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If 2 distributions of data have the same mean value but standard deviation of sample 1 is twice the value of sample 2, explain what the difference in standard deviation value would indicate about the two distributions.

Totally stuck with this one.

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  • $\begingroup$ Is this homework? if so, it should have the homework tag. And welcome to the site! $\endgroup$
    – Peter Flom
    Commented Mar 14, 2013 at 11:44
  • $\begingroup$ It's a task within a research module. I'm new to this site! $\endgroup$
    – Chloe
    Commented Mar 14, 2013 at 11:50
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    $\begingroup$ Think about this as a picture. 2 distributions have the same mean, which is the same as saying they are both centered at the same point on the x-axis. The SD is a measure of how far from the mean, or how spread out the data tends to be. So what would a SD 2X as big as another SD (with same means) say about its distribution? $\endgroup$
    – learner
    Commented Mar 14, 2013 at 11:59
  • $\begingroup$ Would it say that there is a larger variation of data and that the data is more widely distributed in sample 1 than sample 2? $\endgroup$
    – Chloe
    Commented Mar 14, 2013 at 12:02
  • $\begingroup$ Yes, Sample 1 has greater variation than Sample 2. $\endgroup$
    – learner
    Commented Mar 14, 2013 at 12:18

1 Answer 1

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Not knowing the rest of the questions within your research module, I can point you to the following references for further study:

A general description of mean and standard deviation, with an example and useful equations,

A slightly more technical discussion of the above,

A Khan Academy video on the topic.

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