Statistics - Formulas

Following is the pst of statistics formulas used in the Tutorialspoint statistics tutorials. Each formula is pnked to a web page that describe how to use the formula.

A

Adjusted R-Squared - $ {R_{adj}^2 = 1 - [frac{(1-R^2)(n-1)}{n-k-1}]} $

Arithmetic Mean - $ ar{x} = frac{_{sum {x}}}{N} $

Arithmetic Median - Median = Value of $ frac{N+1}{2})^{th} item $

Arithmetic Range - $ {Coefficient of Range = frac{L-S}{L+S}} $

B

Best Point Estimation - $ {MLE = frac{S}{T}} $

Binomial Distribution - $ {P(X-x)} = ^{n}{C_x}{Q^{n-x}}.{p^x} $

C

Chebyshev s Theorem - $ {1-frac{1}{k^2}} $

Circular Permutation - $ {P_n = (n-1)!} $

Cohen s kappa coefficient - $ {k = frac{p_0 - p_e}{1-p_e} = 1 - frac{1-p_o}{1-p_e}} $

Combination - $ {C(n,r) = frac{n!}{r!(n-r)!}} $

Combination with replacement - $ {^nC_r = frac{(n+r-1)!}{r!(n-1)!} } $

Continuous Uniform Distribution - f(x) = $ egin{cases} 1/(b-a), & ext{when $ a le x le b $} \ 0, & ext{when $x lt a$ or $x gt b$} end{cases} $

Coefficient of Variation - $ {CV = frac{sigma}{X} imes 100 } $

Correlation Co-efficient - $ {r = frac{N sum xy - (sum x)(sum y)}{sqrt{[Nsum x^2 - (sum x)^2][Nsum y^2 - (sum y)^2]}} } $

Cumulative Poisson Distribution - $ {F(x,lambda) = sum_{k=0}^x frac{e^{- lambda} lambda ^x}{k!}} $

D

Deciles Statistics - $ {D_i = l + frac{h}{f}(frac{iN}{10} - c); i = 1,2,3...,9} $

Deciles Statistics - $ {D_i = l + frac{h}{f}(frac{iN}{10} - c); i = 1,2,3...,9} $

F

Factorial - $ {n! = 1 imes 2 imes 3 ... imes n} $

G

Geometric Mean - $ G.M. = sqrt[n]{x_1x_2x_3...x_n} $

Geometric Probabipty Distribution - $ {P(X=x) = p imes q^{x-1} } $

Grand Mean - $ {X_{GM} = frac{sum x}{N}} $

H

Harmonic Mean - $ H.M. = frac{W}{sum (frac{W}{X})} $

Harmonic Mean - $ H.M. = frac{W}{sum (frac{W}{X})} $

Hypergeometric Distribution - $ {h(x;N,n,K) = frac{[C(k,x)][C(N-k,n-x)]}{C(N,n)}} $

I

Interval Estimation - $ {mu = ar x pm Z_{frac{alpha}{2}}frac{sigma}{sqrt n}} $

L

Logistic Regression - $ {pi(x) = frac{e^{alpha + eta x}}{1 + e^{alpha + eta x}}} $

M

Mean Deviation - $ {MD} =frac{1}{N} sum{|X-A|} = frac{sum{|D|}}{N} $

Mean Difference - $ {Mean Difference= frac{sum x_1}{n} - frac{sum x_2}{n}} $

Multinomial Distribution - $ {P_r = frac{n!}{(n_1!)(n_2!)...(n_x!)} {P_1}^{n_1}{P_2}^{n_2}...{P_x}^{n_x}} $

N

Negative Binomial Distribution - $ {f(x) = P(X=x) = (x-1r-1)(1-p)x-rpr} $

Normal Distribution - $ {y = frac{1}{sqrt {2 pi}}e^{frac{-(x - mu)^2}{2 sigma}} } $

O

One Proportion Z Test - $ { z = frac {hat p -p_o}{sqrt{frac{p_o(1-p_o)}{n}}} } $

P

Permutation - $ { {^nP_r = frac{n!}{(n-r)!} } $

Permutation with Replacement - $ {^nP_r = n^r } $

Poisson Distribution - $ {P(X-x)} = {e^{-m}}.frac{m^x}{x!} $

probabipty - $ {P(A) = frac{Number of favourable cases}{Total number of equally pkely cases} = frac{m}{n}} $

Probabipty Additive Theorem - $ {P(A or B) = P(A) + P(B) \[7pt] P (A cup B) = P(A) + P(B)} $

Probabipty Multippcative Theorem - $ {P(A and B) = P(A) imes P(B) \[7pt] P (AB) = P(A) imes P(B)} $

Probabipty Bayes Theorem - $ {P(A_i/B) = frac{P(A_i) imes P (B/A_i)}{sum_{i=1}^k P(A_i) imes P (B/A_i)}} $

Probabipty Density Function - $ {P(a le X le b) = int_a^b f(x) d_x} $

R

Repabipty Coefficient - $ {Repabipty Coefficient, RC = (frac{N}{(N-1)}) imes (frac{(Total Variance - Sum of Variance)}{Total Variance})} $

Residual Sum of Squares - $ {RSS = sum_{i=0}^n(epsilon_i)^2 = sum_{i=0}^n(y_i - (alpha + eta x_i))^2} $

S

Shannon Wiener Diversity Index - $ { H = sum[(p_i) imes ln(p_i)] } $

Standard Deviation - $ sigma = sqrt{frac{sum_{i=1}^n{(x-ar x)^2}}{N-1}} $

Standard Error ( SE ) - $ SE_ar{x} = frac{s}{sqrt{n}} $

Sum of Square - $ {Sum of Squares = sum(x_i - ar x)^2 } $

T

Trimmed Mean - $ mu = frac{sum {X_i}}{n} $