σ-algebra or Borel field is a collection of subsets of a sample space S,
and it must satisfy the following three properties:
- The empty set is an element of σ-algebra.
- σ-algebra is closed under complementation.
- σ-algebra is closed under countable unions.
Sample space is a set of all possible outcomes of an experiment.
Measures of central tendency are used to describe the trend of value or values in a dataset.
◆ Arithmetic Mean
◆ Geometric Mean
◆ Harmonic Mean
◆ Truncated Mean
Measures of Dispersion are used to understand the scatterings of data.
◆ Standard Deviation
◆ Coefficient of Variance
Descriptive statistics is a study of managing and describing data properties and exchanging the data into useful information.
◆ Frequency Distribution
◆ Skewness and Kurtosis
Scales of measurement or levels of measurement were developed by American psychologist Stanley Smith Stevens(November 4, 1906 – January 18, 1973).
He classified variables into four levels: nominal, ordinal, interval, and ratio.
Based on the order of four levels, the usable operators get more and more from nominal to ratio.