# Statistics

Statistics is the study of how to collate and interpret numerical information from data. It is the science of learning from data and communicating uncertainty. There are two branches in statistics ‘Descriptive statistics’’ and ‘’ Inferential statistics

Descriptive statistics involves methods of organizing, picturing and summarizing information from data. Inferential statistics involves methods of using information from a sample to draw conclusions about the Population.

Statistics Glossary

# Statistical Symbols

### 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(A B) 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
σ2 variance variance of population values σ2 = 4
std(X) standard deviation standard deviation of random variable X std(X) = 2
σX standard deviation standard deviation value of random variable X σX  =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
ρX,Y correlation correlation of random variables X and Y ρX,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 = (xmax+xmin)/2
Md sample median half the population is below this value
Q1 lower / first quartile 25% of population are below this value
Q2 median / second quartile 50% of population are below this value = median of samples
Q3 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
zx standard score zx = (x-x) / sx
X ~ distribution of X distribution of random variable X X ~ N(0,3)
N(μ,σ2) 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) = λeλx , x≥0
gamma(c, λ) gamma distribution f (x) = λ c xc-1eλx / Γ(c), x≥0
χ 2(k) chi-square distribution f (x) = xk/2-1ex/2 / ( 2k/2 Γ(k/2) )
F (k1, k2) F distribution
Bin(n,p) binomial distribution f (k) = nCk pk(1-p)n-k
Poisson(λ) Poisson distribution f (k) = λkeλ / 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
nPk permutation 5P3 = 5! / (5-3)! = 60
nCk combination 5C3 = 5!/[3!(5-3)!]=10