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The frequency distributions shown above represent two groups of data. Each of the data values is a multiple of 10.

Quantity A = The standard deviation of distribution A
Quantity B = The standard deviation of distribution B

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

The answer is B.
How to answer just by looking at the diagram without doing tedious calculations?

  • $\begingroup$ Hm, you probably have to do the calculation, but that's very easy with the given data. At least to me it looks to close to eyeball it - maybe that's just me. $\endgroup$ – Stefan Mesken Aug 15 '14 at 8:22

First of all, see that both the distributions are symmetric - So the median would be the center value, which is $30$

Since standard deviation measures spread of the data, $B$ will be having a greater standard deviation because more data values in $B$ are away from the median compared to $A$

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    $\begingroup$ Isn't standard deviation the spread of data from the mean? Can we use median to determine standard deviation instead of mean? And I guess here the mean and median are far off. $\endgroup$ – New to Rails Aug 15 '14 at 8:24
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    $\begingroup$ thats a very good question! the short answer is : $\text{mean = median}$ for symmetric distributions $\endgroup$ – ganeshie8 Aug 15 '14 at 8:30
  • $\begingroup$ Could you please share how to deduce that A and B are symmetric distributions? $\endgroup$ – New to Rails Aug 15 '14 at 8:36
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    $\begingroup$ Draw a vertical line through median and fold the graph - if both the sides overlap exactly, then it is symmetric. As the name says, a symmetric distribution has an axis of symmetry at mean=median. See m.everythingmaths.co.za/grade-11/11-statistics/tikzpictures/… $\endgroup$ – ganeshie8 Aug 15 '14 at 8:42

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