Introduction

*NUMERICAL INDICATORS (Parameters):

a) location Indicators (central tendency measures):

a1. The Mode: (denoted by ) the mode is the modality or value which occurs most frequently i.e. the one corresponding to the greatest frequency. Notice that the mode is not necessary unique. We speak about modal class in the case of continuous character.

Example:  the statistical series  2,2,5,7,9,9,9,10,10,11,12,18  has as mode 9.                                                                                              the statistical series  3, 5, 8, 10, 12,15, 16  has no mode.                                                                                   the statistical series 2, 3, 4, 4, 4, 5, 5, 7, 7,7, 9  has two modes 4 et 7. We say that this series is                                                                                        bimodal.     

*A series owing just mode is called unimodal.

*In the case of a continuous variable, we apply the following formula:

with : is the lower limit of the modal class,

                      : is the length of the modal class,

           : the difference between the frequency (relative frequency) of the modal class and the previous one.

           : the difference between the frequency (relative frequency) of the modal class and the following one.

a2. The  Median (denoted by ): is the value that divides the ordered statistical series into two equals parts.

Example:  the statistical series 3, 4, 4, 5, 6, 8, 8, 8, 10 has 6 as median.                                                                     the statistical series 5, 5, 7, 9, 11, 12,15,18  has as median (9+11)/2= 10.

*The median corresponds to the cumulative relative frequency 0,5.

*In the case of a continuous variable,  we apply the following formula:

with  : is the lower limit of the median class,

          : is the lower limit of the median class,

               : is the sample size  

               ): is the difference  between the cumulative frequency of the median class and                                                                                             the cumulative frequency of  the previous one(respectively the following one).

a3. The Mean: Let  be a discrete character having  values .  Its mean is given by:

*If  is a continuous character owing k classes .  Its mean is given by:

where is the midvalue of the class ,i.e. .

b) Dispersion Indicators :

b1.The Variance: If   is a discrete character having  values of mean . Its variance is given by:

or

*If  is a continuous character owing  classes  of mean , It is given by:

where is the midvalue of the class ,

b2. Standard Deviation: 

V. Distribution Function:

The distribution function of a quantitative statistical variable  is the function  which associates to each   the amount  that represents the percentage of individuals for whom  is less than  or equal to . It is an increasing function with values in [0,1].  Its graph is called cummulative frequencies graph.

*Case of a Discrete Statistical Variable:

If   is a discrete statistical variable having  k values , then its distribution function is given by:

 Its curve is the graph of a function in the form of a staircase.

Example:

Population: Families,

Sample: Families living in a building, n=64

X : Children number within a family (a discrete statistical variable).

The distribution function of families according to the number of children is given by:

And its graph is

*Case of a Continuous Statistical Variable:

Let  to be a continuous statistical variable owning k classes .  Its distribution function is given by:

Its curve is the grapf of an increasing continuous function.

Example :

Population: patients

Sample:  n=32 patients.

The character X: blood glucose level. It is a continuous statistical variable.

La fonction de répartition et sa courbe cumulative des fréquences