PGDDSA Study · Semester 1

PGD01C02

Module 3 · Exploratory Data Analytics and Model Development

Box Plots, Pivot Tables and Heat Maps

Core Titles

Key headlines and terms for quick recall

Box plot — five-number summary + outliers
Histogram — distribution of one numeric variable
Scatter plot — relationship between two numerics
Bar chart, Pie chart — categorical
Pivot table — multi-dim aggregate (Excel / pandas pivot_table)
Heatmap — colour-coded matrix
Correlation heatmap — pairwise correlations
Pair plot — scatter matrix of all pairs

Basic Idea

What it is, why it matters, how it works

Box plot

A graphical summary of the five-number summary: min, $Q1$ , median, $Q3$ , max — plus outliers flagged outside $[Q1 - 1.5 \cdot IQR, \; Q3 + 1.5 \cdot IQR]$ .

       |---|         outlier (•)
   |--[ box ]--|     whiskers + box
       median

Reveals.

Median and spread.
Skewness (box position within whiskers).
Outliers as individual points.
Comparison across groups (side-by-side box plots).

Histogram

Bars of counts (or density) per bin of a numeric variable. Shape reveals modality, skewness, gaps.

Bin choice matters — too few hides structure; too many adds noise.

Pivot table

A spreadsheet-style aggregate showing one variable's summary across two grouping variables.

Region \ Quarter	Q1	Q2	Q3	Q4
North	₹2.1M	₹2.4M	₹2.8M	₹3.1M
South	₹1.8M	₹2.0M	₹2.5M	₹2.7M
East	₹1.5M	₹1.6M	₹1.9M	₹2.0M
West	₹2.2M	₹2.3M	₹2.5M	₹2.6M

Use. Quickly slice business metrics by multiple dimensions. Available in Excel, Google Sheets, pandas (df.pivot_table).

Heatmap

Visualise a matrix with colour: darker = higher value.

Common uses.

Correlation heatmap — pairwise correlations between numeric features. Spot multicollinearity instantly.
Confusion matrix — classification performance.
Geographic — population, sales density on a map.
Time-of-day vs day-of-week — when do users log in?
Student vs subject performance — find weak subjects / students at a glance.

Pair plot (scatter matrix)

A grid of scatter plots for every pair of features, with histograms on the diagonal. seaborn pairplot is the standard tool.

Use. Spot pairwise linear / non-linear relationships, clusters, outliers in a multi-feature dataset.

Other essential plots

Bar / column chart — categorical counts.
Pie chart — share of a whole (use sparingly).
Line plot — time series trends.
Violin plot — box + KDE; richer distribution view.
Q-Q plot — checks normality.
Geographic / choropleth — spatial data.

Tools

Python: matplotlib, seaborn, plotly.
R: ggplot2.
Commercial: Tableau, Power BI, Looker.

Why visualisation matters

Humans grok pictures faster than tables.
EDA depends heavily on plots.
Stakeholders absorb dashboards better than statistics.
Anomalies and trends often jump out visually before any statistic catches them.

Mind Map

Visual structure of the concept

EDA VISUALISATIONS
├── One variable
│   ├── Histogram (distribution shape)
│   ├── Box plot (5-number + outliers)
│   ├── Violin plot (box + density)
│   └── Bar (categorical counts)
├── Two variables
│   ├── Scatter (numeric–numeric)
│   ├── Grouped box (numeric–categorical)
│   └── Contingency / mosaic (cat–cat)
├── Aggregates
│   ├── Pivot table (cross-tabulation)
│   └── Heatmap (matrix colour map)
├── Many variables
│   ├── Pair plot (scatter matrix)
│   └── Correlation heatmap
└── Time / space
    ├── Line plot (trend)
    └── Choropleth map

Exam Q&A

Part A (2 marks) and Part B (20 marks) style questions

Part A (2 marks each)

Q1. What does a box plot show? A graphical summary of a dataset's five-number summary — minimum, $Q1$ , median, $Q3$ , maximum — with outliers flagged as individual points outside $[Q1 - 1.5 \cdot IQR, \; Q3 + 1.5 \cdot IQR]$ .

Q2. What is a pivot table? A spreadsheet-style aggregation that summarises one variable across two or more grouping variables — e.g., revenue by region × quarter — available in Excel, Google Sheets, and pandas df.pivot_table.

Q3. How can a heatmap help in evaluating student performance across subjects? A heatmap displays a students × subjects score matrix as a coloured grid. Cold columns reveal weak subjects across the cohort; cold rows reveal struggling students; clusters reveal patterns such as students strong in maths also doing well in physics.

Part B (20 marks)

Q. Describe the role of box plots, pivot tables and heatmaps in Exploratory Data Analysis with examples.

Box plot.

What it shows. The five-number summary visually:

Box spans $Q1$ to $Q3$ .
Median marked inside.
Whiskers extend to the most extreme non-outlier points.
Outliers plotted individually outside $Q1 - 1.5 \cdot IQR$ or $Q3 + 1.5 \cdot IQR$ .

Information revealed.

Centre and spread.
Skewness (box offset within whiskers).
Outliers.
Multiple groups side-by-side compare distributions across categories.

Example use. Plot salary grouped by department — instantly see whether sales pays more than engineering and whether anyone is an outlier.

Pivot table.

What it is. A multi-dimensional aggregate — for each combination of two grouping variables, compute a summary (sum, mean, count) of a third.

Region \ Quarter	Q1	Q2	Q3	Q4
North	₹2.1 M	₹2.4 M	₹2.8 M	₹3.1 M
South	₹1.8 M	₹2.0 M	₹2.5 M	₹2.7 M
East	₹1.5 M	₹1.6 M	₹1.9 M	₹2.0 M
West	₹2.2 M	₹2.3 M	₹2.5 M	₹2.6 M

Insights. Quickly spot best-performing region (North), seasonal trends (Q4 highest), weakest region (East).

pandas one-liner.

df.pivot_table(values="revenue", index="region", columns="quarter", aggfunc="sum")

Heatmap.

What it is. A 2-D colour-coded matrix where each cell's colour intensity encodes a numeric value.

Common uses.

Correlation heatmap — pairwise correlations between numeric features. Identifies multicollinearity at a glance — important before linear regression.
Confusion matrix — actual vs predicted classes. Shows where the classifier confuses categories.
Geographic / spatial — population density, sales by city.
Time × day — login activity by hour of day × day of week.
Student × subject performance — instantly reveals weak subjects (cold columns), struggling students (cold rows), and learning patterns (clusters of strong subjects).

Example — student performance heatmap.

Student \ Subject	Maths	Physics	Chem	Biology	English
Alice	92	88	85	78	70
Bob	45	50	52	80	88
Carol	78	82	75	70	65
...

Plot as a heatmap with red ↔ blue gradient. Cold cluster in top-right (Alice's English) is visible; Bob's cold cluster in STEM is striking; teacher decides Alice needs language coaching and Bob needs maths support.

Why these tools in EDA.

Box plot — pinpoints outliers and compares distributions.
Pivot table — slices business metrics across dimensions.
Heatmap — turns dense matrices into instant patterns.

Together they form the core of fast, visual EDA — the foundation on which good models rest.

Descriptive Statistics: Mean, SD, Skewness, Kurtosis Simple Linear Regression