Statistics

It is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides methods and techniques for summarizing, modeling, and drawing inferences from data.

Statistics is a crucial component of data science because it provides the tools and methods needed to turn raw data into actionable insights and make informed decisions. It helps to identify patterns, relationships, and trends in data, and provides a way to test hypotheses and make predictions based on data.

In data science, statistical methods are used for data exploration and visualization, dimensionality reduction, feature selection, model building and validation, hypothesis testing, and prediction. Additionally, statistical techniques like hypothesis testing, confidence intervals, and hypothesis tests help data scientists assess the significance of results and make confident inferences about the underlying processes and relationships in the data.

In short, statistics provides a foundation for data science by providing the mathematical and computational tools needed to turn data into insights, and by helping data scientists to develop and validate models that can be used for prediction and decision-making.

Syllabus of statics

A typical statistics syllabus may cover the following topics:

1. Descriptive Statistics: Introduction to the summary and descriptive measures of central tendency and variability, including mean, median, mode, range, standard deviation, and variance.

2. Probability: Introduction to the concepts of probability, including sample space, events, and conditional probability, as well as Bayes’ theorem.

3. Random Variables and Probability Distributions: Covers the concepts of random variables, discrete and continuous probability distributions, including the binomial, Poisson, normal, and exponential distributions.

4. Estimation: Introduction to point and interval estimation, including the methods of maximum likelihood and method of moments, as well as hypothesis testing.

5. Inferential Statistics: Covers hypothesis testing, including one- and two-sample tests, chi-squared tests, and t-tests, as well as analysis of variance (ANOVA) and regression analysis.

6. Correlation and Regression: Covers the concepts of correlation, linear regression, and multiple regression, including the methods of least squares and ridge regression.

7. Nonparametric Statistics: Introduction to nonparametric methods, including the Wilcoxon rank-sum test, the Kruskal-Wallis test, and the Mann-Whitney test.

8. Time Series Analysis: Covers the concepts of time series analysis, including stationarity, autocorrelation, and exponential smoothing.

9. Bayesian Statistics:

Introduction to Bayesian methods, including Bayesian inference, Markov Chain Monte Carlo (MCMC), and Bayesian linear regression.

10. Multivariate Analysis:

 Covers the concepts of multivariate analysis, including principal component analysis (PCA), factor analysis, and clustering.

11. Applied Statistics:

 An overview of the application of statistical methods in various domains, such as health sciences, engineering, finance, and marketing.

12. Data Visualization: 

An introduction to the creation of visual representations of data, including histograms, scatter plots, and box plots, as well as the use of data visualization software and libraries.

Our syllabus provides a comprehensive overview of the main topics in statistics, and provides students with the skills and knowledge needed to apply statistical methods to real-world problems. The course aims to equip students with the ability to critically analyze data, make inferences, and communicate results effectively, as well as an understanding of the limitations and assumptions underlying statistical methods.