PEOPLE'S DEMOCRATIC REPUBLIC of ALGERIA
MINISTRY of HIGHER EDUCATION and SCIENTIFIC RESEARCH
NATIONAL POLYTECHNIC INSTITUTE MALEK BENNABI of CONSTANTINE
COURSE HANDOUT
PROBABILITY and STATISTICS
Mohamed BOUKELOUA
Academic year 2023/2024Contents
Introduction 3
Part I: Descriptive Statistics 4
1 Statistical series with one character 5
1.1 Introduction .To calculate them, we
use the method of linear interpolation.Qualitative character
They are measures of "types" and may be represented by names or symbols. They are related to categorical variables. The modalities of a qualitative character are words or symbols. Qualitative characters may also be represented by number codes. 6Quantitative character
They are measures of values or counts and are expressed as numbers. They are related to
numeric variables. Quantitative characters may be discrete or continuous. - Discrete quantitative character (or discrete statistical variable): It is a variable that takes
on distinct and countable values. The set of values of such a variable is finite or countable
(at most countable). The modalities are distinct numbers. - Continuous quantitative character (or continuous statistical variable): It is a variable that
takes on an infinite number of possible values within a given range. The set of values of such
a variable is infinite and uncountable. The modalities are intervals called "Class intervals".Differential diagram (Line graph)
The line graph consists of vertical lines representing the values of X. The height of the line
corresponding to xi is determined by either ni or fi.
Integral diagram (Cumulative frequency curve)
To define this graphic, we need first to define the cumulative absolute frequencies and the
cumulative relative frequencies., ([ek-1, ek[, nk)} be a statistical series corresponding to a
continuous statistical variable X.
Arithmetic mean
The arithmetic mean of X is defined by
X = 1
n
kXi
=1
nici =
kXi
=1
fici,
where ci = ei-1 + ei
2
is the centre of the ith class [ei-1, ei[.96
2Introduction
In the present course, we study fundamental notions in the descriptive statistics and the
probability theory, in accordance with the programs of mathematics of the preparatory
classes leading to the engineering institutes, the common cores of sciences and technology,
mathematics and computer science and the sciences of matter., ([ek-1, ek[, nk)} be a statistical series corresponding to a
continuous statistical variable X.
Variance and standard deviation
The variance of X is defined by
V ar(X) = 1
n
kXi
=1
nici - X 2 = 1
n
kXi
=1
nic2 i - X 2
and the standard deviation of X is defined by
?X = pV ar(X).Example 3 (continued):
To draw the graphical representations of this statistical series, we need to calculate the
magnitudes (di)1