This module introduces visualization as an important tool for exploring and understanding data. First, the basic components of visualizations are introduced with an emphasis on how they can be used to convey information. Also, you will learn how to identify and avoid ways that a visualization can mislead or confuse a viewer. Next, you will learn more about conveying information to a user visually, including the use of form, color, and location. Third, you will learn how to actually create a simple visualization (basic line plot) in Python, which will introduce creating and displaying a visualization within a notebook, how to annotate a plot, and how to improve the visual aesthetics of a plot by using the Seaborn module. Finally, you will learn how to explore a one-dimensional data set by using rug plots, box plots, and histograms.

In this Module, you will learn the basics of probability, and how it relates to statistical data analysis. First, you will learn about the basic concepts of probability, including random variables, the calculation of simple probabilities, and several theoretical distributions that commonly occur in discussions of probability. Next, you will learn about conditional probability and Bayes theorem. Third, you will learn to calculate probabilities and to apply Bayes theorem directly by using Python. Finally, you will learn to work with both empirical and theoretical distributions in Python, and how to model an empirical data set by using a theoretical distribution.

This modules extends what you have learned in previous modules to the visual and analytic exploration of two-dimensional data. First, you will learn how to make two-dimensional scatter plots in Python and how they can be used to graphically identify a correlation and outlier points. Second, you will learn how to work with two-dimensional data by using the Numpy module, including a discussion on analytically quantifying correlations in data. Third, you will read about statistical issues that can impact understanding multi-dimensional data, which will allow you to avoid them in the future. Finally, you will learn about ordinary linear regression and how this technique can be used to model the relationship between two variables.

Often, as part of exploratory data analysis, a histogram is used to understand how data are distributed, and in fact this technique can be used to compute a probability mass function (or PMF) from a data set as was shown in an earlier module. However, the binning approach has issues, including a dependance on the number and width of the bins used to compute the histogram. One approach to overcome these issues is to fit a function to the binned data, which is known as parametric estimation. Alternatively, we can construct an approximation to the data by employing a non-parametric density estimation. The most commonly used non-parametric technique is kernel density estimation (or KDE). In this module, you will learn about density estimation and specifically how to employ KDE. One often overlooked aspect of density estimation is the model representation that is generated for the data, which can be used to emulate new data. This concept is demonstrated by applying density estimation to images of handwritten digits, and sampling from the resulting model.