$$\overset{\overline{}}{x} = \sum_{i = 1}^{k}\frac{x_{i}*n_{i}}{N}$$

$$\overset{\overline{}}{x} = \frac{1}{N}\sum_{i = 1}^{n}x_{i}$$

$$\overset{\overline{}}{x} = \frac{1}{N}\sum_{i = 1}^{n}{n_{i}*{x'}_{i}}$$

$$G = \sqrt[n]{x_{1}*x_{2}*\ldots*x_{n}}$$

$$G = \sqrt[n]{\prod_{i = 1}^{n}x_{i}}\text{\ \ }\bigwedge_{}^{}{\text{\ \ }x_{i} > 0}\ $$

$$\log G\frac{1}{N}\sum_{i = 1}^{n}{= \log x_{i}}\ \bigwedge_{}^{}{x_{i} > 0}$$

$$H = \frac{\sum_{}^{}n_{i}}{\sum_{}^{}\frac{n_{i}}{n_{i}}}\ ,\ x \neq 0$$

$$q_{3} = X_{Q_{3}} + \frac{\frac{3}{4}N - \sum_{i = 1}^{Q_{3} - 1}k^{n_{i}}}{n_{Q_{3}}}*i_{Q_{3}}$$

$$q_{2} = Me = X_{Q_{2}} + \frac{\frac{N}{2} - \sum_{i = 1}^{Q_{2} - 1}k^{n_{i}}}{n_{Q_{2}}}*i_{Q_{2}}$$

$$q_{1} = X_{Q_{1}} + \frac{\frac{N}{4} - \sum_{i = 1}^{Q_{1} - 1}k^{n_{i}}\ }{n_{Q_{1}}}*i_{Q_{1}}$$

$$D = x_{D} + \frac{n_{D} - n_{D - 1}}{(n_{D} - n_{D - 1})(n_{D} - n_{D + 1})}*i_{D}$$

R = x_MAX − x_MIN

$$S^{2}\left( x \right) = \frac{\sum_{i = 1}^{k}\left\lbrack \left( x_{i}^{'} - \overset{\overline{}}{x} \right)^{2}*n_{i} \right\rbrack}{N}$$

$$S\left( x \right) = \sqrt{S^{2}\left( x \right)}$$

$$\overset{\overline{}}{x} - S\left( x \right) \leq x_{\text{typ}} \leq \overset{\overline{}}{x} + S\left( x \right)$$

$$Q = \frac{Q_{3} - Q_{1}}{2}$$

Me − Q ≤ x_typ ≤ Me + Q

$$V_{S}\left( x \right) = \frac{S\left( x \right)}{\overset{\overline{}}{x}}*100\%$$

$$V_{Q}\left( x \right) = \frac{Q}{\text{Me}}*100\%$$

∫_−∞^+∞f(x)dx = 1

∫_−σ^+σf(x)dx = 0, 68

∫_−2σ^+2σf(x)dx = 0, 75

∫_−3σ^+3σf(x)dx = 0, 997

$$\alpha_{3} = \frac{\frac{1}{N}\sum_{}^{}{n_{i}\left( x_{i} - \overset{\overline{}}{x} \right)^{3}}}{\left( \sigma_{x} \right)^{3}} = 0$$

$$\alpha_{4} = \frac{\frac{1}{N}\sum_{}^{}{n_{i}\left( x_{i} - \overset{\overline{}}{x} \right)^{4}}}{\left( \sigma_{x} \right)^{4}} = 3$$

$$\alpha_{3} = \frac{\mu_{3}}{S^{3}\left( x \right)} = \frac{\sum_{i = 1}^{k}\left\lbrack \left( x_{i}^{'} - \overset{\overline{}}{x} \right)^{3}*n_{i} \right\rbrack}{N*S^{3}\left( x \right)}$$

$$\mu_{3} = \frac{\sum_{i = 1}^{k}\left\lbrack \left( x_{i}^{'} - \overset{\overline{}}{x} \right)^{3}*n_{i} \right\rbrack}{N}$$

$$\alpha_{4} = \frac{\mu_{4}}{S^{4}\left( x \right)} = \frac{\sum_{i = 1}^{k}\left\lbrack \left( x_{i}^{'} - \overset{\overline{}}{x} \right)^{4}*n_{i} \right\rbrack}{N*S^{4}\left( x \right)}$$

α₄ ∈ (0;+∞)

$$\mu_{4} = \frac{\sum_{i = 1}^{k}\left\lbrack \left( x_{i}^{'} - \overset{\overline{}}{x} \right)^{4}*n_{i} \right\rbrack}{N}$$

$$r_{\text{xy}} = \frac{\sum_{i = 1}^{n}\left\lbrack \left( x_{i} - \overset{\overline{}}{x} \right)\left( y_{i} - \overset{\overline{}}{y} \right) \right\rbrack}{n*S_{x}*S_{y}}$$

$$S_{x} = \sqrt{\frac{\sum_{i = 1}^{n}\left( x_{i} - \overset{\overline{}}{x} \right)^{2}}{n}}\ \ ;\ \ \overset{\overline{}}{x} = \sum_{i = 1}^{n}x_{i}$$

$$S_{y} = \sqrt{\frac{\sum_{i = 1}^{n}\left( y_{i} - \overset{\overline{}}{y} \right)^{2}}{n}}\ \ ;\ \ \overset{\overline{}}{y} = \sum_{i = 1}^{n}y_{i}$$

R_xy² = r_xy²

y^′ = a + bx

$$b = r\frac{S_{y}}{S_{x}} = \frac{\overset{\overline{}}{x}*\overset{\overline{}}{y} - \overset{\overline{}}{\text{xy}}}{{\overset{\overline{}}{x}}^{2} - \overset{\overline{}}{x^{2}}}$$

$$a = \overset{\overline{}}{y} - b\overset{\overline{}}{y}$$

$$r = \frac{\sum_{i = 1}^{n}{x_{i}y_{i} - \frac{\sum_{i = 1}^{n}{x_{i}\sum_{i = 1}^{n}y_{i}}}{n}}}{\sqrt{\left( \sum_{i = 1}^{n}{{x_{i}}^{2} - n*{\overset{\overline{}}{x}}^{2}} \right)\left( \sum_{i = 1}^{n}{{y_{i}}^{2} - n*{\overset{\overline{}}{y}}^{2}} \right)}}$$

$$R^{2} = \frac{\sum_{i = 1}^{n}\left( y^{'} - \overset{\overline{}}{y^{'}} \right)^{2}}{\sum_{i = 1}^{n}\left( y - \overset{\overline{}}{y} \right)^{2}} = r^{2}$$