S.Y.B.Sc. (IT)
SEMESTER - IV (CBCS)
COMPUTER ORIENTED
STATISTICAL TECHNIQUES
SUBJECT CODE : USIT403
, © UNIVERSITY OF MUMBAI
Prof. Suhas Pednekar
Vice Chancellor
University of Mumbai, Mumbai.
Prof. Ravindra D. Kulkarni Prof. Prakash Mahanwar
Pro Vice-Chancellor, Director
University of Mumbai. IDOL, University of Mumbai.
Programe Co-ordinator : Mandar L. Bhanushe
Head, Faculty of Science and Technology,
IDOL, University of Mumbai – 400098.
Course Co-ordinator : Ms. Gouri Sawant
Assistant Professor B.Sc.I.T,
IDOL, University of Mumbai
Editor : Dr. Aarti Nayak
Assistant Professor, S.K Somaiya College,
Somaiya University
Course Writers : Ms. Kumudini Manwar
Assistant Professor, Sinhgad Institute of Management, Pune
: Mr. Nimesh Punjani
Assistant Professor, Lala Lajpatrai College, Mahalakshmi,
Mumbai - 34
: Mr. Kiran Patil
Assistant Professor, Anandibai Raorane Arts,
Commerce and Science College Vaibhavwadi
: Dr. Manisha Pithadia
Assistant Professor,
Viva College of Arts,Science and Commerce
November 2021, Print I
Published by : Director
Institute of Distance and Open Learning ,
ipin Enterprises University of Mumbai,
Vidyanagari, Mumbai - 400 098.
Tantia Jogani Industrial Estate, Unit No. 2,
Ground Floor, Sitaram Mill Compound,
DTP COMPOSED
J.R. Boricha AND
Marg,PRINTED
Mumbai -BY 400 011
Mumbai University Press
Vidyanagari, Santacruz (E), Mumbai - 400098.
, CONTENTS
Chapter No. Title Page No
Unit I
1. The Mean, Median, Mode, And Other Measures of Central Tendency 1
2. The Standard Deviation And Other Measures of Dispersion 24
3. Introduction To R 42
Unit II
4. Moments, Skewness, And Kurtosis 66
5. Elementary Probability Theory 85
6. Elementary Sampling Theory 107
Unit III
7. Statistical Estimation Theory 122
8. Statistical Decision Theory 131
9. Statistics In R 144
Unit IV
10. Small Sampling Theory 149
11. The Chi-Square Test 169
Unit V
12. Curve Fitting And The Method Of Least Squares 188
13. Correlation Theory 206
*****
, UNIT I
1
THE MEAN, MEDIAN, MODE, AND
OTHER MEASURES OF CENTRAL
TENDENCY
Unit structure
1.0 Objectives
1.1 Introduction
1.2 Index or Subscript, Notation, Summation Notation
1.3 Averages or Measures of Central Tendency
1.4 Arithmetic Mean
1.4.1 Arithmetic Mean Computed from Grouped Data
1.4.2 Properties of the Arithmetic Mean
1.5 Weighted Arithmetic Mean
1.6 Median
1.7 Mode
1.8 Empirical Relation between the Mean, Median, and Mode
1.9 Geometric Mean
1.10 Harmonic Mean
1.11 Relation between the Arithmetic, Geometric, and Harmonic Means
1.12 Root Mean Square
1.13 Quartiles, Deciles and Percentiles
1.14 Software and Measures of Central Tendency
1.15 Summary
1.16 Exercise
1.17 References
1.0 OBJECTIVES
After going through this chapter, students will able to learn
To present huge data in a summarized form
To calculate and interpret the mean, the median and the mode,
To facilitate comparison
To calculate geometric mean, harmonic mean
To trace precise relationship
1
SEMESTER - IV (CBCS)
COMPUTER ORIENTED
STATISTICAL TECHNIQUES
SUBJECT CODE : USIT403
, © UNIVERSITY OF MUMBAI
Prof. Suhas Pednekar
Vice Chancellor
University of Mumbai, Mumbai.
Prof. Ravindra D. Kulkarni Prof. Prakash Mahanwar
Pro Vice-Chancellor, Director
University of Mumbai. IDOL, University of Mumbai.
Programe Co-ordinator : Mandar L. Bhanushe
Head, Faculty of Science and Technology,
IDOL, University of Mumbai – 400098.
Course Co-ordinator : Ms. Gouri Sawant
Assistant Professor B.Sc.I.T,
IDOL, University of Mumbai
Editor : Dr. Aarti Nayak
Assistant Professor, S.K Somaiya College,
Somaiya University
Course Writers : Ms. Kumudini Manwar
Assistant Professor, Sinhgad Institute of Management, Pune
: Mr. Nimesh Punjani
Assistant Professor, Lala Lajpatrai College, Mahalakshmi,
Mumbai - 34
: Mr. Kiran Patil
Assistant Professor, Anandibai Raorane Arts,
Commerce and Science College Vaibhavwadi
: Dr. Manisha Pithadia
Assistant Professor,
Viva College of Arts,Science and Commerce
November 2021, Print I
Published by : Director
Institute of Distance and Open Learning ,
ipin Enterprises University of Mumbai,
Vidyanagari, Mumbai - 400 098.
Tantia Jogani Industrial Estate, Unit No. 2,
Ground Floor, Sitaram Mill Compound,
DTP COMPOSED
J.R. Boricha AND
Marg,PRINTED
Mumbai -BY 400 011
Mumbai University Press
Vidyanagari, Santacruz (E), Mumbai - 400098.
, CONTENTS
Chapter No. Title Page No
Unit I
1. The Mean, Median, Mode, And Other Measures of Central Tendency 1
2. The Standard Deviation And Other Measures of Dispersion 24
3. Introduction To R 42
Unit II
4. Moments, Skewness, And Kurtosis 66
5. Elementary Probability Theory 85
6. Elementary Sampling Theory 107
Unit III
7. Statistical Estimation Theory 122
8. Statistical Decision Theory 131
9. Statistics In R 144
Unit IV
10. Small Sampling Theory 149
11. The Chi-Square Test 169
Unit V
12. Curve Fitting And The Method Of Least Squares 188
13. Correlation Theory 206
*****
, UNIT I
1
THE MEAN, MEDIAN, MODE, AND
OTHER MEASURES OF CENTRAL
TENDENCY
Unit structure
1.0 Objectives
1.1 Introduction
1.2 Index or Subscript, Notation, Summation Notation
1.3 Averages or Measures of Central Tendency
1.4 Arithmetic Mean
1.4.1 Arithmetic Mean Computed from Grouped Data
1.4.2 Properties of the Arithmetic Mean
1.5 Weighted Arithmetic Mean
1.6 Median
1.7 Mode
1.8 Empirical Relation between the Mean, Median, and Mode
1.9 Geometric Mean
1.10 Harmonic Mean
1.11 Relation between the Arithmetic, Geometric, and Harmonic Means
1.12 Root Mean Square
1.13 Quartiles, Deciles and Percentiles
1.14 Software and Measures of Central Tendency
1.15 Summary
1.16 Exercise
1.17 References
1.0 OBJECTIVES
After going through this chapter, students will able to learn
To present huge data in a summarized form
To calculate and interpret the mean, the median and the mode,
To facilitate comparison
To calculate geometric mean, harmonic mean
To trace precise relationship
1
