Paper : Descriptive Statistics
Note : (1) Mathematical derivations and proofs are not expected.
(2) Student should be introduced to MSEXCEL/Spreadsheet.
Objective : The main objective of this course is to acquaint students with some basic
concepts in statistics. They will be introdeuced to some elementary statistical methods
of analysis of data.
At the end of this course students are expected to be able
(i) to compute various measures of central tendency, dispersion, skewness and kurtosis.
(ii) to compute the correlation coefficient for ungrouped bivariate data and interpret it.
(iii) to analyze data pertaining to attributes and to interpret results.
(iv) to analyze data pertaining to Time Series and to interpret the results.
1
(38) Applied Statistics
Paper : Descriptive Statistics
1. Population and Sample (6)
1.1 Types of characteristics :
Attributes : Nominal scale, ordinal scale, Variables : Interval scale, ratio scale,
difference between linear scale and circular scale, discrete and continuous variables,
raw data.
1.2 Types of data : (a) Primary data, Secondary data.
(b) Cross-sectional data, time series data, failure data, industrial data, directional
data.
1.3 Notion of a statistical population : Finite population, infinite population, homogeneous
population and heterogeneous population. Notion of sample, random sample
and non-random sample.
1.4 Methods of sampling (description only) : Simple random sampling with and without
replacement (SRSWR and SRWOR) stratified random sampling.
2. Presentation of Data (14)
2.1 Classification : Discrete frequency distribution, inclusive and exclusive methods of
classification, open end classes, cumulative frequency distribution and relative frequency
distribution.
2.2 Graphical presentation of data : Histogram, frequency curve, ogive curves, stem and
leaf chart.
2.3 Diagramatic presentation : Bar diagram, percentage bar diagram, multiple bardiagram,
subdivided bar-diagram, Pie-diagram. .
2.4 Simple Numerical Problems.
2
3. Measures of Central Tendency (18)
3.1 Concept of central tendency of statistical data : Statistical average, characteristics
of a good statistical average.
3.2 Arithmetic Mean (A.M.) Definition, effect of change of origin and scale, combined
mean of two groups, merits and demerits
3.3 Mode : Definition, formula for computation, graphical method of determination of
mode, merits and demerits.
3.4 Median : Definition, formula for computation, graphical method of determination of
median, merits and demerits.
3.5 Partition Values : Quartiles, Deciles and Percentiles, graphical method of determination
of quartiles, deciles and percentiles for grouped frequency distributions,
Percentile ranks.
Means of Transform Data
3.6 Geometric Mean (G.M.) : Definition, merits and demerits, means of transformed
data
3.7 Harmonic Mean (H. M.) : Definition, merits and demerits
3.8 Weighted Arithmetic Mean
3.9 Simple numerical problems
3.10 Situations where one kind of average is preferable to others.
4. Measures of Dispersion (12)
4.1 Concept of dispersion, characteristics of good measure of dispersion.
4.2 Range : Definition, merits and demerits.
4.3 Semi-interquartile range (Quartile deviation), Merits and demerits.
3
4.4 Mean deviation : Definition, merits and demerits.
4.5 Mean square deviation : Variance and standard deviation (S.D.) : merits and demerits.
4.6 Measures of dispersion: coefficient of variation (C.V.)
4.7 Simple Numerical Problems.
5. Moments (6)
5.1 Raw moments (m
r) for grouped and ungrouped data upto order four.
5.2 Central moments (mr) for ungrouped and grouped data upto order four, Effects of
change of origin and scale.
5.3 Relations between central moments and raw moments upto order four.
5.4 Simple Numerical Problems
END OF THE FIRST TERM
6. Skewness and Kurtosis (12)
6.1 Concept of skewness of frequency distribution, positive skewness, negative skewness,
symmetric frequency distribution.
6.2 Bowley’s coefficient of skewness : interpretation using Box plot.
6.3 Karl Pearson’s coefficient of skewness.
6.4 Measures of skewness based on moments.
6.5 Concepts of kurtosis, leptokurtic, mesokurtic and platykurtic frequency distributions.
6.6 Obtaining measures of kurtosis based on moments.
4
6.7 Simple Numerical Problems.
7. Correlation (14)
7.1 Bivariate data.
7.2 Concept of correlation between two variables, positive correlation, negative correlation,
zero correlation.
7.3 Scatter diagram, conclusion about the type of correlation from scatter diagram.
7.4 Karl Pearson’s coefficient of correlation (r) : Definition, computation for ungrouped
data and interpretation.
Properties : (i) −1 ≤ r ≤ +1 , (ii) Effect of change of origin and scale.
