A distribution message says the values are spread across a range in a particular shape, and it's the type analysts skip most often. The habit is to report a mean and move on, and the mean is frequently a number that describes nothing in the dataset.
Worked example: forty loans at an NBFC
A synthetic lending book makes the case. Forty loans at an NBFC, ticket sizes in rupees lakh, ranging from 0.62 to 7.20. The mean ticket is 3.0888 lakh, and not one loan lies within ten percent of that mean. The book is two clusters, a two-wheeler cluster of 22 loans averaging 0.9241 lakh and a used-car cluster of 18 loans averaging 5.7344 lakh, whose means sit 4.81 lakh apart. The overall mean falls between the clusters, inside a band running from 1.28 to 4.60 lakh, 3.32 lakh wide, where the business has never written a loan.
Four forms are available and they hide different things.
A bar chart of the mean by branch hides everything. The four branch means come out at 0.7818, 1.0664, 5.1389 and 6.3300 lakh, which looks like a story about branches and is actually the same two-cluster structure sliced by geography. Any chart of means will do this. The mean is a summary, and summarising is the very operation that destroys the shape you were trying to show.
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What does a box plot hide that a histogram shows?
A box plot hides bimodality, and it hides it completely. The five-number summary here is 0.62, 0.895, 1.185, 5.54 and 7.20. The box spans from 0.895 to 5.54, an interquartile range of 4.645, and it draws as a solid rectangle covering the entire middle of the range. You'd take that rectangle to mean the middle half of loans lies in that band, spread somehow across it. Twenty loans do lie in the band, and not one of them is between 1.28 and 4.60. The chart's most visually dominant element covers a region containing no data. Box plots are excellent for comparing several groups at once, as row 17 of the heuristic says. Whenever the underlying shape is in question, they must carry the observations overlaid.
A histogram shows the shape if the bin width lets it. At 0.50 lakh bins the structure is unmistakable: 15 loans in the 0.50 to 1.00 bin, 7 in the next, then six empty bins, then the second cluster spread from 4.50 to 7.50. At 2.00 lakh bins it survives, with 22 loans in the first bin, zero in the second and 18 above 4.00. At a single 8.00 lakh bin there is one bar and no information at all. You chose the bin width, and it changes the conclusion. A histogram that doesn't state its bin width on the chart is unfinished.
When is a dot plot better than either?
A dot plot of every observation hides nothing at forty points. One dot per loan on a horizontal scale, jittered vertically if they collide. The reader sees the two clusters, the empty gap, the long right tail of the used-car cluster and the single loan at 7.20 without any parameter having been chosen on their behalf. Below about two hundred observations it's usually the right answer. Beyond that the dots merge into a smear and the histogram takes over.
The working rule: show the observations if you can, summarise only when you must, and when you summarise, say which summary you chose. Mean and median disagree here by a factor of 2.6, and the disagreement is the finding.