Here are 10 test scores: 73, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 78.3. Does this set have an outlier and, if so, how does removing it affect the mean?

A.
This data set has no outliers.

B.
The set has 73 as an outlier and removing it increases the mean by about 0.5.

C.
The set has 73 as an outlier and removing it decreases the mean by about 10.

D.
The set has 73 as an outlier and removing it decreases the mean by about 0.5.

Question

Here are 10 test scores: 73, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 78.3. Does this set have an outlier and, if so, how does removing it affect the mean?	
 
 A.
This data set has no outliers.
 
 B.
The set has 73 as an outlier and removing it increases the mean by about 0.5.
 
 C.
The set has 73 as an outlier and removing it decreases the mean by about 10.
 
 D.
The set has 73 as an outlier and removing it decreases the mean by about 0.5.

anonymous · Answer

It doesn't look like there is an outlier.  An outlier is some value that is totally detached from the others.  Your interval is from 73 to 84, and pretty continuous.

anonymous · Answer

If you have a value of 2 in there, it would significantly reduce the class average (mean) and be considered an outlier.  However, you could remove the 73 and calculate the mean, and see what the difference is, to determine whether or not B,C or D could be correct answers, if you choose A and it is wrong.

mathmale · Answer

Surely like the "logic" part of your user name!  ... as well as the fact that you actually apply logic to problem solving.

Your response makes a lot of sense.  And I appreciate your "supposing we have a value of 2 in there."

I assume you already know how to obtain a 5-number summary.

zarkon · Answer

what test are you supposed to use to detect outliers?...there is more than one

mathmale · Answer

If so, would you please calculate Q1, Q3 and the IQR?  A data value is an outlier if its distance to the right of Q3 is greater than 1.5IQR, or to the left of Q1 is less than 1.5 IQR.

anonymous · Answer

I apologize if my advice/answer is incorrect. :)  Thanks for the feedback.  Perhaps the best part of my advice is gaming the answers to reduce the multiple choice options. :D

anonymous · Answer

And @mathmale I do not know what Q1, Q3 or IQR are, only the basic definition of an outlier.

zarkon · Answer

mathmale is using Tukey’s method.  You should check to see what method you are supposed to use (most likely it is this one since it is one of the simpler methods)

anonymous · Answer

@tolliver1998 I found a good tutorial to use to determine outliers: http://www.wikihow.com/Calculate-Outliers

anonymous · Answer

This seems to follow the advice of @mathmale and @Zarkon .  Good luck. :)

mathmale · Answer

Again, kudos to you for all the effort you've put into solving this problem (especially looking up material on the 'Net)!

anonymous · Answer

@mathmale Thank you, I appreciate that :)