7.5 Spearman’s rank correlation coefficient : Definition, computation and interpretation
7.6 Simple Numerical Problems.
8. Regression (10)
8.1 Concept of regression, linear of regression, interpretation of slope and intercept.
8.2 Regression coefficient (byx, bxy) : Definition, computation, statement of properties
(1) byx · bxy = r2 , (2) byx · bxy ≤ 1, (3) Effect of change of origin and scale.
8.3 Simple Numerical Problems.
9. Theory of Attributes (10)
9.1 Attributes : Classification, notion of dichotomy and manifold classification, classfrequency,
order of class, positive class-frequency, negative class frequency, quantra
class, ultimate class frequency, relationship among different class frequencies of different
order (up to three attributes), dot operator, fundamental set of class frequencies.
5
9.2 Consistency of data upto 3 attributes.
9.3 Concepts of independence and association of two attributes.
9.4 Yule’s coefficient of association (Q), interpretation.
10.5 Simple Numerical Problems.
10. Time Series (10)
10.1 Meaning of Time Series
10.2 Various components of a time series (Explanation and illustrations of each component)
10.3 Additive and multiplicative methods for analysis of a time series.
10.4 Methods of estimating trends
(i) Freehand or graphical method (ii) Method of least square
(iii) Method of semi-averages (iv) Method of moving averages.
10.5 Simple Numerical Problems.
Reference Books
1. Goon Gupta and Das Gupta : Fundamentals of Statistics, Vol. I, Ed. 5,
The World Press Pvt. Ltd., Kolkata, 1986.
2. Gupta, S. P. Statistical Methods, Ed. 12, Sultan Chand and Sons, New
Delhi.
3. Gupta, S. C. Fundamental of Statistics by Himalaya Publishing House.
4. Walpole R. F. : Introduction to Statistics, Macmilan Co. ew York.
5. Gupta, S. C. and Kapoor, V. K. : Fundamentals of Mathematical Statistics,
Ed. 3, Sultan Chand and Sons, New Delhi, (1987) .
6
6. Goon Gupta and Das Gupta : Fundamentals of Statistics, Vol. II, Ed. 6,
The World Press Pvt. Ltd., Kolkata, 1986.
7. R. I. Levin and D. S. Rubin : Statistics for Management, Prentice Hall of
India Pvt. Ltd., New Delhi.
7
Note : (1) Mathematical derivations and proofs are not expected.
(2) Student should be introduced to MSEXCEL/Spreadsheet.
Objective : The main objective of this course is to acquaint students with some basic
concepts in statistics. They will be introdeuced to some elementary statistical methods
of analysis of data.
At the end of this course students are expected to be able
(i) to compute various measures of central tendency, dispersion, skewness and kurtosis.
(ii) to compute the correlation coefficient for ungrouped bivariate data and interpret it.
(iii) to analyze data pertaining to attributes and to interpret results.
(iv) to analyze data pertaining to Time Series and to interpret the results.
1
(38) Applied Statistics
Paper : Descriptive Statistics
1. Population and Sample (6)
1.1 Types of characteristics :
Attributes : Nominal scale, ordinal scale, Variables : Interval scale, ratio scale,
difference between linear scale and circular scale, discrete and continuous variables,
raw data.
1.2 Types of data : (a) Primary data, Secondary data.
(b) Cross-sectional data, time series data, failure data, industrial data, directional
data.
1.3 Notion of a statistical population : Finite population, infinite population, homogeneous
population and heterogeneous population. Notion of sample, random sample
and non-random sample.
1.4 Methods of sampling (description only) : Simple random sampling with and without
replacement (SRSWR and SRWOR) stratified random sampling.
2. Presentation of Data (14)
2.1 Classification : Discrete frequency distribution, inclusive and exclusive methods of
classification, open end classes, cumulative frequency distribution and relative frequency
distribution.
2.2 Graphical presentation of data : Histogram, frequency curve, ogive curves, stem and
leaf chart.
2.3 Diagramatic presentation : Bar diagram, percentage bar diagram, multiple bardiagram,
subdivided bar-diagram, Pie-diagram. .
2.4 Simple Numerical Problems.
2
3. Measures of Central Tendency (18)
3.1 Concept of central tendency of statistical data : Statistical average, characteristics
of a good statistical average.
3.2 Arithmetic Mean (A.M.) Definition, effect of change of origin and scale, combined
mean of two groups, merits and demerits
3.3 Mode : Definition, formula for computation, graphical method of determination of
mode, merits and demerits.
3.4 Median : Definition, formula for computation, graphical method of determination of
median, merits and demerits.
