THE NATIONAL ANTHEM
Jana-gana-mana adhinayaka, jaya he
Bharatha-bhagya-vidhata.
Punjab-Sindh-Gujarat-Maratha
Dravida-Utkala-Banga
Vindhya-Himachala-Yamuna-Ganga
Uchchala-Jaladhi-taranga
Tava subha name jage,
Tava subha asisa mage,
Gahe tava jaya gatha.
Jana-gana-mangala-dayaka jaya he
Bharatha-bhagya-vidhata.
Jaya he, jaya he, jaya he,
Jaya jaya jaya, jaya he!
PLEDGE
India is my country. All Indians are my brothers and
sisters.
I love my country, and I am proud of its rich and varied
heritage. I shall always strive to be worthy of it.
I shall give my parents, teachers and all elders respect, and
treat everyone with courtesy.
To my country and my people, I pledge my devotion. In
their well-being and prosperity alone lies my happiness.
Prepared by :
State Council of Educational Research and Training (SCERT)
Poojappura, Thiruvananthapuram - 695012, Kerala.
Website : www.scertkerala.gov.in e-mail : scertkerala@gmail.com
Phone : 0471 - 2341883, Fax : 0471 - 2341869
Typesetting and Layout : SCERT
© Department of Education, Government of Kerala
To be printed in quality paper - 80gsm map litho (snow-white)
Forward
This Textbook of Statistics for Class-XII has been designed to help
the students to grasp basic statistical concepts and techniques. Real
life opportunities and situations have been provided for applying
them in relevant situations.
Two major divisions of Statistics namely Descriptive statistics and
Inferential statistics were considered while developing this material.
The chapters on Descriptive statistics will provide you with a
perspective to look at data and to communicate information
effectively and efficiently. The chapters on Inferential statistics will tell
you, how statistics supplies powerful concepts to estimate the
pervasive effect of chance and will help us to generalise beyond limited
sets of actual observations. Scopes for doing practicals have also been
provided, wherever possible.
Novel and emerging ideas and concepts in Statistics have been
discussed in the Textbook. This will equip you with a global outlook to
enter into the field of statistics, as a professional. The learning
outcomes envisaged in each chapter will enable you to look for the
purpose of learning each chapter. In the end you can assess yourself
- your level in achieving the concepts and ideas. Suggestions and
comments about this book are most welcome.
Dr. S.Raveendran Nair
Director
SCERT; Kerala
Textbook Development Team
1.
2.
3.
4.
5.
MANOJ. K
HSS Panagad , Thrissur.
ANWAR SHAMEEM. Z. A
GHSS Kuttiadi, Kozhikode.
SAJISHKUMAR. M
MNKM HSS,
Chittilamchery, Palakkad.
BIJU . G. V
GHSS Kulakkada, Kollam.
SREESAN.M.B
Karimpuzha HSS, Thottara
Palakkad.
6.
MOHAMMED ASLAM.K
PPM HSS Kottukkara,
Malappuram .
7. MARY GEORGE
St. Raphael’s CGHSS, Ollur, Thrissur.
8. DEEPA KOSHY
PSVPM HSS, Ayravon, Pathanamthitta.
9. HASIM. M. C
GHSS Aroli, Kannur
10. SAKKEER.M
Govt. VHSS Meppayyur,
Kozhikode.
Experts
P.K. VENUGOPAL
Associate Professor (Rtd.), Department of Statistics
Sree Kerala Varma College, Thrissur.
Dr. K. K. HAMSA
Associate Professor, Department of Statistics
Farook College, Kozhikode.
Dr. C. GOKULADASAN PILLAI
Former Curriculum Head, SCERT, Kerala
Academic Co-ordinator
Dr. Chandini. K. K
Head, Higher Secondary and Teacher Training
State Council of Educational Research and Training (SCERT),
Vidhyabhavan, Poojappura, Thiruvananthapuram-695 012
Contents
1.
Correlation Analysis
1.1
1.2
1.3
2.
3
4.
2.1
2.2
Meaning of Regression
Linear regression
2.3
Regression equations
Elementary Calculus
5.2
29
6.
45
3.4
3.5
Definite Integrals
Random Variables
4.6
4.7
Distribution Function
4.5
7.
111
6.1
6.2
Normal Distribution - Concept
Normal Probability Density
Function
6.3
Standard Normal Distribution
Sampling Distributions
7.4
7.5
7.6
8.
85
Binomial Probability
Distribution
Poisson Probability
Distribution
Normal Distribution
7.1
7.2
7.3
57
Random Variable
Discrete Random Variable
Probability mass function
(pmf)
Cumulative distribution
function (cdf)
Mathematical Expectation,
Mean and Variance
Continuous Random Variables
4.4
Discrete Probability
Distributions
5.1
Derivative of a Function
Second Order Derivative
Applications of second order
derivatives
Integration
4.1.
4.2.
4.3
5.
Meaning of Correlation
Types of Correlation
Methods of Studying
Correlation
Regression Analysis
3.1
3.2
3.3
7
Parameter and statistic
Sampling Distribution
Distribution of Sample
Mean
Central Limit Theorem and
its importance
Chi - square, t and F
distributions
Relation among Z, Chi-square,
t and F statistics
Estimation of Parameters
8.1
8.2
8.3
8.4
129
149
Point Estimation
Method of Moments
Interval Estimation
Confidence interval for the
population mean
9.
Testing of Hypothesis
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
165
Statistical Hypothesis
The Two types of Errors
Level of Significance and
Power of a Test
Test Statistic and Critical
Region
One - Tailed and Two - Tailed
Tests
Tests of significance of single
mean
Tests for significance for
equality of two population
means (Z test)
Chi - square test for
independence of attributes
10. Analysis of Variance
207
10.1 Types of Variations
10.2 Causes of Variation
10.3 Assumptions of ANOVA
10.4 One - Way ANOVA
11. Statistical Quality Control
11.1
11.2
11.3
11.4
Meaning of Quality
Quality Control
Statistical Process Control
Variation and Causes of
Variation
227
11.5
11.6
11.7
11.8
11.9
11.10
Control Charts
Types of Control Charts
Construction of Control Charts
Control Charts for Variables
Control Charts for Attributes
Uses of Statistical Quality
Control
12. Time Series Analysis
255
12.1 Time Series
12.2 Components of Time series
12.3 Uses of Analysis of Time Series
12.4 Trend Analysis
13. Index Numbers
281
13.1 Classification of Index
Numbers
13.2 Types of Index Numbers
13.3 Consumer Price index
13.4 Characteristics of Index
Numbers
13.5 Uses of index Numbers
Appendix A - Answers
Appendix B -Glossary
Appendix C - References
Appendix D - Statistical Tables
301
305
309
310
Appendix E - R Code
316