Fundamentals of Statistics

1027 Pages·1972·27.298 MB·English

by  D. N. Elhance

FUNDAMENT ALS OF
STATISTICS
BY
D. N. ELHANCE,
M. COM.,
H,ad qf thl D,partm,nt and Dean of 1M Faculty of Commerce.
Uniuersity of Jodhpur,
JDdhpur.
KITAB MAHAL ALLAHABAD
1972
B.~. No. 64.
Indian Veterinary Research Institute
Library.
MUKTESWAR.
Class,
a
Register No.98:2_ 'Room No. 31
Inward No. Shelf No. E:.L-H
Received Book~o.
;' 10;
~/'~; Ii,' .
MGIPC-S4-28 VRjo2-12·2 '63-1,00 J.

First Idition,_ 1957
Second Edttio~ 1958
Third Edition, 1960
Fourth Edition, 1962
Fifth Edition, 1964
Sixth Edition. 1965
Seventh Edition. 1966
Eighth Edition, 1967
Ninth Edition, 1968
Tenth Edition, 1969
Eleventh Edhion, 1970
Tyveltth Ed~itp-?'f 1971
Thirteenth Edition: 197~
,-
Printed by: Eagle Offset Printers. 15. Thornhill Road, Allahabad
Published by: Kitab Mahal, 15. Thornhill Road. Allahabad
IN MEMORY
OF
MY FATHER

PREFACE TO THE THIRTBB'lTfI EDlrfO~
A new edition of the now famous book on Statistics has come out
maintaining its old traditions intact but with new approaches all round
to register and record the various changing aspects.
Calculations have been re-calculated in order to eliminate any
slightest variations which may haye crept in during the past years
Change to metric system has also been completed.
In its present fOJ;m the utility of the book has increased consider.
ably, and University students as well as administrators will find suffi.
cient material for their guidance and assistance.
The author will feel grateful to the discriminating student com
munity and the general users of the book for their indulgence in pinpoin
ting any error.
D. N. ELHANCB
PREFACE TO THE SIXTH EDITION
The present edition of this book has many new features. Two
new chapters-Designs of Experiments and Statistical Q:lality Control
have been added in this volume. The chapter on Growth of Statistics
in India has been made uptodate.and latest figures have been substituted
for old ones.
Some chapters of this book have been reVised and new points have
been included in them. A large number of fresh questions have been
added at the end of each chapter to make the book more useful to exa
minees. The entire portion of Indian Statistics has been brought ·upto
ate.
I hope the present volume would be found useful by the students
of the subject. J am grateful to a number of students and friends" ho
gave me valuable sug,gestions for the improvement of the book and
1 am confident that they would continue to do so in future also.
D. N. ELHANCB
PREFACE TO THE SECOND EDITION
From the various reviews which appeared in a large number of
journals and papers, I conclude that the first edition of this book was
very well received. In the present edition I have rearranged certain
chapters and made the chapter on Growth of Statistics in India upto
date. Besides, I have included a large number of new questions at the
end of each chapter.
The book is now divided in two volumes. V.olume I covers tbe
eatire B. Com., B.A. and B.Sc. course of statistics of all the universi
ties of India and Pakistan. Volume II contains chapters on Probability,
1 heoretical Frequency Distributions and Sampling. Tbe two volumes
ale available separately as well as in a combined form.
I am grateful to a la-rge number of friends who have given me
valuable s.uggestions for the improvement of the book. 1 hope the
students of the subject would lind the book more useful than before.
151h April. 1958. D. N. ELHANCB
PREFACE TO THE FIRST EDITION
The science of statistics has assumed great importance in recent
years. It was once known as the "Science of Kings" and its scope
was extremely limited, but today the science of statistics has become
an all-important science, without which no other science can progress.
Modern age is the age of statistics and it is very correctly said that the
extent of the economic development of a country can best be known
by finding out the extent to which statistical organisation has developed
there. Till recent! y the foreign government of our country and even
our countrymen were very indifferent towards statistics. After inde
·pendence of the country the era of economic planning started and along
with it the importanc of statistics increased considerably, In fact
economic planning cannot be imagined in the absence of statistical
data.
It is a matter of great satisfaction that the impottance of statistics
o
Is gradually being realised in our country and they are occupying the
place of honour which they should have got much earlier. Statistics
is now taught in almost all the universities of the country and there are
a number of statistical institutes which impart special trainihg in ~his
subject. This book is an attempt to furnish a simple, non-mathemat1cal
text for those who desire to equip themselves with a knowledge of the
elementary statistical methods used in modern times. The treatment
of this subject has been as far as possible of a non-mathematical character
because most of the students who study this subject do not always have
a mathematical background. This book has been written primarily
for use of M.A., M.Com., and B.Com. students who study this subject.
The book covers the entire course which is prescribed for the statistics
paper in these examinations in various universities of the country as
also the courses prescribed in LA.S. and P.C.S. examinations of the
paper. A large -pumber of questions have been given at the end of
each chaptet with a view to help the students in solving numetical pt'o
blems and thus familiarising themselves with different types of formula~
used in statistical analysis.
I am grateful to my colleagues in the Faculty of Commerce, Alla~
habad University, who have given me some ver} valuable suggestions,
Thanks are also due to Mr. S.V. Erasmus, my secretary, who worked
almost like a machine for all the days during which this book was
written. Kitab Mahal, my publishers deserve congratulations for the
nice printing and get-up of the book.
IJI December, 1956. D. N. ELHANCE
CONTENTS
Page
CHAPTER
)'r Meaning and Definition of Statistics 1
2. Origin and Growth of Statistics 8
/ Importance, Limitations and Functions of Statistics 16
4. Preliminaries to the Collection of Data 33
5. Collection of Primary and Secondary Data 41
6. Accuracy, Approximation and Errors 53
....:w---Classification, Seriation and Tabulation 63
8. Ratios, Percentages and Logarithms 80
C
Measures of Central Tendency 87
%.
Measures of Dispersion 178
11. Moments, Skewness and Kurtosis 236
12. Index Numbers 250
~. Diagrammatic Representation of Data 300
..)..4. Graphic Representation of Data 347
15. Analysis of Time Series 405
1Jj. Correlation 454
17. Regression and Ratio of Variation 508
18. Theory of Attributes and Consistence of Data 528
19. Association of Attributes 546
20. Interpolation 577
...
21. Business Forecasting 610
/22 Interpretation of Data 619
,.23: Probability 629
24. Theoretical Frequency Distributiolls 654
25. Theory of Sampling 676
26. Sampling of Attributes 689
27. Sampling of Variables (Large Samples) 706
28. Chi-square Test and Goodness of Fit 736
29. 'Sampling of Variables (Small Samples) 757
30. Analysis of Variance 783
31. Designs of Experiments 796
32. Statistical Quality Control 802
33. Growth of Statistics in India 814
34. Mathematical Tables 994