Statistics track

Statistics · Phase 12

Data Visualization

Charts as analysis: match the type, cut the junk, label directly.

In plain English

A chart is an argument. Its job is to make one comparison so obvious that the reader reaches your conclusion before reading the text.

The advanced view

Encoding choice follows perceptual accuracy: position beats length beats angle beats area beats colour. Chart type follows the comparison — time series for trend, bar for ranking, scatter for relationship, waterfall for bridging, stacked bar for composition. Action titles carry the insight; the exhibit supports it.

Visualisation is not decoration, it is analysis: a good chart answers a question. Match the chart type to the relationship — comparison is a bar, trend is a line, distribution is a histogram, correlation is a scatter, composition is a stacked bar (or a pie only for five categories or fewer). Remove chartjunk, use colour to highlight the point rather than everything, label directly instead of using legends, and respect the data-ink ratio.

In finance specifically: candlesticks for price action, heatmaps for correlation matrices, waterfalls for revenue and EBITDA bridges, tornado charts for sensitivity, and sparklines for inline trends in dashboards. In a case interview the same discipline applies verbally — state what the chart shows, then the so-what, before anyone asks.

Chart choices

Waterfall

Bridge from one figure to another. The default for explaining a profit or revenue change.

Heatmap

Correlation matrices and segment grids where magnitude and sign both matter.

Tornado

Sensitivity ranked by impact. Shows which assumption actually drives the answer.

Small multiples

Repeat one chart across segments instead of overloading a single panel.

Why it works

Position-based encodings work because human vision judges aligned positions with far lower error than areas or angles. That is the empirical reason pie charts underperform bar charts and why a bubble chart hides differences a scatter would reveal — it is a fact about perception, not a matter of taste.

Common pitfalls

  • ×Truncating an axis to exaggerate a difference.
  • ×Titling a chart with its contents ('Revenue by region') instead of its message.
  • ×Encoding more than two variables when the argument needs one comparison.

How it is used — turn a table into an argument

Step 1 of 4

  1. 1Data: EBIT fell from 50 to 38 with five moving parts.

Deeper

Deeper: the chart is the argument

Write the message first, then choose the chart that proves it. The title should be the conclusion ('Input costs drove three-quarters of the EBIT decline'), not the contents ('EBIT bridge 2024'). If you cannot write that sentence, the analysis is not finished.

Encode honestly: start bars at zero, keep one comparison per chart, label directly rather than with a legend, and use colour only to highlight the point. In an interview the same discipline applies verbally — say what the exhibit shows, then the so-what, before you are asked.

Must know cold

  • Waterfall for bridges, line for trend, scatter for relationship, small multiples for segments.
  • Title = conclusion. Axis = units. Source = date.
  • Never truncate a bar axis; you may truncate a line axis with a note.
  • One chart, one message.

Exercises

Try each one on paper before revealing the worked solution.

Exercise 1

You must show that margin decline is concentrated in one region and one product. Which exhibit?

Exercise 2

Rewrite 'Revenue by quarter and channel' as a proper chart title given online grew 30% while retail fell 5%.

Figure — encode the comparison you are making
R² = 0.25R² = 0.60R² = 0.90unexplainedmodeltotal variance in y

Bars compare magnitudes against a common baseline, so a shared axis starting at zero is non-negotiable. Every chart should answer one question stated in the title; if you need a legend to know what is being compared, redraw it.

References

  • Wickham, H. and Grolemund, G. (2017). R for Data Science. O'Reilly, Sebastopol.

Statistics glossary for this phase

The terms an interviewer expects you to use precisely — with the pitfall attached to each.

Median

The middle value once the data is sorted.

In finance

Use it for skewed data such as deal sizes, household income or customer spend.

Pitfall

×Quoting a mean where a few whales dominate makes the typical customer look far richer than they are.

Standard deviation

Typical distance of a value from the mean; the square root of variance.

In finance

The working definition of risk: volatility of returns, variability of demand.

Pitfall

×Adding standard deviations. Variances add (with covariance), not standard deviations.

Order of magnitude

The nearest power of ten of a quantity.

In finance

In market sizing, being right to a factor of two beats being precise and wrong.

Pitfall

×Losing a factor of 1,000 between thousands, millions and billions late in the arithmetic.

Trend vs. seasonality

Trend is the long-run drift; seasonality is the repeating within-year pattern.

In finance

Quarterly revenue reads badly until you compare like quarters or deseasonalise.

Pitfall

×Annualising a strong Q4 and calling it run-rate growth.

Practise this

The drills and cases where this phase turns into arithmetic you do out loud.