Visualising Data Made Easy | CFA Level I Quantitative Methods

PREREQUISITE LESSON

This lesson is a prerequisite for the course. While you won’t be directly tested on its content in the exam, it’s assumed you’ve gained this knowledge or skill during your university studies. We strongly recommend reviewing this lesson, as its content may be essential for understanding subsequent parts of the curriculum.

Welcome to our guide on summarising and visualising data! In this article, we’ll dive into the fascinating world of data visualisation and help you make sense of complex data sets. So, without further ado, let’s get started!

Understanding Population and Sample

First, let’s quickly go over the difference between population and sample.

• Population: The complete set of all possible members in a group of interest.
• Sample: A subset of the population, often selected randomly or based on specific criteria.

Now that we know the basics, let’s dive into the world of data visualisation and summarisation!

Creating a Frequency Distribution

One common method to summarise and visualise data is a frequency distribution, which organises data based on specified intervals. Here are the steps to create one:

1. Define the intervals: Determine the lower and upper limits of your data, ensuring they cover all observations.
2. Tally and count observations: Assign each observation to the appropriate interval and count the number of observations in each interval.

With these steps, you have formed a histogram – a graphical representation of the frequency distribution.

Presenting Data with Frequency Polygons and Relative Frequency

Another way to present data is by drawing a frequency polygon using the midpoint of each interval and plotting the frequency for each midpoint.

While we’ve been working with absolute frequency so far, you might also encounter relative frequency, which is the absolute frequency divided by the total number of observations, represented as a percentage.

Visualising Data with Bar Charts, Line Charts, and More

There are many visualisation tools to help analysts study and identify patterns in data, such as:

• Bar charts: Ideal for illustrating relative differences in sizes, degrees, or magnitudes across categories or entities being compared.
• Stacked bar charts: Used when there are multiple categories of data to visualise.
• Grouped/clustered bar charts: Appropriate when comparing individual categories across entities.
• Line charts: Suited for visualising time series data.
• Bubble line charts: Adds a dimension to a line chart, such as representing a company’s net profit margin with bubble size.
• Dual-scale line charts: Displays two lines with their own scales on each side, representing different variables over time.

Analysing Categorical Data with Contingency Tables, Heat Maps, and Tree Maps

Contingency tables, also known as cross-tabulations or crosstabs, display the relationship between two or more categorical variables in a matrix format. They enable you to identify patterns, relationships, and potential associations between the variables.

Heat maps are a powerful way to visualize data in contingency tables. They use color intensity to represent the frequency or magnitude of an additional variable, making it easier to spot trends and patterns. For example, a heat map can display the relationship between age groups and product preferences, with color intensity reflecting the number of purchases.

Tree maps are another useful tool for visualizing hierarchical data. They display data as nested rectangles, where the size and color intensity of each rectangle correspond to a particular variable’s value. This allows for a clear, visually appealing representation of complex data structures. For instance, a tree map can show the breakdown of sales by region, with subcategories for each product type.

A confusion matrix is a specific type of contingency table often used in machine learning and classification problems. It compares the actual class labels with the predicted class labels, providing insight into the performance of a classification model. The confusion matrix allows you to assess the accuracy, precision, recall, and F1 score of your model, helping you identify areas for improvement and better understand the model’s strengths and weaknesses.

Other Visualisation Tools

Beyond the visualisations mentioned earlier, there are several other tools that can help you better understand and communicate data:

• Pie charts: Used for showing the relative proportion of each category within a dataset. However, they are not as effective when comparing multiple categories or datasets.
• Scatter plots: Useful for illustrating the relationship between two continuous variables, allowing analysts to identify patterns, correlations, and potential outliers.
• Box plots: Provide a visual summary of a dataset’s central tendency, dispersion, and skewness by displaying the median, quartiles, and outliers.

Conclusion

Understanding how to visualise and summarise data is crucial for making informed decisions in finance, economics, and other fields. By mastering the tools and techniques mentioned in this guide, you’ll be well-equipped to analyse and interpret complex data sets. Remember, the key to effective data visualisation is to select the right tool for your specific dataset and communication needs.