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 | 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 |
| 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 |
The symbol 'μ' 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.
