Numerical Systems

Introduction Positional Notation Converting Between Bases Binary Addition Binary Multiplication Challenges (Python) Challenges (Java)

Modular Arithmatic

Introduction The Modulus Operator Cyphers Modular Arithmetic Modular Inverse Challenges (Java)

Algorithms

Introduction Algorithms Time Functions Asymptotic Complexity Summation Challenges

Propositional Logic

Introduction Propositional Logic Conjunction and Disjunction Implication and Equivalence Bitwise Operators Challenges

Set Theory

Introduction Sets Subsets and Supersets Set Operations Challenges

Graph Theory

Introduction Graphs Directed Graphs Structure of Language Search Trees Neural networks Game Object Trees Challenges Graph Question Generator

Proof

Introduction Proof Proof by Cases Proof by Contradiction Proof by Induction Challenges

Maths to Code

Maths to Code Challenges Question Generator

Descriptive Statistics

Introduction Statistics Measures of Central Tendency Measures of Spread Data Visualisation Correlation Challenges

Probability

Introduction Probability Basics Combinatorics Probability Trees Law of Total Probability Bayes Rule Challenges

Inferential Statistics

Introduction Probability Distributions Samples and Populations Hypothesis Testing Z Scores Student's T-Test Challenges

Data Visualisation

Charts make your data look fancy and also help you understand what your data is showing. In this video I introduce the most useful kinds of charts for your data.

Eleven-minute video

You can also view this video on YouTube

You can find the slides here and also as .odp.

Key Points

Data visualisation is important to help other people (and yourself) understand your data. In the academic literature there are standard ways certain types of data are represented.

There are loads of different types of plot. Here are some of the most useful to know.

Bar charts

Compares values on a common scale
Shows the ratio between values
Appropriate for categorical variables

Pie charts

Shows proportions of a whole
Looks nice
Hard to visually compare values and generally avoided in the research literature

Histogram

Like a bar chart, but continuous values are grouped into bins
Appropriate for continuous variables

Density Plots

Density plots show how many observations of a variable exist in a particular range.

Single-variable density plots are often used to show probability distributions. They show the relative liklihood of getting data in a particular range. For example, the density plot below shows that our data approximates a normal distribution due to its characteristic bell curve shape.

You can also produce 2D density plots, which shows clusters of data points.

Box plots

Visualises distribution of data
Shows median, upper quartile, lower quartile, and highest and lowest values
Commonly used for illustrating hypothesis tests

Heat Map

Heatmaps use colour to show mangnitude of a variable.

For example, a heatmap might represent a level in a video game and show through colour the amount of time a player spends at different places.

Scatterplot

Shows dots representing data points for two variables x and y.
Independant varaible (IV) placed on x axis
Dependant variable (DV) on y axis

Questions

1. Check your understanding

Does this show a correlation between the two variables?

Generate

Summary

In this section we have learned about data visualisation.

You should be able to draw bar charts, histograms, box plots, and scatter plots
You should be able to interpret density plots and heatmaps

You may now move on to the descriptive statistics challenges

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Getting Started

Introducing Mathematics