Chapter 1: Introduction to Statistics

• Overview of Statistics and its applications in data science
• Basic statistical concepts: population, sample, variable, data types, and measures of central tendency and dispersion
• Sampling techniques and sampling distributions

1.1 Overview of statistics and its applications in data science

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It is an important tool in data science, which involves the extraction of insights and knowledge from data using various techniques and algorithms.

Statistics is used in various stages of the data science workflow, including data pre-processing, exploratory data analysis, feature engineering, model training and evaluation, and interpretation of results.

It provides a framework for making sense of data, identifying patterns, relationships, and drawing conclusions based on evidence.

Some of the applications of statistics in data science include:

• Descriptive statistics: This involves summarizing and describing the main features of a dataset, such as measures of central tendency (e.g. mean, median, mode) and measures of dispersion (e.g. variance, standard deviation), and can be used to identify outliers and anomalies.

• Inferential statistics: This involves making inferences about a population based on a sample of data. Inferential statistics can be used to test hypotheses, estimate parameters, and make predictions. Some common inferential statistical techniques include hypothesis testing, confidence intervals, and regression analysis.

• Regression analysis: This involves examining the relationship between a dependent variable and one or more independent variables. Regression analysis can be used to make predictions and identify important predictors of a target variable. There are various types of regression analysis, including linear regression, logistic regression, and time series regression.

• Time series analysis: This involves analyzing data that is collected over time, such as stock prices or weather data. Time series analysis can be used to identify trends, patterns, and seasonality in the data.

• Bayesian statistics: This involves using prior knowledge and assumptions to update probabilities based on new data. Bayesian statistics can be used to make predictions and estimate probabilities in situations where there is uncertainty.

In summary, statistics is a fundamental tool in data science, used to analyze and interpret data, make predictions, and drive insights. By applying statistical techniques to data, data scientists can uncover patterns and relationships that can inform decisions and drive innovation.