Statistics – Formulas ”; Previous Next Following is the list of statistics formulas used in the Tutorialspoint statistics tutorials. Each formula is linked 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 – $ bar{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) = $ begin{cases} 1/(b-a), & text{when $ a le x le b $} \ 0, & text{when $x lt a$ or $x gt b$} end{cases} $ Coefficient of Variation – $ {CV = frac{sigma}{X} times 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 times 2 times 3 … times n} $ G Geometric Mean – $ G.M. = sqrt[n]{x_1x_2x_3…x_n} $ Geometric Probability Distribution – $ {P(X=x) = p times 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 = bar x pm Z_{frac{alpha}{2}}frac{sigma}{sqrt n}} $ L Logistic Regression – $ {pi(x) = frac{e^{alpha + beta x}}{1 + e^{alpha + beta 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!} $ probability – $ {P(A) = frac{Number of favourable cases}{Total number of equally likely cases} = frac{m}{n}} $ Probability Additive Theorem – $ {P(A or B) = P(A) + P(B) \[7pt] P (A cup B) = P(A) + P(B)} $ Probability Multiplicative Theorem – $ {P(A and B) = P(A) times P(B) \[7pt] P (AB) = P(A) times P(B)} $ Probability Bayes Theorem – $ {P(A_i/B) = frac{P(A_i) times P (B/A_i)}{sum_{i=1}^k P(A_i) times P (B/A_i)}} $ Probability Density Function – $ {P(a le X le b) = int_a^b f(x) d_x} $ R Reliability Coefficient – $ {Reliability Coefficient, RC = (frac{N}{(N-1)}) times (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 + beta x_i))^2} $ S Shannon Wiener Diversity Index – $ { H = sum[(p_i) times ln(p_i)] } $ Standard Deviation – $ sigma = sqrt{frac{sum_{i=1}^n{(x-bar x)^2}}{N-1}} $ Standard Error ( SE ) – $ SE_bar{x} = frac{s}{sqrt{n}} $ Sum of Square – $ {Sum of Squares = sum(x_i – bar x)^2 } $ T Trimmed Mean – $ mu = frac{sum {X_i}}{n} $
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