# statistics bar graph

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 – ${r = \frac{N \sum xy – (\sum x)(\sum y)}{\sqrt{[N\sum x^2 – (\sum x)^2][N\sum y^2 – (\sum y)^2]}} }$
• 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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