Arithmatic mean

For Ungrouped data: \begin{align} AM & = \frac{\sum_{i=1}^n x_i}{n} \end{align} For grouped data: \begin{align} AM & =\frac{\sum_{i=1}^n f_i x_i}{\sum_{i=1}^n f_i} \end{align}

Geometric Mean

For Ungrouped data: \begin{align} GM & = (\prod_{i=1}^{n} x_i)^\frac{1 }{n} \end{align} For Grouped data: \begin{align} GM & = (\prod_{i=1}^{k} {x_i}^{f_i})^\frac{1}{n} \end{align}

Harmonic Mean

For Ungrouped data: \begin{align} HM & = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} \end{align} For Grouped data: \begin{align} HM & = \frac{\sum_{i=1}^{N} f_i}{\sum_{i=1}^{N} \frac{f_i}{\frac{f_i}{x_i}}} \end{align}

Median

For Ungrouped data: $\frac{n+1}{2}$th value when \(n\) is odd and \(\frac{\frac{n}{2}th\space value + (\frac{n}{2} +1)th\space value }{2}\) when \(n\) is even.

For Grouped data: \begin{align} M_e & = L + \frac{\frac{N}{2}-F}{f} \times C \end{align}

Mode

For Ungrouped data: Visible highest value.

For Grouped Data: \begin{align} M_o & = L + \frac{\Delta_1}{\Delta_1 + \Delta_2} \times C \end{align}

Quartile

\begin{align} Q & = L + \frac{\frac{N}{4}i - F}{f} \times C \end{align}

Decile

\begin{align} D & = L + \frac{\frac{N}{10}i - F}{f} \times C \end{align}

Quartile Deviation

\begin{align} QD & = \frac{Q_2 - Q_1}{2} \end{align}

Mean Deviations

For Ungrouped Data: \begin{align} MD\space of \space\bar{x} & = \frac{\sum_{i=1}^{n} \lvert x_i - \bar{x} \rvert}{n} \\ MD\space of \space M_e & = \frac{\sum_{i=1}^{n} \lvert x_i - M_e \rvert}{n}\\ MD\space of \space M_o & = \frac{\sum_{i=1}^{n} \lvert x_i - M_o \rvert}{n} \end{align}

For Grouped Data: \begin{align} MD\space of \space\bar{x} & = \frac{\sum_{i=1}^{n} f_i \lvert x_i - \bar{x} \rvert}{n} \\ MD\space of \space M_e & = \frac{\sum_{i=1}^{n} f_i \lvert x_i - M_e \rvert}{n}\\ MD\space of \space M_o & = \frac{\sum_{i=1}^{n} f_i \lvert x_i - M_o \rvert}{n} \end{align}

Variance

For Ungrouped Data: \begin{align} V\space of\space x & = \frac{1}{n} \sum_{i=1}^{n}(x_i -\bar{x})^2 \end{align}

For Grouped Data: \begin{align} V\space of\space x & = \frac{1}{N} \sum_{i=1}^{n} f_i (x_i -\bar{x})^2 \end{align}

Standard Deviation

Ungrouped: \begin{align} SD\space of\space x & = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2} \end{align}

Grouped: \begin{align} SD\space of\space x & = \sqrt{\frac{1}{N} \sum_{i=1}^{n} f_i(x_i - \bar{x})^2} \end{align}

Co-efficient of Variation

\begin{align} CV & = \frac{Standard\space Deviation}{\bar{x}} \times 100 \end{align}

Probability

\begin{align} P(A)& =\frac{Favourable\space outcome\space\ of\space an\space event}{Total\space number\space of\space outcomes\space of\space the\space experiment}\\ &= \frac{m}{n} \end{align}

Probability:Additive law

\begin{align} P(A \cup B) & = P(A) + P(B) - P(A \cap B) \end{align}

Probability: Multiplicative law

\begin{align} P(AB) & = P(A) \times P(B/A) \\ & = P(B) \times P(A/B) \end{align}

Conditional Probability

\begin{align} P(A/B)&= \frac{P(AB)}{B}\\ P(B/A)&= \frac{P(AB)}{A} \end{align}

Bayes's Theorem

\begin{align} P(B_k/A)&=\frac{P(B_k) \cdot P(A/B_k)}{\sum_{i=1}^{n} P(B_i) \cdot P(A/B_i)} \end{align}

Binomial Distribution

\begin{align} f(k;n,p)&= {n \choose k}p^k(i-p)^{n-k} \end{align}

Poisson Distribution

\begin{align} f(k;\lambda)&=\frac{\lambda^k e^{-\lambda}}{k!} \end{align}

Normal Distribution

\begin{align} f(x,\mu,\sigma)&=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x-\mu)^2}{2\sigma ^2}} \end{align}

Simple Linera Regression

\begin{align} \hat{y_i}&=\hat{\alpha} + \hat{\beta}x_i \begin{cases} \hat{\alpha}&=\bar{y}-\hat{\beta}\bar{x} \\ \hat{\beta}&=\frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(x_i - \bar{x})^2} \end{cases} \end{align}

Co-efficient of Correlation

\begin{align} r&=\frac{\sum{x_i y_i}-\frac{\sum x_i \sum y_i}{n}}{\sqrt{\{\sum{{x_i}^2}-\frac{(\sum x_i)^2}{n}\}\{\sum{{y_i}^2}-\frac{(\sum y_i)^2}{n}\}}} \end{align}