BIT Basic Statistics

Unit 1: Introduction (5 Hrs.)

Basic concept of statistics (definitions, concept of descriptive and inferential statistics), application of Statistics in different fields including information technology, limitations of statistics; scales of measurement (nominal, ordinal, interval and ratio), variables (Discrete, continuous and categorical), types of data (cross-sectional and longitudinal) and data source (primary and secondary), data preparation — editing, coding, and transcribing.

Unit 2: Diagrammatical and Graphical Presentation of Data (3 Hrs.)

Bar diagrams; Pie diagrams; Pareto chart; Graph of frequency distribution (Histogram, frequency polygon, frequency curve, less than ogive and more than ogive, stem and leaf display) and their interpretations.

Unit 3: Descriptive Statistics (7 Hrs)

Measures of central tendency: Definition of measures of central tendency, arithmetic mean and its mathematical properties, weighted mean, median, mode, empirical relations between mean, median and mode; choice of measure of central tendency, interpretations.

Measures of dispersion: Need of measures of dispersion, absolute and relative measures, range, quartile deviation, mean deviation, standard deviation and their relative measures including coefficient of variation, choice of appropriate measure of dispersion, interpretations.

Measures of skewness: Concept of skewness, types of skewness, Pearson's coefficient of skewness, Bowley's coefficient of skewness; Exploratory Data Analysis (EDA): Five number summary, box and whisker plots, outliers, use of five number summary and boxplots to assess the skewness of data distribution.

Measures of kurtosis: Concept of kurtosis, types of kurtosis, measure of kurtosis based on percentiles; overall assessment of nature of data distribution.

Moments: Introduction of moments, central moments and raw moments, relations between central moments and raw moments, measures of skewness and kurtosis based on moments.

Problems and illustrative examples related to IT.

Unit 4: Introduction to Probability (7 Hrs.)

Concepts of probability, definitions of probability (mathematical, statistical and subjective approach), terminologies used in probability, laws of probability (additive and multiplicative), conditional probabilities, Bayes theorem: prior and posterior probabilities.

Problems and illustrative examples related to IT.

Unit 5: Random Variables and Mathematical Expectation (3 Hrs.)

Concept of a random variable and its types, probability distribution of a random variable, mathematical expectation of a discrete random variable, standard deviation and variance of discrete random variable, addition and multiplication theorems of expectation and variance (without proof).

Problems and illustrative examples related to IT.

Unit 6: Probability Distributions (6 Hrs.)

Probability distribution function, Binomial distribution, Poisson distribution, Normal distribution and their characteristic features; applications of these distributions in IT related data problems.

Problems and illustrative examples related to computer science and IT.

Unit 7: Sampling and Sampling Distribution (7 Hrs.)

Definitions of population, sample survey vs. census survey, sampling error and non-sampling error, concept of parameter and statistic, types of sampling (concept of simple random, stratified, cluster and systematic sampling, concept of non-probability sampling), standard error of mean, standard error of proportion, sampling distribution of mean and proportion, need of inferential statistics, concept of central limit theorem, concept of estimation (point and interval), confidence interval estimation for mean & proportion, problem specific interpretations of confidence interval.

Problems and illustrative examples related to IT.

Unit 8: Correlation and Linear Regression (7 Hrs.)

Bivariate data, bivariate frequency distribution, correlation between two variables, Karl Pearson's coefficient of correlation (r), assumptions of Pearson's correlation coefficient, properties of correlation coefficient, Spearman's rank correlation including repeated ranks, interpretation of correlation coefficient, need of regression analysis, fitting of lines of regression by the least squares method, interpretation of regression coefficients, coefficient of determination (R²) and its interpretation, residual plots for assessing the goodness of fit of the model.

Problems and illustrative examples related to IT.

Practical (Computational Statistics): Practical problems to be covered in the Computerized Statistics laboratory, using any statistical software such as Microsoft Excel, SPSS, STATA, etc. whichever convenient.