à propos de Statistiques

G. M. Clarke and D. Cooke
A basic course in Statistics
Third Edition 1992
Edward Arnold 
A division of Hodder \& Stoughton
London Melbourne Auckland

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A \emph{population} is the collection of items under discussion. It may be finite \coupure or infinite; it may be
real \coupure or hypothetical \coupure.

A \emph{variate} is any quatity or attribute whose value varies from one unit of investigation to another.

An \emph{observation} is the value taken by a variate for a particular unit of investigation.

A \emph{quantitative variate} is a variate whose values are numerical.

A \emph{qualitative variate} or \emph{attribute} is a variate whose values are not numerical.

A \emph{continuous variate} is a variate which may take all values within a given range.

A \emph{discrete variate} is a variate whose values change by steps.

The \emph{frequency distribution} of a (discrete) variable is the set of all possible values of the variate,
together with the associated frequencies.

A \emph{class-interval} is a subdivision of the total range of values which a (continuous) variate may take.

The \emph{class-frequency} is the number of observations of the variate which fall in a given interval.

The \emph{frequency distribution} of a (continuous) variable is the set of class-intervals for the variate,
together with the associated class-frequencies.

The \emph{frequency polygon} is obtained by plotting class-frequencies or relative frequencies as ordinates
against the centre-points of class-intervals as abscissae. Then the plotted points are joined by straight lines.

Cumulative frequency diagram. We first prepare a cumulative frequency table. We form the cumulative frequencies
from the frequency table by adding in the frequencies, one by one, beginning from the left. (remarque : les tables
comportent en première ligne les classes, en deuxième les effectifs \&c) The cumulative frequency corresponding
to each class interval gives the total frequency in that interval and in all intervals to the left of it; it
therefore gives us the total frequency of observations that fall below the upper end-point of the class interval.
Hence it is the upper end-point that we put in the table and use in the graph.


Tables and diagrams

We have already seen the convenience of tables and diagrams in summarizing data. We now make some general
comments about them.

\emph{Data tables} are used widely in the collection, manipulation and summary of date. Tables allow the relations
between numbers to be exhibited clearly and reduce mistakes when collecting and handling data; they aid the 
calculation of derived quantities and the interpretation of date. Three main types of table may be recognized:
(1) raw data tables, or record sheets, (2) calculation tables, (3) summary tables.

Many points about table construction will appear so obvious to the reader that it does not seem profitable
to discuss them. Nonetheless, tables are often poorly constructed so we shall now give a check-list of points
to heed. The points under `summary tables' owe a great deal to the recommendations of A.S.C. Ehrenberg.

Points to note when constructing tables

\begin{itemize}
\item General
\begin{itemize}
\item Make the table self-explanatory: provide a title, a brief description of the source of the date, state in
what units the figure are expressed, label rows and columns where appropriate.
\end{itemize}
\item Raw data table
\begin{itemize}
\item Plan the record sheet so that: (a) recording is straightforward and unambiguous; (b) derived quantities may
be worked out conveniently on the sheet (e.g. allow room for totals). \label{refij}
\item Keep the table as simple as possible, subject to \ref{refij}.
\item When recording numbers, carry enough figures so that information is not thrown away but do not record
many meaningless digits. When in doubt, a rule of thumb is to record to 3 significant figures. \label{refiv}
\item Make alteration clearly; strike out a wrong numbe and write the correct value beside it, rather than 
attempting to alter figures.
\item Distinguish between zero values and missing observations.
\end{itemize}
\item Calculation tables
\begin{itemize}
\item When possible carry out calculations on the record sheet. (Transfer of data from one sheet to another
introduces errors.)
\item When data are transferred from the record sheet, double-check the numbers transferred. Check, for example,
that the total of columns of transferred numbers equals the total of the original numbers on the record sheet,
as well as reading the numbers over again.
\item Give the calculation a logical pattern on the sheet.
\item Choose units that will simplify the calculation. Consider a suitable coding; for example, decimal numbers
may be multiplied by a power of ten to convert them to integers.
\end{itemize}
\item Summary tables
\begin{itemize}
\item Make the table clear and simple with the main numbers for comparison close to each other. It is usually
easier to compare numbers in the same column than those in the same row.
\item If the table is becoming complicated break it down into smaller tables.
\item Arrange rows and columns in some natural order or in size order. Wher possible, put big numbers at the top
of the table.
\item Give row and column averages or totals, where they are meaningfull.
\item Choose units that the reader will understand and that will keep the table simple, e.g. a unit of millions
of \pounds{} may be convenient. State the unit of measurement.
\item Give a clear title and a verbal summary of the main points of the table.
\item Round all numbers to two effective digits. Effective digits are those which vary within a set of data.
Each of the following sets of date are quoted to two effective digits: (a) 129, 136, 119, 151;
(b) $6\cdot2$, $7\cdot3$, $4\cdot2$, $3\cdot8$; (c) 290, 530, 640,310. Note that this does not contradict \ref{refiv}
above; that remains an appropriate rule when collecting and processing data (as opposed to presenting a summary).
\end{itemize}

Diagrams. In a table use is made of geometrical ordering of rows and columns to exhibit relations between the numbers
in the table. In diagrams (which we take to include graphs), the magnitude of numbers is represented geometrically in order to aid comparisons.

In this chapter, frequency diagrams have been considered. A simple plot of the values of the observations on a line is often useful when assessing the nature of data and detecting wild observations. Plots of pairs of variates (see scatter diagrams \coupure) are also useful.

These diagrams are adequate for the projects suggested in this book but the reader will find elaborations of these diagrams, and other types, in the presentation of statistical data in newspapers and magazines. The reader should inspect examples critically and decide whether they are helpful or whether they mislead.

As with tables, we give a check-list of points to heed when constructing diagrams.

Points to note when constructing graphs

\begin{itemize}
\item Make the graph self-explanatory: provide a title and a brief description of the source, label the axes, state the units, mark in the scales and give a key if it is needed.
\item Choose a scale that: (a) is convenient; (b) ensures that most of the graph-paper is used.
\item Beware of misleading if the origin is not included.
\end{itemize}
