MHB How to find if there are outliers, given mean, median, etc

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To identify outliers without a histogram, a boxplot can be useful, but it's not strictly necessary. The conventional definition of an outlier involves data points lying beyond 1.5 times the interquartile range (IQR) from the first or third quartiles. In this case, the IQR is calculated as 5.9, leading to a lower threshold of 1.95 and an upper threshold of 25.55 for outliers. Since the maximum value is 25.8, there are mild upper outliers present. Understanding these concepts is crucial for effectively analyzing data in statistics.
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Hi guys, I'm getting ready for a stats exam and one of the questions looks like this
View attachment 3406
If I'm not given a histogram, how can this be solved?
 

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I think a boxplot can be useful here. Have you tried to draw the boxplot?
 
chriskeller1 said:
Hi guys, I'm getting ready for a stats exam and one of the questions looks like this
https://www.physicsforums.com/attachments/3406
If I'm not given a histogram, how can this be solved?

You do not need to do a box plot but you can adopt the conventional definition of outlier that corresponds to the whiskers of a box and whiskers plot. Then your definition of an outlier is any datum that lies beyond 1.5 times IQR of the 1st or 3rd quartiles.

Now the IQR=16.7-10.8=5.9, any datum that is less than 10.8-1.5 IQR= 1.95 or larger than 16.7 + 1.5 IQR = 25.55 is an outlier. Since the maximum is 25.8 there must be (mild) upper outliers.

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