Determine skewness if only mode and median given? > For a given set of data the mean is 10.5 and the mode is 9. What c an we deduce about the skewness of the data? > > A The data is positively skewed. > > B The data is negatively skewed. > > C The data is symmetrical. > > D We cannot deduce anything about the skewness. Answer: D I dont know why the answer is D. My book says. > mode = median = mean for a symmetrical data set > > mode < median < mean for a positively skewed data set > > mode > median > mean for a negatively skewed data set As you can see the mean is greater than the mode. Then the answer should be **A**. Looking forward to your answers.

Does you book have the three rules

* mode = median = mean for a symmetrical data set
* mode < median < mean for a positively skewed data set
* mode > median > mean for a negatively skewed data set



or did you find them somewhere else? According to the section in Wikipedia the rules are wrong. If you found them in your book then the book is obviously inconsistent.

I do believe that the answer would be D because the skewness is heavily weighed to measure the tails of the distribution. There are just a lot of really weird probability distributions that could be postulated.

Think of a broad Gaussian distribution with a mean of 9 mixed with a very very narrow Gaussian which has a mean 11. The tails are dominated by the Gaussian with mean 9. This sort of splits hairs because with sufficient measurement precision the slight skewness could be detected. For an experimentally determined distribution though the skewness could easily be within the noise limits of the measurements.