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.

Statistical Symbols

from: http://www.rapidtables.com/math/symbols/Statistical_Symbols.htm

Probability and statistics symbols table

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
σ²	variance	variance of population values	σ² = 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
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	s² = 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,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) = λe^–λx , x≥0
gamma(c, λ)	gamma distribution	f (x) = λ c x^c-1e^–λx / Γ(c), x≥0
χ²(k)	chi-square distribution	f (x) = x^k^/2-1e^–x/2 / ( 2^k/2Γ(k/2) )
F (k₁, k₂)	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	$_{n}P_{k}=\frac{n!}{(n-k)!}$	₅P₃ = 5! / (5-3)! = 60
_nC_k	combination	$_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}$	₅C₃ = 5!/[3!(5-3)!]=10