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 |
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) = _{n}C_{k} p^{k}(1-p)^{n-k} | |
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) | 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 |
_{n}P_{k} | permutation | _{5}P_{3} = 5! / (5-3)! = 60 | |
_{n}C_{k} | combination | _{5}C_{3} = 5!/[3!(5-3)!]=10 |