# Statistics

HIGHER SECONDARY – FIRST YEAR

Untouchability is a sin Untouchability is a crime Untouchability is inhuman

TAMILNADU

TEXTBOOK CORPORATION

College Road , Chennai- 600 006

i

©Government of Tamilnadu

First Edition – 2004 Reprinit - 2005

Chairperson Dr. J. Jothikumar Reader in Statistics Presidency College Chennai – 600 005. Thiru K.Nagabushanam S.G.Lecturer in Statistics Presidency College Chennai – 600 005.

Reviewers Thiru R.Ravanan

S.G.Lecturer in Statistics Presidency College Chennai – 600 005.

Authors Tmt. V.Varalakshmi

S.G.Lecturer in Statistics S.D.N.B. Vaishnav College for women Chrompet, Chennai – 600 044.

Tmt. N.Suseela

P.G.Teacher Anna Adarsh Matric Hr. Sec. School Annanagar, Chennai–600 040.

Thiru G.Gnana Sundaram

P.G.Teacher S.S.V. Hr. Sec. School Parktown, Chennai – 600 003.

Tmt.S.Ezhilarasi

P.G.Teacher P.K.G.G. Hr. Sec. School Ambattur, Chennai–600 053.

Tmt. B.Indrani

P.G.Teacher P.K.G.G. Hr. Sec. School Ambattur, Chennai – 600 053.

Price: Rs. This book has been prepared by the Directorate of School Education on behalf of the Government of Tamilnadu. This book has been printed on 60 G.S.M paper Printed by offset at: ii

CONTENTS

Page

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Definitions, Scope and Limitations Introduction to sampling methods Collection of data, Classification and Tabulation Frequency distribution Diagramatic and graphical representation Measures of Central Tendency Measures of Dispersion, Skewness and Kurtosis Correlation Regression Index numbers

1 11 28 49 68 94 141 191 218 241

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1. DEFINITIONS, SCOPE AND LIMITATIONS

Introduction: In the modern world of computers and information technology, the importance of statistics is very well recogonised by all the disciplines. Statistics has originated as a science of statehood and found applications slowly and steadily in Agriculture, Economics, Commerce, Biology, Medicine, Industry, planning, education and so on. As on date there is no other human walk of life, where statistics cannot be applied. 1.2 Origin and Growth of Statistics: The word ‘ Statistics’ and ‘ Statistical’ are all derived from the Latin word Status, means a political state. The theory of statistics as a distinct branch of scientific method is of comparatively recent growth. Research particularly into the mathematical theory of statistics is rapidly proceeding and fresh discoveries are being made all over the world. 1.3 Meaning of Statistics: Statistics is concerned with scientific methods for collecting, organising, summarising, presenting and analysing data as well as deriving valid conclusions and making reasonable decisions on the basis of this analysis. Statistics is concerned with the systematic collection of numerical data and its interpretation. The word ‘ statistic’ is used to refer to 1. Numerical facts, such as the number of people living in particular area. 2. The study of ways of collecting, analysing and interpreting the facts. 1.4 Definitions: Statistics is defined differently by different authors over a period of time. In the olden days statistics was confined to only state affairs but in modern days it embraces almost every sphere of 1 1.1

human activity. Therefore a number of old definitions, which was confined to narrow field of enquiry were replaced by more definitions, which are much more comprehensive and exhaustive. Secondly, statistics has been defined in two different ways – Statistical data and statistical methods. The following are some of the definitions of statistics as numerical data. 1. Statistics are the classified facts representing the conditions of people in a state. In particular they are the facts, which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement. 2. Statistics are measurements, enumerations or estimates of natural phenomenon usually systematically arranged, analysed and presented as to exhibit important interrelationships...

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