TATISTICS

h Edition

test Syllabus issued by ute of Chartered Accountants of India]

RORA

U) or of Mathematics llege elhi, Delhi

d.

: Ph: 23632120; [email protected] : Ph: 2738811, 2735640; [email protected] : Ph: 40186018; [email protected] : Ph: 2291317, 2291318; [email protected] : Ph: 4645630; [email protected] : Ph: 2576207, 2576208; [email protected] : Ph: 23357458, 23353914; [email protected] : Ph: 4003633; [email protected] : Ph: 25000297; [email protected] : Ph: 2250230; [email protected] : Ph: 2260011; [email protected] : Ph: 2361178; [email protected] : Ph: 2771238; [email protected] Company Limited, 2007

ed. No part of this publication may be reproduced or copied in any material form ng it in any medium in form of graphics, electronic or mechanical means and whe al to some other use of this publication) without written permission of the copyr ill entail legal action and prosecution without further notice. ll disputes with respect to this publication shall be subject to the jurisdiction of the C ew Delhi, India only.

DEDICATION This book is dedicated to the Loving, Encouraging and Everlasting memories of our Esteemed Parents who were a permanent source of inspirations to us. Dr. P. N. Arora & Mrs. S. Arora

e Institute of Chartered Accountant of India; either as solved problem e book has been written in a simple and lucid language to enable the stude prescribed in the syllabus. Each chapter of the book reveals a refreshi valuable points, the student is unlikely to find in any other book. the salient features of the book are:

y concept has been explained with the help of solved examples king rules, showing the various steps for the applications of formu given erous solved examples have been given in each chapter, to facilita rstanding the concepts and help them to solve the unsolved problem iple choice questions with answers as well as hints/solutions for selec been provided for practice stion bank has been provided at the end of each chapter for pr rstand the concepts diagrams and graphs have been neatly and correctly drawn in suc tudents have the complete understanding of the problem by simp m

to express our sincere thanks to the management team of S. Ch and untiring efforts in the publication of the book. Thanks are eam for their help and guidance.

PAPER 2

usiness Laws and Business Correspondence & Reporting (100 Mark Section A: Business Laws (60 Marks) Section B: Business Correspondence and Reporting (40 Marks)

PAPER 3

Business Mathematics, Logical Reasoning and Statistics (100 Marks Part A: Business Mathematics (40 Marks) Part B: Logical Reasoning (20 Marks) Part C: Statistics (40 Marks)

PAPER 4

siness Economics and Business & Commercial Knowledge (100 Ma Part I: Business Economics (60 Marks) Part II: Business and Commercial Knowledge (40 Marks)

ciples and Practice of Accounting

100 Marks

Descriptive/S

100 Marks

Descriptive/S

ness Laws and Business Correspondence & orting

Section A: Business Laws (60 Marks)

Section B: Business Correspondence and

ntals of nting arks) tive

le Law arks) tive

onomics arks) tive

Aptitude arks) tive

Principles and Practices of Accounting (100 Marks) Subjective

Business Laws (60 Marks = ICA + SOGA + PA = 45 Marks + LLP + Companies Ac (40 Marks) Business Correspondence and Repor Subjective

Business Economics (60 Marks) Business and Commercial Knowledge (40 Mark Objective Business Mathematics (40 Marks) Logical Reasoning (20 Marks) Statistics (40 Marks) Objective

STATISTICS

:

cal Description of Data al Representation of Data, Diagrammatic Representation of Dat tion, Graphical Representation of Frequency Distribution — Histogra , Ogive, Pie-chart.

e of Central Tendency and Dispersion es of Central Tendency and Dispersion: Mean Median, Mode, Me s and Quartile Deviation, Standard Deviation, Coefficient of Variation, Deviation.

ility lity: Independent and Dependent Events; Mutually Exclusive Even und Probability and mathematical Expectation.

tical Distributions ical Distributions: Binomial Distribution, Poisson Distribution—Basi mal Distribution—Basic Applications.

tion and Regression ion and Regression: Scatter Diagram, Karl Pearson’s Coefficient of Co

ation Analysis

ssion Analysis

Series Analysis

bility

ed Value or Mathematical Expectation

etical Distributions

Numbers

bles

ODUCTION

tistics’ has been derived from the Latin word ‘Status’ which means a po ot either to the Italian word ‘Statista’ or the German word ‘Statistik’ each cal state. For several decades, the word ‘statistics’ was associated solely w gures pertaining to the economic, demographic and political situations y, collected and brought out by the local governments. a tool in the hands of mankind to translate complex facts into simple and u facts.

