Demystifying Statistical Symbols: A Guide to Understanding Data Analysis Notations
Probability and statistics symbols table and definitions.
Symbol  Symbol Name  Meaning / definition  Example 

P( A)  probability function  probability of event A  P( A) = 0.5 
P( A ∩ B)  probability of events intersection  probability that of events A and B  P( A∩ B) = 0.5 
P( A ∪ B)  probability of events union  probability that of events A or B  P( A ∪ B) = 0.5 
P( A  B)  conditional probability function  probability of event A given event B occured  P( A  B) = 0.3 
f ( x)  probability density function (pdf)  P( a ≤ x ≤ b) = ∫ f ( x) dx  
F( x)  cumulative distribution function (cdf)  F( x) = P( X≤ x)  
μ  population mean  mean of population values  μ = 10 
E( X)  expectation value  expected value of random variable X  E( X) = 10 
E( X  Y)  conditional expectation  expected value of random variable X given Y  E( X  Y=2) = 5 
var( X)  variance  variance of random variable X  var( X) = 4 
σ ^{2}  variance  variance of population values  σ ^{2 } = 4 
std( X)  standard deviation  standard deviation of random variable X  std( X) = 2 
σ _{ X }  standard deviation  standard deviation value of random variable X  σ _{X} = 2 
median  middle value of random variable x  
cov( X, Y)  covariance  covariance of random variables X and Y  cov( X,Y) = 4 
corr( X, Y)  correlation  correlation of random variables X and Y  corr( X,Y) = 0.6 
ρ _{ X , Y }  correlation  correlation of random variables X and Y  ρ _{ X , Y } = 0.6 
∑  summation  summation  sum of all values in range of series  
∑∑  double summation  double summation  
Mo  mode  value that occurs most frequently in population  
MR  midrange  MR = ( x _{max } + x _{min} ) / 2  
Md  sample median  half the population is below this value  
Q _{1}  lower / first quartile  25% of population are below this value  
Q _{2}  median / second quartile  50% of population are below this value = median of samples  
Q _{3}  upper / third quartile  75% of population are below this value  
x  sample mean  average / arithmetic mean  x = (2+5+9) / 3 = 5.333 
s ^{ 2 }  sample variance  population samples variance estimator  s ^{} ^{2} = 4 
s  sample standard deviation  population samples standard deviation estimator  s = 2 
z _{x}  standard score  z _{x} = ( x x) / s _{x}  
X ~  distribution of X  distribution of random variable X  X ~ N(0,3) 
N( μ, σ ^{ 2 })  normal distribution  gaussian distribution  X ~ N(0,3) 
U( a, b)  uniform distribution  equal probability in range a,b  X ~ U(0,3) 
exp(λ)  exponential distribution  f ( x) = λe ^{ λx } , x≥0  
gamma( c, λ)  gamma distribution  f ( x) = λ c x ^{c1} e ^{ λx } / Γ( c), x≥0  
χ ^{ 2 }( k)  chisquare distribution  f ( x) = x ^{k} ^{/21} e ^{ x/2 } / ( 2 ^{k/2 }Γ( k/2) )  
F ( k _{ 1 } , k _{ 2 })  F distribution  
Bin( n, p)  binomial distribution  f ( k) = _{n}C _{k} p ^{k} (1 p) ^{nk}  
Poisson(λ)  Poisson distribution  f ( k) = λ ^{k}e ^{ λ } / k!  
Geom( p)  geometric distribution  f ( k) = p(1 p) ^{ k}  
HG( N, K, n)  hypergeometric distribution  
Bern( p)  Bernoulli distribution 
Symbol  Symbol Name  Meaning / definition  Example 

n!  factorial  n! = 1⋅2⋅3⋅...⋅ n  5! = 1⋅2⋅3⋅4⋅5 = 120 
_{n}P _{k}  permutation  _{5} P _{3} = 5! / (53)! = 60  
_{n}C _{k}

combination  _{5} C _{3} = 5!/[3!(53)!]=10 
The symbol 'Î¼' represents the population mean, which is the average value of a variable in an entire population. It's a fundamental concept in statistics used for measuring central tendency.