PART IL—THE THEORY OF VARIABLES.
CHAPTER VI.
THE FREQUENCY-DISTRIBUTION.
1. Introduetory—2. Necessity for classification of observations: the frequency
distribution—3. Illustrations—4. Method of forming the table—5.
Magnitude of class-interval—6. Position of intervals—7. Process of
classification—8. Treatment of intermediate observations—9. Tabulation—10.
 Tables with unequal intervals—11. Graphical representation
 of the frequency-distribution—12. Ideal frequency-distributions
—13. The symmetrical distribution—14. The moderately asymmetrical
 distribution—15. The extremely asymmetrical or J-shaped distribution—16.
 The U-shaped distribution.
1. TeE methods described in Chaps. I.-V. are applicable to all
observations, whether qualitative or quantitative ; we have now
to proceed to the consideration of specialised processes, definitely
adapted to the treatment of quantitative measurements, but not
as a rule available (with some important exceptions, as suggested
by Chap: I. § 2) for the discussion of purely qualitative observations.
 Since numerical measurement is applied only in the case
of a quantity that can present more than one numerical value,
that is, a varying quantity, or more shortly a variable, this section
of the work may be termed the theory of variables. As common
examples of such variables that are subject to statistical treatment
 may be cited birth- or death-rates, prices, wages, barometer
readings, rainfall records, and measurements or enumerations (e.g.
of glands, spines, or petals) on animals or plants.
2. If some hundreds or thousands of values of a variable have
been noted merely in the arbitrary order in which they happened
to occur, the mind cannot properly grasp the significance of the
record : the observations must be ranked or classified in some
way before the characteristics of the series can be comprehended,
and those comparisons, on which arguments as to causation
depend, can be made with other series. The dichotomous classi-75