Lesson 7 of 22

Exploratory Data Analysis

Describe centre, spread, shape, relationships, and unusual observations without turning discovery into confirmation.

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Motivation

Why begin here

EDA reveals scale, structure, and quality problems before a model compresses the data into coefficients.

Why this matters

Describe centre, spread, shape, relationships, and unusual observations without turning discovery into confirmation.

Packages and data

Reproducible setup

Base stats; ggplot2 is optional for polished graphics.

Explanation 1

The live starter code is self-contained and uses only runner-compatible functions.

Explanation 2

Book-only outputs are labelled when the separate source dataset or advanced package was not supplied.

Explanation 3

R code, paths, function names, and formulas remain left-to-right in every locale.

Terminology

Core ideas and notation

Centre

Typical location measured by statistics such as mean or median.

Median resists extreme values

Spread

Variation measured by SD, IQR, or quantiles.

Report the unit and period

Exploration

Pattern discovery that generates questions and checks assumptions.

Not untouched confirmatory evidence

Notation and formulas

Key relationship

IQR = Q3 - Q1

The IQR spans the middle half and is less sensitive to tails than the standard deviation.

Step 1Define every variable and unit.
Step 2Check assumptions and information timing.
Step 3Calculate, verify, and interpret in context.

Worked example

Worked analysis

Scenario

What do centre, spread, and quantiles reveal about an illustrative inflation sample?

Variable: Eight embedded inflation observations.
Model choice: The IQR spans the middle half and is less sensitive to tails than the standard deviation.
Calculation: The mean exceeds the median because the upper tail includes 4.8 and 6.2; quantiles make the sample context visible.
Interpretation: The sample is right-skewed, so centre should be described with both mean and median.
Reasonableness check: Histogram appearance depends on bin boundaries, and eight observations cannot establish a population distribution.

R check

x <- c(1.4,1.9,2.1,2.3,2.7,3.4,4.8,6.2)
print(c(mean=mean(x), median=median(x), sd=sd(x), IQR=IQR(x)))
print(quantile(x, c(.25,.5,.75)))
hist(x, breaks=5, main='Inflation distribution', xlab='Percent')

Hints

Start by naming the question and unit.
Inspect intermediate values before the final result.
Explain what the calculation cannot establish.

The sample is right-skewed, so centre should be described with both mean and median. Limitation: Histogram appearance depends on bin boundaries, and eight observations cannot establish a population distribution.

Visual

Distribution shape

Counts thin into the upper tail.

R connection

Live, editable R practice

Run the self-contained starter code in the protected STATLAB R runner. The code prints an auditable result and avoids network or unrestricted file access.

Live R Lab

INTRO-R-CH07: Exploratory Data Analysis

Run a self-contained example, verify its output, and explain one limitation for exploratory data analysis.

Editable R code

Results

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

State the question, data, and units.

Run and inspect the printed output.

Interpret the result and one limitation.

Common mistake

Points beyond 1.5 IQR are flags, not automatically errors.

STATLAB Tip

Describe what the plot shows, a plausible interpretation, and what evidence is still needed.

Guided practice

Scenario

Plot an empirical CDF and compare its quartiles with quantile().

Hints

Reuse a small tested object.
Change one element at a time.
Finish with an interpretation and limitation.

Compare your result with the definition, units, and model assumptions—not only with a target number.

Exercises

Independent practice

Complete these without looking at the selected solutions. More than one defensible program may exist.

Explanation 1

Compare mean, median, SD, and IQR.

Explanation 2

Draw histograms with two bin counts.

Explanation 3

List two reasons a scatterplot is not causal evidence.

Selected solutions

Check one defensible route

These are compact solution routes. Confirm dimensions, units, and any changed modelling choices.

Explanation 1

c(mean=mean(x), median=median(x), sd=sd(x), IQR=IQR(x))

Explanation 2

Use hist(x, breaks=3) and hist(x, breaks=8); observations do not change.

Explanation 3

Confounding and reverse timing remain possible.

Chapter summary

What to carry forward

Describe centre, spread, shape, relationships, and unusual observations without turning discovery into confirmation.

Explanation 1

Report centre, spread, shape, and context.

Explanation 2

Graphics have tuning choices.

Explanation 3

Investigate unusual observations.

Explanation 4

Exploration is not confirmation.

Terminology

Chapter cheat sheet

mean()/median()

centre

Use in Exploratory Data Analysis.

sd()/IQR()

spread

Use in Exploratory Data Analysis.

quantile()

cut points

Use in Exploratory Data Analysis.

ecdf()

cumulative distribution

Use in Exploratory Data Analysis.

References and provenance

Safavi (2026), Chapter 7. Student notes: Mohammad Safavi, Ph.D., STATLAB Academy, Version 1.0.

Resource

Download the complete student notes

The authoritative 125-page English PDF accompanies this native lesson.

Download

Reflection

Pause and write

What assumption in exploratory data analysis most affects the conclusion?

Name the assumption, evidence you would seek, and how the recommendation might change.

Exit check

Chapter knowledge check

Reach 70% to complete the chapter. Explanations appear after submission.

Checkpoint