Statistics

Range

• [a,b) - inclusive a, exclusive b

Descriptive Statistics

Characteristics

• discrete characteristics: number of dots on a die
• continuous characteristics: body height

Absolute frequency $H(a_i)$ is the number of occurrences.

Relative frequency:

• without classes: $h(a_i)=\frac{1}{n}H(a_i)$
• with classes: $h(K_i)=\frac{1}{n}H(K_i)$

Marginal frequencies (in contingency tables):

• absolute MF: $H_{i.}={\sum }_{j=1}^m{H}_{ij}$
• relative MF: $h_{i.}={\sum }_{j=1}^m{h}_{ij}$

Data Representation

• Table
• Histogram
• Boxplot
• Contingency table (joint occurrence of characteristics in the sample)

Measures of Central Tendency

• Mean $\bar{x}=\frac{1}{n}{\sum }_i^n{x}_i$
• Median $\bar{x}=\frac{1}{n}{\sum }_{i=1}^n{x}_i$
• Variance / Standard deviation
• Quantiles / Interquartile range
• Marginal frequencies for classes: $H_i={\sum }_{j=1}^m{H}_{ij}$ and $h_i={\sum }_{j=1}^m{h}_{ij}$

Graphical Analysis

Determine the linear relationship between two characteristics $X$ and $Y$:

• Covariance
• Cross-correlation coefficient ($r_{xy}\ge 0.7$ indicates correlation)
• Empirical coefficient of determination $r_{xy}^2$

Scale Transformation

When scaling central tendency & dispersion parameters linearly:

• Mean: $\bar{y}=a\bar{x}+b$
• Variance: $s_y^2=a^2{s}_x^2$

Regression

If a dataset has a high coefficient of determination $r_{xy}^2\ge 0.5$, and the scatter plot shows a linear relationship, you can use linear regression to calculate the optimal parameters for $a$ and $b`.

• Linear Regression
• Logistic Regression