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How does skew and range affect standard deviation

  1. Sep 26, 2014 #1
    1. The problem statement, all variables and given/known data

    How does skew and range affect the standard deviation; does one affect it more than the other?

    2. Relevant equations

    None

    3. The attempt at a solution

    It seems as though if the range increases, the standard deviation increases because the SD is a measure of how spread apart from the mean each observation is. However, I have no idea how skew for a data set would affect the SD of that data set. Also, I am not really sure what the question is asking.
     
  2. jcsd
  3. Sep 28, 2014 #2

    Mark44

    Staff: Mentor

    How is skew defined in your textbook? Range, standard deviation, and mean are pretty well-known terms, but skew is not so well known.
     
  4. Oct 3, 2014 #3
    The effects of skewness on mean, range, and standard deviation are clearly demonstrated in the accompanying graphic. Additionally, if you understand how mean, range, and standard deviation are calculated, the differences in the mean, range, and standard deviation between a Normal distribution with skewness parameter 0 and a skewed Normal distribution with skewness parameter 2 should be intuitively obvious and with an appropriate amount of thought, these differences should be able to be explained conceptually and mathematically.

    Note: While the two pairs of arrows were meant to demonstrate visually the phenomena discussed above, I am afraid they serve no value without some explanation. Therefore, the point of the two pairs of arrows (pun intended) is to demonstrate by the lengths of corresponding arrows that the skewed data is less dispersed in both directions than the Normal data at a randomly selected level. I suspect the vertical lines "hide" the differences in the lengths of the arrows, but if you measure them, the differences in lengths become obvious.

    I will be delighted to clarify any points or answer any questions and would appreciate any comments, suggestions, or criticisms.

    Jim
     

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