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 
Symbols and Their Meanings
Chapter (1st used)  Symbol  Spoken  Meaning 

Sampling and Data  The square root of  same  
Sampling and Data  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  xbar  sample mean  
Descriptive Statistics  mu  population mean  
Descriptive Statistics  s  s  sample standard deviation 
Descriptive Statistics  s squared  sample variance  
Descriptive Statistics  sigma  population standard deviation  
Descriptive Statistics  sigma squared  population variance  
Descriptive Statistics  capital sigma  sum  
Probability Topics  brackets  set notation  
Probability Topics  S  sample space  
Probability Topics  Event A  event A  
Probability Topics  probability of A  probability of A occurring  
Probability Topics  probability of A given B  prob. of A occurring given B has occurred  
Probability Topics  prob. of A or B  prob. of A or B or both occurring  
Probability Topics  prob. of A and B  prob. of both A and B occurring (same time)  
Probability Topics  A′  Aprime, 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  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  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  zscore  same 
The Normal Distribution  Z  standard normal dist.  same 
The Central Limit Theorem  Xbar  the random variable Xbar  
The Central Limit Theorem  mean of Xbars  the average of Xbars  
The Central Limit Theorem  standard deviation of Xbars  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 tdistribution  same 
Confidence Intervals  df  degrees of freedom  same 
Confidence Intervals  student t with α/2 area in right tail  same  
Confidence Intervals  pprime  sample proportion of success  
Confidence Intervals  qprime  sample proportion of failure  
Hypothesis Testing  Hnaught, Hsub 0  null hypothesis  
Hypothesis Testing  Ha, Hsub a  alternate hypothesis  
Hypothesis Testing  H1, Hsub 1  alternate hypothesis  
Hypothesis Testing  alpha  probability of Type I error  
Hypothesis Testing  beta  probability of Type II error  
Hypothesis Testing  X1bar minus X2bar  difference in sample means  
Hypothesis Testing  mu1 minus mu2  difference in population means  
Hypothesis Testing  P1prime minus P2prime  difference in sample proportions  
Hypothesis Testing  p1 minus p2  difference in population proportions  
ChiSquare Distribution  Kysquare  Chisquare  
ChiSquare Distribution  Observed  Observed frequency  
ChiSquare Distribution  Expected  Expected frequency  
Linear Regression and Correlation  y = a + bx  y equals a plus bx  equation of a straight line 
Linear Regression and Correlation  yhat  estimated value of y  
Linear Regression and Correlation  sample correlation coefficient  same  
Linear Regression and Correlation  error term for a regression line  same  
Linear Regression and Correlation  SSE  Sum of Squared Errors  same 
FDistribution and ANOVA  F  Fratio  Fratio 
Formulas
Symbols you must know  
Population  Sample  
Size  
Mean  
Variance  
Standard deviation  
Proportion  
Single data set formulae  
Population  Sample  
Arithmetic mean  
Geometric mean  
,  Interquartile 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 first success.  Probability when is the number of failures before first success  
Mean  Mean  
Variance  Variance  
Poisson distribution formulae  
Probability equation  
Mean  
Variance  
Uniform distribution formulae  
for  
Mean  
Variance  
Exponential distribution formulae  
Cumulative probability  
or  Mean and decay factor  
Variance 
The following page of formulae requires the use of the ““, ““, “” or “” tables.  
Ztransformation 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 where 

Interval for difference between two population proportions 

Tests for GOF, Independence, and Homogeneity where O = observed values and E = expected values 

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) 

Use when sigma is known 
Use when is unknown 
Use when is uknown 
Simple linear regression formulae for  
Correlation coefficient  
Coefficient b (slope)  
yintercept  
Estimate of the error variance  
Standard error for coefficient b  
Hypothesis test for coefficient β  
Interval for coefficient β  
Interval for expected value of y  
Prediction interval for an individual y  
ANOVA formulae  
Sum of squares regression  
Sum of squares error  
Sum of squares total  
Coefficient of determination 
The following is the breakdown of a oneway ANOVA table for linear regression.  
Source of variation  Sum of squares  Degrees of freedom  Mean squares  Fratio 
Regression  or  
Error  
Total 