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# Boxplot skewed or symmetric

Posted on 2011-04-24
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Last Modified: 2012-05-11
Dear experts.

I am asking this question to clear up confusion that I have.

Please see the attached image.

I cant decide whether it is skewed to the left or symmetic.

My reason for this is because although the box lies to one side of the full line, the line in the box itself is in the middle.

When determining whether data is skewed or symmetric what do I actually look at because from whichever way I see the question either answer could be valid?

Many thanks in advance for your help.

Steve

box-plot-capture.JPG
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Question by:steve_york
9 Comments

LVL 37

Expert Comment

Since the 'whiskers' are just the single min and max, I would put a lot more weight on the box when making observations. 1 2 2 2 2 4 4 5 5  3 3 3 3 10 is fairly symmetric data, but the right whisker would be way out there.
That said. The box is a bit skewed to the left too. Not a ton, but it's noticable.
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LVL 27

Expert Comment

To answer your question requires more information.  What is being shown?  what do the "whickers" represent? Is there any data between the box and "whiskers"?, What does the vertical line in the box represent?
TommySzalapski:'s comments are very relevant (especially the last one. How symmetric does the data have to be to be called symmetric.  "Skewed" does not mean "anti-symmetric"
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Author Comment

Hi Experts,

Thank you for your input so far.

The vertical line represents the number of customers waiting in a bank.

It's a confusing one for me because it would appear their is not a direct answer either way?

Also, when you refer to whiskers, what do you mean by this term?

Thanks,

Steve

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LVL 27

Expert Comment

"Also, when you refer to whiskers, what do you mean by this term?"
The two vertical lines at the end of the long horizontal line
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LVL 27

Expert Comment

I, in particular, do not understand what the vertical scale on your diagram represents
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Author Comment

The data for this is:

4.2
5.6
3.0
5.1
4.8
2.3
3.5
3.2
4.5
6.1
0.4
5.1
6.5
6.2
3.8

Based on this, there is data in the whiskers.

With regard to how symmetric the data has to be to called symmetric i dont know as this is for a uni assignment but I suppose i could argue that it is both couldnt i?

Steve
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LVL 37

Accepted Solution

The vertical line in the middle of the box is the mean, the ends of the box are the quartiles and the whiskers are the min and max.

The only way to know if it is 'symmetric' or 'skewed' is to have a formal definition of each. How do they define 'symmetric'? I could see it defined as the mean and the median being the same (or within some threshold). I would consider that to be symmetric. Since your data has 8 elements greater than the mean and 7 less, you could certainly make a claim of symmetry.

Without formal definitions, though, you can't say anything. There must be a definition somewhere or, no offense, but your instructor/book has problems.
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LVL 27

Expert Comment

TommySzalapski: has good comments. He answered my question about y axis and cleared up my thinking.
By his definition of symmetry your data is symetric. However if you were to define symmetry as "the sum of the moments about the mean to be zero" the data would not by symmetric. The diofficulty is with the point 0.4.
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Author Closing Comment

Thanks for your help experts.
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