Statistical Symbols

Demystifying Statistical Symbols: A Guide to Understanding Data Analysis Notations

Probability and statistics symbols table and definitions.

Probability and statistics symbols table

Symbol Symbol Name Meaning / definition Example
P( A) probability function probability of event A P( A) = 0.5
P( AB) probability of events intersection probability that of events A and B P( AB) = 0.5
P( AB) probability of events union probability that of events A or B P( AB) = 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 mid-range 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 c-1 e - λx / Γ( c), x≥0
χ 2 ( k) chi-square distribution f ( x) = x k /2-1 e - x/2 / ( 2 k/2 Γ( k/2) )
F ( k 1 , k 2 ) F distribution
Bin( n, p) binomial distribution f ( k) = nC k p k (1 -p) n-k
Poisson(λ) Poisson distribution f ( k) = λ ke - λ / k!
Geom( p) geometric distribution f ( k) =  p(1 -p) k
HG( N, K, n) hyper-geometric distribution
Bern( p) Bernoulli distribution

Combinatorics Symbols

Symbol Symbol Name Meaning / definition Example
n! factorial n! = 1⋅2⋅3⋅...⋅ n 5! = 1⋅2⋅3⋅4⋅5 = 120
nP k permutation 5 P 3 = 5! / (5-3)! = 60
nC k

combination 5 C 3 = 5!/[3!(5-3)!]=10

What does the symbol 'Î¼' represent in statistics?

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.