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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
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Adjusted R-Squared – $ {R_{adj}^2 = 1 – [frac{(1-R^2)(n-1)}{n-k-1}]} $
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Arithmetic Mean – $ bar{x} = frac{_{sum {x}}}{N} $
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Arithmetic Median – Median = Value of $ frac{N+1}{2})^{th} item $
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Arithmetic Range – $ {Coefficient of Range = frac{L-S}{L+S}} $
B
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Best Point Estimation – $ {MLE = frac{S}{T}} $
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Binomial Distribution – $ {P(X-x)} = ^{n}{C_x}{Q^{n-x}}.{p^x} $
C
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Chebyshev”s Theorem – $ {1-frac{1}{k^2}} $
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Circular Permutation – $ {P_n = (n-1)!} $
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Cohen”s kappa coefficient – $ {k = frac{p_0 – p_e}{1-p_e} = 1 – frac{1-p_o}{1-p_e}} $
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Combination – $ {C(n,r) = frac{n!}{r!(n-r)!}} $
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Combination with replacement – $ {^nC_r = frac{(n+r-1)!}{r!(n-1)!} } $
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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 } $
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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]}} } $
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Cumulative Poisson Distribution – $ {F(x,lambda) = sum_{k=0}^x frac{e^{- lambda} lambda ^x}{k!}} $
D
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Deciles Statistics – $ {D_i = l + frac{h}{f}(frac{iN}{10} – c); i = 1,2,3…,9} $
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Deciles Statistics – $ {D_i = l + frac{h}{f}(frac{iN}{10} – c); i = 1,2,3…,9} $
F
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Factorial – $ {n! = 1 times 2 times 3 … times n} $
G
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Geometric Mean – $ G.M. = sqrt[n]{x_1x_2x_3…x_n} $
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Geometric Probability Distribution – $ {P(X=x) = p times q^{x-1} } $
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Grand Mean – $ {X_{GM} = frac{sum x}{N}} $
H
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Harmonic Mean – $ H.M. = frac{W}{sum (frac{W}{X})} $
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Harmonic Mean – $ H.M. = frac{W}{sum (frac{W}{X})} $
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Hypergeometric Distribution – $ {h(x;N,n,K) = frac{[C(k,x)][C(N-k,n-x)]}{C(N,n)}} $
I
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Interval Estimation – $ {mu = bar x pm Z_{frac{alpha}{2}}frac{sigma}{sqrt n}} $
L
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Logistic Regression – $ {pi(x) = frac{e^{alpha + beta x}}{1 + e^{alpha + beta x}}} $
M
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Mean Deviation – $ {MD} =frac{1}{N} sum{|X-A|} = frac{sum{|D|}}{N} $
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Mean Difference – $ {Mean Difference= frac{sum x_1}{n} – frac{sum x_2}{n}} $
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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
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Negative Binomial Distribution – $ {f(x) = P(X=x) = (x-1r-1)(1-p)x-rpr} $
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Normal Distribution – $ {y = frac{1}{sqrt {2 pi}}e^{frac{-(x – mu)^2}{2 sigma}} } $
O
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One Proportion Z Test – $ { z = frac {hat p -p_o}{sqrt{frac{p_o(1-p_o)}{n}}} } $
P
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Permutation – $ { {^nP_r = frac{n!}{(n-r)!} } $
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Permutation with Replacement – $ {^nP_r = n^r } $
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Poisson Distribution – $ {P(X-x)} = {e^{-m}}.frac{m^x}{x!} $
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probability – $ {P(A) = frac{Number of favourable cases}{Total number of equally likely cases} = frac{m}{n}} $
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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)}} $
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Probability Density Function – $ {P(a le X le b) = int_a^b f(x) d_x} $
R
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Reliability Coefficient – $ {Reliability Coefficient, RC = (frac{N}{(N-1)}) times (frac{(Total Variance – Sum of Variance)}{Total Variance})} $
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Residual Sum of Squares – $ {RSS = sum_{i=0}^n(epsilon_i)^2 = sum_{i=0}^n(y_i – (alpha + beta x_i))^2} $
S
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Shannon Wiener Diversity Index – $ { H = sum[(p_i) times ln(p_i)] } $
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Standard Deviation – $ sigma = sqrt{frac{sum_{i=1}^n{(x-bar x)^2}}{N-1}} $
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Standard Error ( SE ) – $ SE_bar{x} = frac{s}{sqrt{n}} $
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Sum of Square – $ {Sum of Squares = sum(x_i – bar x)^2 } $
T
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Trimmed Mean – $ mu = frac{sum {X_i}}{n} $
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