An independent study reference written by Dr Phuc V. Nguyen. It is not official subject material — for assessment requirements always follow your subject outline and vUWS.

Visual Communicationbeginner

The purpose of visualisation

Q: An analyst has fitted a regression and reports a strong, statistically significant slope. What is the best reason to still plot the raw points before circulating the result?

The plot can reveal that the fit is driven by a few extreme points, or by two separate groups. A slope estimate is a summary. It cannot tell you whether the pattern is a genuine linear trend across all observations, or an artefact of a handful of outliers, a curve, or two clusters sitting at different ends of the range. Only the picture separates those cases. Plotting changes nothing about significance, and it cannot establish causation.

Q: A team must report four quarterly revenue figures to a board and wants each figure read exactly. What is the most defensible presentation?

A small labelled table, because exact lookup is the task. The stated job is exact lookup of four numbers, and a table does that better than any graphic. Charts earn their place when the reader has to compare many values, see a shape, or spot an exception. Choosing the form from the reading task, rather than from a preference for pictures, is the underlying judgement.

A chart is a measuring instrument for the eye. Visualisation does three distinct jobs. Exploration, where you look for structure nobody has described yet. Confirmation, where you check whether an assumption survives contact with the data. Explanation, where you move a specific decision along. Summary statistics compress a dataset to a handful of numbers, and compression discards shape. A mean, a standard deviation and a correlation can be identical across datasets that look nothing alike. Plotting the points is how you find out which dataset you actually have, before you commit to a model or a recommendation.

Why it matters

Think of a summary statistic as a description of a person read out over the phone. Height, weight, age. Accurate, and still useless for picking them out of a crowd. The chart is the photograph. You do not replace the numbers with it, you look at both. Most of the time the photograph is what tells you something has gone wrong, because the eye notices a gap, a cluster or an outlier long before an average does.

Before you read on — recall

An analyst has fitted a regression and reports a strong, statistically significant slope. What is the best reason to still plot the raw points before circulating the result?

Formulas

Pearson correlation, and why one number is not enough

r = \dfrac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2}\,\sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}

Correlation rescales the joint movement of two variables onto a range from minus one to plus one. It is a single number, so it cannot separate a clean straight line from a curve, from a flat cloud with one extreme point, or from two distinct groups sitting at opposite corners. Anscombe built four small datasets that share

r = 0.816

and the same fitted line while looking completely different once plotted.

Worked examples

Scenario

A pricing analyst reports that price and units sold have a correlation of about minus zero point eight across two hundred products, and recommends a broad price cut.

Solution

Plotting the two hundred points shows two clusters rather than one relationship. Everyday consumables sit at low prices and high volumes, and a smaller premium range sits at high prices and low volumes. Within each cluster the slope is close to flat. The strong negative correlation comes from the gap between the two groups, not from customers responding to price. A cut priced off the pooled line would give away margin on the premium range without lifting its volume. The chart changed the recommendation, the correlation alone would not have.

Scenario

A subscription team reports a mean time to cancellation of about seven months, and plans a retention offer at month six.

Solution

A histogram of cancellation timing shows two spikes, one in the first twenty-one days and another around month fourteen when the introductory discount ends. Almost nobody cancels near month seven. The mean sits in the empty valley between the two peaks, which is what an average does to a distribution with two modes. The offer as designed would reach few of the people who actually leave. Splitting it into an early onboarding intervention and a renewal-pricing intervention puts effort where the cancellations are.

Common mistakes

✗Visualisation is the last step, something you do once the analysis is finished. Most of the charts an analyst makes are never shown to anyone. They are working charts made during exploration and cleaning, and they are where problems in the data usually surface first.
✗If the summary statistics are correct, a chart can only add polish. Summary statistics are lossy by construction. Datasets with identical means, standard deviations and correlations can have completely different shapes, so the chart carries information the numbers cannot.
✗A more attractive chart is a more useful chart. Decoration and accuracy are separate qualities. The test of a chart is whether the reader draws the conclusion the data supports, and heavier styling usually makes that harder.
✗Any chart beats a table. When the reader needs an exact value, or when there are only three or four numbers, a small labelled table is clearer than a graphic.

Revision bullets

•Three jobs: exploration, confirmation, explanation
•Summary statistics compress, and compression loses shape
•Anscombe: same mean, variance, correlation and fitted line, four different pictures
•The Datasaurus Dozen extends the same point to thirteen datasets
•Most working charts are made for the analyst, not for an audience
•A small labelled table beats a chart when exact values matter

Quick check

An analyst has fitted a regression and reports a strong, statistically significant slope. What is the best reason to still plot the raw points before circulating the result?

A team must report four quarterly revenue figures to a board and wants each figure read exactly. What is the most defensible presentation?

Connected topics

Analytics Workflow Correlation vs Cause Visual Variables Choosing a Chart Data Storytelling Truncated Axes Design Thinking

More in Visual Communication

Dashboards Visual Mistakes Chart Ethics

Sources

Anscombe (1973)
Anscombe, F. J. "Graphs in Statistical Analysis." The American Statistician, 27(1), 17-21, 1973.
The four-dataset demonstration that identical summary statistics can hide completely different structure.
Matejka & Fitzmaurice (2017)
Matejka, J., & Fitzmaurice, G. "Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing." Proceedings of CHI 2017, 1290-1294.
The Datasaurus Dozen, a modern generalisation of the Anscombe point to thirteen datasets.
Munzner (2014)
Munzner, T. Visualization Analysis and Design. CRC Press, 2014.
Frames visualisation design around what is being shown, why, and how it is encoded.

How to cite this page

Dr. Phil's Quant Lab. (2026). The purpose of visualisation. Derivatives Atlas. https://phucnguyenvan.com/concept/ba-purpose-of-visualisation