3.5 Partition Values : Quartiles, Deciles and Percentiles, graphical method of determination
of quartiles, deciles and percentiles for grouped frequency distributions,
Percentile ranks.
Means of Transform Data
3.6 Geometric Mean (G.M.) : Definition, merits and demerits, means of transformed
data
3.7 Harmonic Mean (H. M.) : Definition, merits and demerits
3.8 Weighted Arithmetic Mean
3.9 Simple numerical problems
3.10 Situations where one kind of average is preferable to others.
4. Measures of Dispersion (12)
4.1 Concept of dispersion, characteristics of good measure of dispersion.
4.2 Range : Definition, merits and demerits.
4.3 Semi-interquartile range (Quartile deviation), Merits and demerits.
3
4.4 Mean deviation : Definition, merits and demerits.
4.5 Mean square deviation : Variance and standard deviation (S.D.) : merits and demerits.
4.6 Measures of dispersion: coefficient of variation (C.V.)
4.7 Simple Numerical Problems.
5. Moments (6)
5.1 Raw moments (m
r) for grouped and ungrouped data upto order four.
5.2 Central moments (mr) for ungrouped and grouped data upto order four, Effects of
change of origin and scale.
5.3 Relations between central moments and raw moments upto order four.
5.4 Simple Numerical Problems
END OF THE FIRST TERM
6. Skewness and Kurtosis (12)
6.1 Concept of skewness of frequency distribution, positive skewness, negative skewness,
symmetric frequency distribution.
6.2 Bowley’s coefficient of skewness : interpretation using Box plot.
6.3 Karl Pearson’s coefficient of skewness.
6.4 Measures of skewness based on moments.
6.5 Concepts of kurtosis, leptokurtic, mesokurtic and platykurtic frequency distributions.
6.6 Obtaining measures of kurtosis based on moments.
4
6.7 Simple Numerical Problems.
7. Correlation (14)
7.1 Bivariate data.
7.2 Concept of correlation between two variables, positive correlation, negative correlation,
zero correlation.
7.3 Scatter diagram, conclusion about the type of correlation from scatter diagram.
7.4 Karl Pearson’s coefficient of correlation (r) : Definition, computation for ungrouped
data and interpretation.
Properties : (i) −1 ≤ r ≤ +1 , (ii) Effect of change of origin and scale.
7.5 Spearman’s rank correlation coefficient : Definition, computation and interpretation
7.6 Simple Numerical Problems.
8. Regression (10)
8.1 Concept of regression, linear of regression, interpretation of slope and intercept.
8.2 Regression coefficient (byx, bxy) : Definition, computation, statement of properties
(1) byx · bxy = r2 , (2) byx · bxy ≤ 1, (3) Effect of change of origin and scale.
8.3 Simple Numerical Problems.
9. Theory of Attributes (10)
9.1 Attributes : Classification, notion of dichotomy and manifold classification, classfrequency,
order of class, positive class-frequency, negative class frequency, quantra
class, ultimate class frequency, relationship among different class frequencies of different
order (up to three attributes), dot operator, fundamental set of class frequencies.
5
9.2 Consistency of data upto 3 attributes.
9.3 Concepts of independence and association of two attributes.
9.4 Yule’s coefficient of association (Q), interpretation.
10.5 Simple Numerical Problems.
10. Time Series (10)
10.1 Meaning of Time Series
10.2 Various components of a time series (Explanation and illustrations of each component)
10.3 Additive and multiplicative methods for analysis of a time series.
10.4 Methods of estimating trends
(i) Freehand or graphical method (ii) Method of least square
(iii) Method of semi-averages (iv) Method of moving averages.
10.5 Simple Numerical Problems.
Reference Books
1. Goon Gupta and Das Gupta : Fundamentals of Statistics, Vol. I, Ed. 5,
The World Press Pvt. Ltd., Kolkata, 1986.
2. Gupta, S. P. Statistical Methods, Ed. 12, Sultan Chand and Sons, New
Delhi.
3. Gupta, S. C. Fundamental of Statistics by Himalaya Publishing House.
4. Walpole R. F. : Introduction to Statistics, Macmilan Co. ew York.
5. Gupta, S. C. and Kapoor, V. K. : Fundamentals of Mathematical Statistics,
Ed. 3, Sultan Chand and Sons, New Delhi, (1987) .
6
6. Goon Gupta and Das Gupta : Fundamentals of Statistics, Vol. II, Ed. 6,
The World Press Pvt. Ltd., Kolkata, 1986.
7. R. I. Levin and D. S. Rubin : Statistics for Management, Prentice Hall of
India Pvt. Ltd., New Delhi.
7
No comments:
Post a Comment