# statistics

Reading time:The symbol (–) placed above an expression signifies that its mean value applies.

## definitions

#### sum

#### arithmetic mean

#### weighted arithmetic mean

#### mediane

The median for a series of numbers arranged by increasing value is the middle value, or the arithmetic mean of the two central values (when there is an even number of values).

#### mode

The mode of a series of numbers is the number most frequently encountered, i.e. the one that has the greatest frequency. The mode may not exist or it may not be unique.

Empirical relation between the mean, the median and the mode (figure 1) :

**Mode**

The following empirical relation applies to moderately asymmetrical unimodal density curves :

#### geometric mean G :

#### quadatic mean QM :

#### average deviation AD :

#### standard deviation SD

#### variance V

## property of the type deviation

In the case of a normal distribution or of a Laplace-Gauss distribution (figure 2), it would seem that :

**Distribution or of a Laplace-Gauss distribution**

## graphic method for adjusting a curve

Using a scatter chart (figure 3), it is often possible to represent a continuous curve that is close to the data. This type of curve is called an adjustment curve.

**Dispersion diagram**

The most classic method is the least squares method.

#### definition

Among all the curves that are close to a series of data, the one that provides the best match is the one that confirms the following property :

D_{1}, D_{2}, D_{N} being the distances between the curve and the experimental points (figure 4).

**The curve and the experimental points**

This is called the **curve of the least squares**.