Step 2: Data Classification, Grouped Frequency & Graphical Encodings
Organizing raw observations into structured tables and multi-dimensional charts reveals hidden distributions.
1. Types of Data & Frequency Distributions
- Raw (Ungrouped) Data: Data recorded in original form as collected.
- Grouped Frequency Distribution: Grouping raw values into class intervals $[a, b)$:
- Class Limits: Lower class limit $a$ and upper class limit $b$.
- Class Width (Size $h$): $h = b - a$.
- Class Mark ($x_i$): The midpoint: $x_i = \frac{a + b}{2}$.
2. Graphical Encodings
- Bar Charts: Bars of uniform width with equal spacing between them. The height is strictly proportional to frequency.
- Histograms: Contiguous rectangles over class intervals with zero gaps. The area of each rectangle is proportional to its frequency:
$$\text{Area} \propto \text{Frequency}$$
- When class widths are unequal, adjusted heights must be used:
$$\text{Adjusted Frequency Height} = \frac{\text{Minimum Class Width}}{\text{Current Class Width}} \times \text{Class Frequency}$$
- Frequency Polygons: Constructed by plotting line segments connecting the class marks $(x_i, f_i)$ of a histogram.
- Stacked Bar Charts: A single bar partitioned into component sections to visualize sub-composition and absolute aggregate sum simultaneously.