Attributes Variables and types of data
Types of characteristics:
Attributes: Nominal scale, ordinal scale,
Variables: Interval scale, ratio scale,
discrete and continuous variables,
difference between linear scale and circular scale
Types of data:
(a) Primary data, Secondary data
(b) Cross-sectional data, time series data, directional data.
Statistical population: Finite population, infinite population, homogeneous population and heterogeneous population. Notion of a sample and a random sample Methods of sampling (Description only): Simple random sampling with and without replacement (SRSWR and SRSWOR) stratified random sampling, systematic sampling, cluster sampling and two-stage sampling.
Presentation of Data.Interpretation of Data from table and graph. data validation.
Frequency Classification: Raw data and its classification, ungrouped frequency distribution, Sturges' rule, grouped frequency distribution, cumulative frequency distribution, inclusive and exclusive methods of classification, Open end classes, and relative frequency distribution.
Measures of Central Tendency:
Concept of central tendency of statistical data, Statistical averages, characteristics of a good
statistical average. Arithmetic Mean (A.M.): Definition, effect of change of origin and scale, combined mean of a number of groups, merits and demerits, trimmed arithmetic mean.
Mode and Median Definition, formulae (for ungrouped and grouped data), merits and demerits. Empirical relation between mean, median and mode.
Partition Values Quartiles, Deciles and Percentiles (for ungrouped and grouped data),
Geometric Mean (G.M.): Definition, formula, merits and demerits. Harmonic Mean (H.M.): Definition. Formula, merits and demerits. Order relation between arithmetic mean, geometric mean, harmonic mean
Weighted Mean: weighted A.M., G.M. and H.M.
Situations where one kind of average is preferable to others.
Concept of dispersion, characteristics of good measure of dispersion.
Range, Semi-interquartile range (Quartile deviation): Definition, merits and demerits,
Mean deviation Definition, merits and demerits, minimality property
Variance and standard deviation Definition, merits and demerits, effect of change of origin and scale, combined variance for n groups (derivation for two groups).
Mean squared deviation: Definition, minimality property of mean squared deviation (with proof), Measures of dispersion for comparison coefficient of range, coefficient of quartile deviation and coefficient of mean deviation, coefficient of variation (C.V.)
Raw moments (μ,) for ungrouped and grouped data.
Central moments (m) for ungrouped and grouped data, Effect of change of origin and scale. Relations between central moments and raw moments, upto 4th order .
Concept of skewness of frequency distribution, positive skewness, negative skewness, symmetric frequency distribution.
Bowley's coefficient of skewness: Bowley's coefficient of skewness lies between -1 to 1 (with proof), interpretation using Box plot.
Karl Pearson's coefficient of skewness.
Measures of skewness based on moments (B1, 1).
Concepts of kurtosis, leptokurtic, mesokurtic and platykurtic frequency distributions.
Measures of kurtosis based on moments (2, 2).
Attributes: Concept of a Likert scale, classification, notion of manifold classification, dichotomy, class- frequency, order of a class, positive class-frequency, negative class frequency, ultimate class frequency, relationship among different class frequencies (up to three attributes), and dot operator to find the relation between frequencies, fundamental set of class frequencies.
Consistency of data up to 2 attributes.
Concepts of independence and association of two attributes. Yule's coefficient of association (Q), -1 ≤ Q ≤ 1, interpretation.
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