both occurring
Probability Topics	P(A∩B)P(A∩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	G1	green on first pick	same
Probability Topics	P(G1)	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	≥≥	greater than or equal to	same
Discrete Random Variables	≤≤	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	X–X–	X-bar	the random variable X-bar
The Central Limit Theorem	μx–μx–	mean of X-bars	the average of X-bars
The Central Limit Theorem	σx–σx–	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	tα2tα2	student t with α/2 area in right tail	same
Confidence Intervals	p'p′	p-prime	sample proportion of success
Confidence Intervals	q'q′	q-prime	sample proportion of failure
Hypothesis Testing	H0H0	H-naught, H-sub 0	null hypothesis
Hypothesis Testing	HaHa	H-a, H-sub a	alternate hypothesis
Hypothesis Testing	H1H1	H-1, H-sub 1	alternate hypothesis
Hypothesis Testing	αα	alpha	probability of Type I error
Hypothesis Testing	ββ	beta	probability of Type II error
Hypothesis Testing	X1––X2¯¯¯¯¯X1––X2¯	X1-bar minus X2-bar	difference in sample means
Hypothesis Testing	μ1−μ2μ1−μ2	mu-1 minus mu-2	difference in population means
Hypothesis Testing	P′1−P′2P′1−P′2	P1-prime minus P2-prime	difference in sample proportions
Hypothesis Testing	p1−p2p1−p2	p1 minus p2	difference in population proportions
Chi-Square Distribution	X2Χ2	Ky-square	Chi-square
Chi-Square Distribution	OO	Observed	Observed frequency
Chi-Square Distribution	EE	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	yˆy^	y-hat	estimated value of y
Linear Regression and Correlation	rr	"r""r"	same
Linear Regression and Correlation	ρρ	rho ("row")rho ("row")	population correlation coefficient
Linear Regression and Correlation	εε	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

Table B2 Symbols and their Meanings

Formulas

 

	Symbols you must know
Population		Sample
	Size
	Mean
	Variance
	Standard deviation
	Proportion
Single data set formulae
Population		Sample
	Arithmetic mean
	Geometric mean
	Inter-quartile range
	Variance
Single data set formulae
Population		Sample
	Arithmetic mean
	Geometric mean
	Variance
	Coefficient of variation

 

Basic probability rules
	Multiplication rule
	Addition rule
or	Independence test

 

Hypergeometric distribution formulae
	Combinatorial equation
	Probability equation
	Mean
	Variance
Binomial distribution formulae
	Probability density function
	Arithmetic mean
	Variance
Geometric distribution formulae
	Probability when  is the number of failures before first success
	Mean
	Variance
Poisson distribution formulae
	Probability equation
		Mean
		Variance
Uniform distribution formulae
for		PDF
		Mean
	Variance

Exponential distribution formulae
	Cumulative probability
or	Mean and decay factor
	Variance

 

The following page of formulae requires the use of the " \(Z\) ", " \(t\) ", " \(\chi^2\) " or " \(F\) " tables.

 

	Z-transformation for normal distribution
	Normal approximation to the binomial
Probability (ignores subscripts) Hypothesis testing	Confidence intervals [bracketed symbols equal margin of error] (subscripts denote locations on respective distribution tables)
	Interval for the population mean when sigma is known
	Interval for the population mean when sigma is unknown but
	Interval for the population mean when sigma is unknown but
	Interval for the population proportion
	Interval for difference between two means with matched pairs  where  is the deviation of the differences
	Interval for difference between two means when sigmas are known
	Interval for difference between two means with equal variances when sigmas are unknown
	Interval for difference between two population proportions
	Tests for GOF, Independence, and Homogeneity
	Where  is the sample variance which is the larger of the two sample variances
The next 3 formulae are for determining sample size with confidence intervals. (note: E represents the margin of error)
\(n=\frac{Z_{\left(\frac{a}{2}\right)}^2 \sigma^2}{E^2}\)	Use when sigma is known \(E=\bar{x}-\mu\)
\[n=\frac{Z_{\left(\frac{a}{2}\right)}^2(0.25)}{E^2}\]	Use when \(p^{\prime}\) is unknown \(E=p^{\prime}-p\)
\(n=\frac{Z_{\left(\frac{a}{2}\right)}^2(0.25)}{E^2}\)	Use when \(p^{\prime}\) is unknown
\(n=\frac{Z_{\left(\frac{a}{2}\right)}^2\left[p^{\prime}\left(q^{\prime}\right)\right]}{E^2}\)	Use when \(p^{\prime}\) is unknown\(E=p^{\prime}-p\)

Simple linear regression formulae for
	Correlation coefficient
	Coefficient b (slope)
	y-intercept
	Estimate of the error variance
	Standard error for coefficient
	Hypothesis test for coefficient
	Interval for coefficient
	Interval for expected value of
	Prediction interval for an individual

 

ANOVA formulae
	Sum of squares regression
	Sum of squares error
	Sum of squares total
	Coefficient of determination

 

The following is the breakdown of a one-way ANOVA table for linear regression.
Source of variation	Sum of squares	Degrees of freedom	Mean squares	-ratio
Regression	SSR	1 or
Error	SSE
Total