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A report gives only the five-number summary of the daily visitors to a small museum over a made-up…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A report gives only the five-number summary of the daily visitors to a small museum over a made-up season: 3, 18, 24, 30 and 61. Find the IQR and both fences. Is there at least one outlier? Can the smallest value be an outlier? In a box plot that marks outliers, the right whisker ends at the largest value inside the upper fence. Can you tell exactly where it ends?
Need a reminder? The key ideaShow
The fences are 1.5 IQR beyond the quartiles; a value beyond a fence is an outlier.
Check an outlier for a mistake before you do anything else.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The IQR and the fences. IQR . . Lower fence ; upper fence .
Step 2. Outliers. The maximum, 61, is above 48, so there is at least one outlier. The minimum, 3, is above 0, so no value is a low outlier.
Step 3. The whisker. It ends at the largest value that is 48 or less. The summary does not say what that value is, only that it is at least .
Answer: IQR 12, fences 0 and 48; at least one outlier (61); the smallest value is not an outlier; the end of the right whisker cannot be found from the summary.
Watch out. A summary hides how many values lie between 48 and 61. There could be one outlier or several.
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