An Introduction to Statistical Analysis

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F. S. Crofts & Company, 1925 - 257 páginas
 

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Contenido

Artificial Zeros
11
Counting Discrete Objects
12
Arithmetic Computations
13
Numbers Arising in Mathematical Theory
14
Computations with Approximations
15
Indirect Measurements
16
Accuracy of Measurements and Other Approximations
17
The Integer of a Singlenumber Approximation а
18
The Significant Figures of a Singlenumber Approxi mation
19
Simplifying Approximations
20
COMPUTATIONS WITH APPROXIMATIONS 24 General Theory Concerning the Addition of Quantities Represented by Approximations
23
Multiplication of Quantities Represented by Ap proximations
25
Products of Singlenumber Approximations
27
Abbreviated Multiplication
28
Division of Quantities Represented by Approxi
30
SECTION PAGE 29 Quotients of Singlenumber Approximations
32
Abbreviated Division
34
Products or Quotients Only One of the Given Num bers Being an Approximation
35
Square Roots
38
General Exercises in Computation
40
LOGARITHMS AND THEIR USES 34 Fundamental Principles
41
Some Additional Forms
44
Logarithms
46
Tables of Logarithms
49
Logarithms with Fewer Figures
55
Antilogarithms
57
Laws of Logarithms
59
Use of Logarithms in Computation
61
GRAPHS FROM EMPIRICAL DATA 42 Graphs
68
Differences Containing Many Significant Figures
69
Bar Graphs
71
The Logarithmic Scale
72
A Logarithmic Scale for Twofigure Numbers
74
Graphs with a Logarithmic Scale
76
Associated Variables
78
Graphs of Associated Variables
79
Misrepresentative Graphs
84
Examples for Practice in Graph Making
93
FREQUENCY DISTRIBUTIONS 55 Definitions with Illustrations
98
The Individualized Scale Line
99

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Página 86 - The general arrangement of a diagram should proceed from left to right. " 2. Where possible represent quantities by linear magnitudes, as areas or volumes are more likely to be misinterpreted. " 3. For a curve the vertical scale, whenever practicable, should be so selected that the zero line will appear on the diagram.
Página 88 - ... 7. When the scale of a diagram refers to dates, and the period represented is not a complete unit, it is better not to emphasize the first and last ordinates, since such a diagram does not represent the beginning or end of time.
Página 85 - The committee is making a study of the methods used in different fields of endeavor for presenting statistical and quantitative data in graphic form. As civilization advances there is being brought to the attention of the average individual a constantly increasing volume of comparative figures and general data of a scientific, technical and statistical nature. The graphic method permits the presentation of such figures and data with a great saving of time and also with more clearness than would otherwise...
Página 92 - ... 16. All lettering and all figures on a diagram should be placed so as to be easily read from the base as the bottom, or from the right-hand edge of the diagram as the bottom. Fig. 16. 17. The title of a diagram should be made as clear and complete as possible. Sub-titles or descriptions should be added if necessary to insure clearness.
Página 61 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 91 - ... 12. The horizontal scale for curves should usually read from left to right and the vertical scale from bottom to top. "13. Figures for the scales of a diagram should be placed at the left and at the bottom or along the respective axes.
Página 90 - The curve lines of a diagram should be sharply distinguished from the ruling. 11. In curves representing a series of observations, it is advisable, whenever possible, to indicate clearly on the diagram all the points representing the separate observations.
Página 72 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm, m — ax, and n = a».
Página 85 - Chairman, American Society of Mechanical Engineers. 7 East 42d Street, New York City. Leonard P. Ayres, Secretary, American Statistical Association. 130 East 22d Street, New York City. NA Carle, American Institute of Electrical Engineers. Robert E. Chaddock, American Association for the Advancement of Science. Frederick A Cleveland, American Academy of Political and Social Science. HE Crampton, American Genetic Association. Walter S.
Página 89 - ... 8. When curves are drawn on logarithmic co-ordinates, the limiting lines of the diagram should each be at some power of ten on the logarithmic scales. 9. It is advisable not to show any more co-ordinate lines than necessary to guide the eye in reading the diagram.

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