Data Visualisation (Chart Types)

Context: FIT1043_MOC · picking a chart by data type · a preliminary form of analysis · rendered in matplotlib

Quick Revision

• 🎯 Objective: choose the chart that matches the data type ➔ numeric → histogram/boxplot; categorical → bar/pie/frequency table.
• 📦 Core Components: histogram (continuous) vs bar chart (categorical) | pie (≤6 categories) | motion chart (5-D).
• ⚡ Key Constraint: visualisation is preliminary — it gives a “feel” and reveals patterns, but a flat screen limits you to ~2 dimensions.

📝 How It Works

1. Purpose

• Preliminary analysis ➔ get a “feel” for the data; can quickly reveal patterns.
• Dimension limit ➔ paper/screen is 2-D; tricks push to 5–7 dims (colour/size/time), but readability drops.

2. Charts by Data Type

• Numeric (discrete + continuous) ➔ histograms, box plots, motion charts.
• Categorical ➔ frequency tables (a summary, not a graph), bar graphs, pie charts.
• Bar chart ➔ compares groups or shows change over time.
• Pie chart ➔ proportions of a whole; usable for ≤6 categories (more becomes unreadable).

3. Histograms (bin continuous data)

• Definition ➔ a bar chart of bin counts for continuous data (bar charts alone are for categorical).
• Bins ➔ $K$ equally spaced bins of width $w=\frac{\max \{y\}-\min \{y\}}{K}$; bin count $v_k=\#\{y_j\in (\min \{y\}+(k-1)w,\min \{y\}+kw)\}$.
• Choosing $K$ ➔ too few hides shape, too many looks ragged (e.g. 20 → 50 smoother → 100 ragged).

4. Motion Charts

• What ➔ interactive multi-dimensional viz (GapMinder, Hans Rosling; Google renamed them bubble charts).
• Five dimensions ➔ x-axis, y-axis, bubble size, bubble colour, and time.
• Trade-off ➔ + deep trends, good for exploration, intuitive; − not for static media, controls complex/overwhelming.

⚖️ Core Decision Matrix

Data type	Charts	Note
Numeric-continuous	histogram, box plot	histogram needs binning
Numeric (either)	motion/bubble chart	multi-dimensional/time
Categorical	bar graph, frequency table	bar compares groups
Categorical (proportions)	pie chart	≤6 categories only

When It Flips: a histogram and a bar chart look alike but differ by data type — histograms bin continuous numeric data (bars touch, order matters), bar charts show categorical counts (bars separate, order free).

📊 Exam Execution Trace

Applied Exercise

Problem: Data spans $\min =0$, $\max =100$, using $K=20$ bins. Bin width? Which bin holds $y=47$? Derivation Proof / Hand-Calculation Walkthrough:

$$\begin{array}{rl}w& =\frac{\max -\min }{K}=\frac{100-0}{20}=5\\ \text{bin index}& =\lceil \frac{47-0}{5}\rceil =\lceil 9.4\rceil =10(\text{covers }45\text{–}50)\end{array}$$

Final Extracted Output: width $5$; $y=47$ falls in bin 10 (the 45–50 interval).

🧠 Active Recall

A histogram and a bar chart look identical — what actually distinguishes them?

• Hint: Continuous vs categorical.

Answer

• Short answer: A histogram bins continuous numeric data (adjacent, ordered bins); a bar chart shows categorical counts (separate bars, no inherent order).
• Why: Binning ➔ histogram bars represent ranges $w=(\max -\min )/K$; bar-chart bars represent discrete categories.

Why cap pie charts at ~6 categories, and what five dimensions can a motion chart show?

• Hint: Readability + encoding channels.

Answer

• Short answer: Beyond ~6 sectors the eye can’t compare relative sizes; a motion chart encodes x, y, bubble size, bubble colour, and time.
• Why: Perceptual limits ➔ too many sectors/dimensions overwhelm interpretation.