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Assuming that I'm able to augment their knowledge about boxplot I can give the below insights for box plot

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First Quartile(Q1)
Second Quartile(Q2)
Third Quartile(Q3)
Inter Quartile Range(IQR) = Q3-Q1
Inner Fence:
   Lower bound = Q1 - (1.5 * (Q3-Q1))
   Upper bound = Q3 + (1.5 * (Q3-Q1))
Outer Fence:
   Lower bound = Q1 - (3 * (Q3-Q1))
   Upper bound = Q3 + (3 * (Q3-Q1))

Total Number of Outliers(< Q1 or > Q3)

Let's assume this much is articulated and (hopefully) understood by the 'receiver'.

What is the cleanest, easiest way to explain someone the concept of boxplot? What does it intuitively mean? If one is to explain this to a person or manager who was not aware of statistics, how would one go about it "Storytelling with Boxplot Visualization"?

Thalassophile
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    The last line in your list of characterizations is incorrect: values beyond the first or third quartiles are definitely not "outliers," because--by definition--half the data lie in those regions! – whuber Jun 20 '20 at 13:10
  • Are you trying to use a boxplot to explain something about a dataset or are you trying to explain to someone what a boxplot is? – Ryan Volpi Jun 21 '20 at 03:01
  • @RyanVolpi both – Thalassophile Jun 21 '20 at 05:03
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    If your audience doesn't know what a boxplot is, I suspect using it would more likely obscure whatever story you want to tell. Your question lists nine conclusions from the boxplot. That alone is likely too much information to communicate a clear message. When you add to that the definition of a boxplot and a description of the ways to interpret it, I believe your 'reciever' will have missed the story. – Ryan Volpi Jun 21 '20 at 05:55
  • @whuber How to get the number of outliers? Is that values Upper bound of Inner Fence?? – Thalassophile Jun 21 '20 at 09:36
  • Minimally if the reader doesn't know the definitions of median and quartiles, those need to be explained first. I don't often see use of 3 IQR beyond the quartiles as a threshold. I'd argue that 1.5 IQR beyond the quartiles as a threshold, which is still very often used, is long since past its sell-by date as it confuses as much as it clarifies. – Nick Cox Feb 06 '24 at 15:18

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