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. Tabula- 
tion—10. Tables with unequal intervals—11. Graphical representa- 
tion of the frequency-distribution—12. Ideal frequency-distributions 
—13. The symmetrical distribution—14. The moderately asymmetri- 
cal distribution—15. The extremely asymmetrical or J-shaped dis- 
tribution—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 observa- 
tions. 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 treat- 
ment 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- 
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