Choosing the Right Plot
For each analytical question, name the plot you would produce first, explain what feature of the data it would reveal that a summary statistic would hide, and name one pitfall of that plot.
- "Is our API latency worse in the EU region than in the US region?" (2 million requests, timestamped, with region.)
- "Do users with more support tickets spend more?" (50,000 users; tickets is a small integer 0–15; spend is dollars.)
- "Which of these 40 numeric features are redundant with each other?"
- "Has the average order value changed since the pricing update?"
- What plot would you avoid for question 1, and why?
1. Latency by region — ECDF (or overlaid box plots)
Plot the ECDF of latency for EU and US on the same axes (log-scale x helps for latency). It shows every percentile simultaneously: the two curves may coincide at the median and diverge only above p95 — exactly the tail behaviour that a mean or even a single p99 number cannot express. Pitfall: ECDFs are unfamiliar to many stakeholders; translate to "at p99 the EU is 400 ms slower" for the write-up. Overlaid box plots are the accessible alternative but hide the shape of the tail.
2. Tickets vs spend — box plots (or violin plots) of spend per ticket count
With tickets as a small integer, a scatter plot collapses into 16 vertical stripes with massive overplotting. Instead show the distribution of spend at each ticket count as boxes: it reveals whether the median rises, whether the spread widens, and whether the relationship is monotone or U-shaped (a few high-ticket users may be angry churners, others heavy users). Pitfall: box plots hide sample size — annotate n per box, since ticket counts of 12+ may be a handful of users. If you must scatter, jitter x and use alpha.
3. Redundant features — correlation heatmap (Pearson and Spearman)
A 40×40 heatmap, ideally with hierarchical clustering to group related features, reveals blocks of highly correlated variables — the "same thing measured seven ways" clusters. Pitfall: correlation is linear (Pearson) or monotone (Spearman) only, so two features related through a non-monotone function will look independent; and a heatmap can only show pairwise redundancy, not that one feature is a linear combination of three others. Confirm suspicious pairs with a scatter plot.
4. Order value over time — line plot of daily median (and mean) with the update date marked
Resample to days, plot the median and mean order value, and draw a vertical line at the pricing change. It reveals whether there is a level shift at the change, whether it was gradual or immediate, and whether pre-existing trend or weekly seasonality could explain it. Pitfall: the aggregation window matters — daily may be noisy, monthly may hide a short-lived spike; and a change in the mean with an unchanged median suggests a change in the tail (a few large orders), not in typical behaviour. Establishing that the update caused the shift is the Causal Inference Basics subject.
5. What to avoid for latency — a bar chart of mean latency per region
Latency is heavy-tailed; the mean is dominated by a small number of very slow requests and can differ between regions purely because of a few timeouts. Two bars also convey nothing about the shape of the distribution, which is the whole question. A histogram overlay is acceptable but bin choice and 2 million points make ECDFs cleaner.
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