Statistics 简明教程
Statistics - Formulas
以下是 Tutorialspoint 统计教程中使用的统计公式列表。每个公式都链接到一个网页,描述了如何使用该公式。
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} $
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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{[N\sum x^2 - (\sum x)^2][N\sum 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{mx}{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)} $
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Probability Multiplicative Theorem - $ {P(A\ and\ B) = P(A) \times P(B) \\[7pt] P (AB) = P(A) \times P(B)} $
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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} $