If we have the following histogram:

enter image description here

And, want to describe it based on one of the following options, which one do you think is correct? Why?

  1. positively skewed
  2. symmetric
  3. none of the above
  4. negatively skewed

My initial suggestion would be "3. none of the above".

What do you think?


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    $\begingroup$ It would be good to write down your reasoning for choosing 3. $\endgroup$ – nico Apr 9 '12 at 12:37
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    $\begingroup$ @nico: (+1) I think you are right and we all want to see some motivation and thought put into homework questions. It usually is helpful to point the OP to the FAQ in these instances, too, I find. $\endgroup$ – cardinal Apr 9 '12 at 14:39
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    $\begingroup$ 5. It is red and has intelligibile labels. $\endgroup$ – user88 Apr 10 '12 at 11:57

I think you should ask yourself, if it isn't symmetric, then why not? Is it really likely that something that is not symmetric is not skewed in either the negative or positive direction?

What is the feature about this histogram that makes you think it isn't symmetric? Then, how would you describe that feature?

  • $\begingroup$ (+1) Good leading questions. But yes, it is possible for an asymmetric histogram not to be skewed: stats.stackexchange.com/questions/24853. $\endgroup$ – whuber Apr 9 '12 at 0:39
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    $\begingroup$ Yes, I thought of that as I wrote the answer. But in this case... $\endgroup$ – Peter Ellis Apr 9 '12 at 0:53
  • $\begingroup$ This should really be a comment, as it does not answer the question. $\endgroup$ – nico Apr 9 '12 at 12:36
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    $\begingroup$ @nico: It's not my answer, but if you think leading questions don't make good answers, maybe you should ask about that in meta? $\endgroup$ – Neil G Apr 9 '12 at 13:17
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    $\begingroup$ @nico: My feeling is that Peter has responded to the question exactly as expected and intended given this is a homework question. $\endgroup$ – cardinal Apr 9 '12 at 14:36

Check out the wikipedia article http://en.wikipedia.org/wiki/Skewness.

I see that the mean and standard deviation are provided, not clear what is the statistic below that. If you are able to infer the median from this histogram, you could also calculate the Karl Pearson coefficient of skewness. This is defined as 3(mean - median) /Standard Deviation

If this statistic is greater than zero, the distribution is positively skewed, if negative then distribution is negatively skewed (this test might not work for bi-modal distributions though)


The answer here is "1. positively skewed".

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    $\begingroup$ You should really explain why $\endgroup$ – nico Apr 9 '12 at 12:36

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