The measure of the central tendency in statistics is a number used to describe a set of values by a single number (for short). For example, instead of listing the salaries of all employees of an organization, they talk about the average salary . There are many measures of central tendency; the final choice of measure is always left to the investigator.
In the simplest cases (and most often), the following measures are used as measures of the central trend:
- arithmetic average ;
- geometric mean ;
- harmonic mean .
These three measures have been proposed by the Pythagoreans , therefore they are also called “Pythagorean means” ( English pythagorean means ) [1] .
In practical studies, the resulting set of values is rarely described by a normal distribution and, in addition, it may contain so-called “ outliers ”. Therefore, when choosing a measure of central tendency, it is important to consider the stability (robustness) of emissions of the chosen measure of central tendency applied in each particular case.
Major measures of central tendency
- The arithmetic average is the sum of all observed values divided by their number.
- Weighted average is an average value that takes into account weights for each value.
- The accounted average is the arithmetic mean, when calculating which all excluded (in accordance with the percentage set by the researcher) the largest and smallest values are replaced by the largest and smallest “remaining” values, respectively.
- The harmonic mean is the number of observations divided by the sum of the inverted values of the observations.
- The geometric mean is the root of the degree of the number of values from the total product of all values.
- The median is a value that divides the observations in ascending (descending) order in half.
- Fashion is the most common meaning.
- M-score .
- Kolmogorov Mean is a particular case of the Cauchy mean . General view of the system of axioms (requirements for averages), leading to the so-called associative averages.
- Tukey average .
- The truncated average is the arithmetic average after the removal of the established (by the researcher) percentage of the largest and smallest values.
Notes
- ↑ Cantrell, David W., “Pythagorean Means” from MathWorld .