Moyennes

Moyennes is a term used in statistics to refer to measures of central tendency that summarize a dataset by a single value considered typical or representative. The concept encompasses several different notions, including the arithmetic mean, the geometric mean, the harmonic mean, the median and the mode. Each measure has its own interpretation, strengths and limitations, and is appropriate for different kinds of data and distributions.

The arithmetic mean is the sum of all observations divided by the number of observations. It is often denoted by x̄ for a sample or μ for a population, and it is widely used for interval or ratio data with a roughly symmetric distribution. The mean can be heavily influenced by extreme values or outliers.

The geometric mean is the nth root of the product of n positive observations and is commonly used for growth rates, ratios or multiplicative processes. It tends to dampen the impact of very large or very small values and requires positive data.

The harmonic mean is the reciprocal of the average of reciprocals and is especially useful for averaging rates or ratios, such as speeds or densities. It is appropriate when the quantity of interest is inversely related to the measured values.

The median is the middle value of a dataset when it is ordered; it remains meaningful in the presence of outliers and skewed distributions. For even sample sizes, the median is typically the average of the two central values. The mode is the most frequently occurring value and can be unique, multiple or nonexistent, particularly in continuous data.

Choosing which moyenne to use depends on the data type, distribution and the presence of outliers. In practice, the mean is common for symmetric data, the median for skewed data, and the geometric or harmonic means for specific multiplicative or rate-based contexts.