NING AND DEFINITION OF STATISTICS

Statistics: The word Statistics is used in two different senses— its plural form, it refers to the numerical data collected in a syste inite aim or object in view such as the number of persons suffering fr ies of Delhi or number of unemployed girls in different states of India

ion makes it clear that statistics (in plural form or numerical data) shou acteristics: ics are aggregate of facts ics are affected by a large number of causes ics are always numerically expressed ics should be enumerated or estimated ics should be collected in a systematic manner ics should be collected for a pre-determined purpose ics should be placed in relation to each other

stics as Statistical Methods or Statistics in Singular S

the definitions of statistics used in singular sense, i.e., statistics as statis methods provide a set of tools which can be profitably used by differe ey deem fit. The term statistics in this context has been defined different definitions are given below:

may be called the science of counting”.

—A

ion covers only one aspect, i.e., counting, but the other aspects such as , have been ignored. As such, the definition is inadequate and incomplete

may be defined as the collection, presentation, analysis and interpretation o

— Croton an

ion given by Croxton and Cowden is simple, clear and concise.

This enables us to compare ourselves with other countries of the world. Exchange: In the field of exchange, an economist studies markets, law etermined by the forces of demand and supply, cost of production, monopol anking, etc. A systematic study of all these can be made only with the he Econometrics: With the help of econometrics, economics has become Econometrics is the combination of economics, mathematics and statistics Public Finance: Public finance studies the revenue and expenditure activiti Budget, (a statistical document), fiscal policy, deficit financing, etc., are t conomics which are based on statistics. nput-Output Analysis: The input-output analysis is based on statistic xplain the relationship between the input and the output. Sampling, Time umbers, Probability, Correlation and Regressions are some other conc sed in economic analysis.

tics and Commerce: Statistical methods are widely applied in the solut siness and trade activities such as production, financial analysis, costin ng, business, market research, distribution and forecasting, etc. A shrew s makes a proper and scientific analysis of the past records in order to pre of the business conditions. Index numbers help in predicting the fu ss and economic events. Statistics or statistical methods help the business lysing the business activities such as: Organisation of Business: Businessman makes extensive use of statistica t the conclusion which guides him in establishing a new firm or business Production: The production department of an organisation prepares the for he production of the commodity with the help of statistical tools. cientific Management and Business Forecasting: Better and efficien

ated with statistical methods. Professor Karl Pearson in his Grammar o n, “The whole doctrine of heredity rests on statistical basis”.

tics and Mathematics: Mathematics and Statistics have been closely ther ever since the 17th century when the theory of probability was found to ious statistical methods. Bowley was right when he said, “A knowledge knowledge of foreign language or of algebra: it may prove of use at a rcumstances”. we observe that:

nces without statistics bear no fruit, statistics without sciences have no ro

tics and Research: Statistical techniques are indispensable in research cement in knowledge has taken place because of experiments conducted istical methods.

tics and Natural Sciences: Statistics finds an extensive application in phy ally in engineering, physics, chemistry, geology, mathematics, astrono y, meteorology, zoology, etc.

ics and Education: There is an extensive application of statistics in Educa essary for formulation of policies to start new courses, infrastructure req s, consideration of facilities available for new courses, etc.

tics and Business: Statistics is an indispensable tool in all aspects of b enters business he enters the profession of forecasting because success s the result of precision in forecasting and failure in business is very often ations, which arise in turn due to faulty reasoning and inaccurate analy affecting a particular phenomenon. Boddington observes, “The successfu

tical data should be uniform and homogeneous.

ISTICAL TOOLS USED IN ECONOMIC ANALY

are some of the important statistical techniques which are applied in econ tion of data ation res of central tendency res of dispersion series bility numbers ing and its uses ess forecasting of significance and analysis of variance ical quality control

LECTION OF DATA

ormation collected through censuses and surveys or in a routine manner o w data. The word data means information (its literary meaning is given attached to data indicates that the information thus collected and recorded c diately and directly. It has to be converted into more suitable form or proc e sense to be utilised gainfully. A raw data is a statistical data in origina techniques are used to redefine, process or summarize it. wo types of statistical data:

us or U.G.C. mation obtained from the official publications of the central, state, and the loc g with crop statistics, industrial statistics, trade and transport statistics, et mation obtained from the official publications of the foreign governments fo sations.

SSIFICATION OF DATA

f arranging things in groups or classes according to their common char led the classification of data.

tion is the process of arranging data into sequences and groups accord aracteristics or separating them into different but related parts.

fication is the process of arranging the available data into various homog s according to some common characteristic or attribute or objective of in

UISITES OF A GOOD CLASSIFICATION

acteristics of a good classification are: uld be exhaustive uld be unambiguous uld be mutually exclusive uld be stable uld be flexible uld have suitability uld be homogeneous