Data Science interview question · Descriptive statistics · junior level
You need to show delivery times for 20 cities. Would you use histograms, box plots, violin plots or ECDFs, and why?
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Why it is asked
Choosing a chart is choosing what the reader can see. The interviewer checks that you know what each chart hides, not only how to draw it.
The answer
I would start with box plots sorted by median, with each city's order count printed next to it, and then open a histogram or ECDF for any city that looks unusual, because a box plot can hide a distribution with two peaks.
What each chart does:
- Box plot: the box runs from Q1 to Q3 (the 25th and 75th percentiles, the middle half of orders), the line inside is the median, the whiskers reach the furthest points within 1.5 x IQR (interquartile range, the box length), and dots beyond them are outliers. Twenty boxes fit side by side, so it is the best first view.
- Histogram: bars count orders in bins of equal width. It shows shape, but changes with the bin width; 20 of them need small multiples (a grid of small charts sharing axes).
- Violin plot: a box plot with a smoothed histogram on each side. It shows peaks, but the smoothing can invent shape for a city with few orders.
- ECDF (empirical cumulative distribution function): for every x, the share of orders delivered within x minutes. It has no bins, any percentile can be read off it, and a few cities overlay cleanly.
Example from a simulation with 400 orders per city: City A and City B have almost the same box (median 32.0 minutes, Q1 23.8 vs 24.1, Q3 40.6 vs 40.9). Their histograms differ: A has one broad hump, B has two peaks near 24 and 41 minutes. Only 6% of B's orders take 29 to 35 minutes, against 18.5% of A's.
Always show sample size: 40 orders look as certain as 40,000.
What the interviewer listens for
- Box plots compare many groups at once but can hide two peaks.
- Histograms show shape but depend on the bin width.
- ECDFs need no bins and show every percentile.
- Small multiples (a grid of small charts) with shared axes, and the sample size per city.
Follow-ups the interviewer may ask
- How would you order the 20 boxes? Hint: by median, or by p90 if the slow tail is the business problem, never alphabetically.
- A violin plot shows a bump for a city with 30 orders. Do you trust it? Hint: no; smoothing invents shape with few points, so show the raw points.
- What would you show a non-technical audience? Hint: the median and p90 per city, plus the share of orders later than the promised time.
Common mistakes
- Trusting a box plot alone when the shape matters.
- Comparing histograms drawn with different bins or axes.
- Hiding sample sizes, so a tiny city looks as reliable as a big one.
Written by Roni Das, who builds distributed systems and AI systems for a living.
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