Mastering Frequency Tables and Data Visualization

Frequency Tables for Data Organization

A frequency table is the easiest way to organize data. To construct a frequency table from the data, essentially we have to count how many times each event occurs among the data. Depending on the type of variable, we can add more or less information to the frequency table.

• Absolute frequency: Count how many times each value appears in the table.
• Relative frequency: Count how many times each value appears in the table, divided by the size of the sample.
• Cumulative absolute frequency: The sum of all previous absolute frequencies (e.g., how many people own 3 cars or less?).
• Cumulative relative frequency: The sum of all previous relative frequencies (e.g., what proportion of people own 3 cars or less?).

Discrete Variables

For discrete variables, the table typically includes: Absolute Frequency, Relative Frequency, Cumulative Absolute Frequency, and Cumulative Relative Frequency.

Grouping Data in Intervals

Ideally, when grouping data in intervals, we should follow these tips:

• Between 5 and 10 intervals;
• All intervals have the same length.

Key metrics for intervals include:

• Length: The length of the interval.
• Density: The quotient of the absolute frequency divided by the length of the interval.
• Class mark: The middle point of the interval.

Continuous Variables

For continuous variables, the table includes: Absolute Frequency, Relative Frequency, Cumulative Absolute Frequency, Cumulative Relative Frequency, Length, Density, and Class Mark.

Data Visualization and Graphical Representation

Graphs allow for a quick understanding of the distribution of the data. A good graph will highlight significant features of the data. Graphs are also very useful when comparing two sets of data. Different situations call for different types of graphs; it is important to know which graph to use in each situation. Different types of variables allow for different types of graphs.

Bar Charts for Categorical Variables

A bar chart is a graph (typically used for categorical variables) displaying a bar for each category.

• The height or length of each bar is proportional to the frequency (absolute or relative) of the corresponding category.
• Its main purpose is to compare categories among them.
• The bars can be horizontal or vertical; this is a matter of choice.

Pie Charts for Qualitative Variables

Pie charts (circle graphs) are mostly used to display qualitative variables. It shows a circle divided into slices, each slice representing a category.

• The size of each slice is proportional to the absolute or relative frequency of the corresponding category.
• Again, the purpose of the graph is to compare categories among them. It is also very useful when comparing a single category against the rest (proportion).