Suppose i have 4 values i.e 5,4,3,2

Std Dev of 5,4,3,2 is 1.29

Std Dev of 5,4 is 0.71
Std Dev of 3,2 is 0.71

Now Suppose i only have the standard deviation values i.e 0.71 & 0.71
How can i achieve 1.29 from these values?
I will not have the initial data. I will not have the means.
I will only have standard deviation values.
Please help.

  • $\begingroup$ Can't be done.. $\endgroup$ Commented Oct 2, 2018 at 10:28
  • 1
    $\begingroup$ Do you also have the means of your two groups? If so edit that into your question. $\endgroup$
    – mdewey
    Commented Oct 2, 2018 at 12:42
  • $\begingroup$ No, I dont have the means. $\endgroup$ Commented Oct 2, 2018 at 14:19

1 Answer 1


In the absence of the means you cannot do what you want. The reason is that there is no way of adding back the variability between the groups. So to take your example the standard deviation of 0.71 could have come from a pair of values like 100 101 and clearly the sd of 101, 100, 3, 2 is much larger than 5, 4, 3, 2.

Your only hope would be getting the data source to provide more information but from your question I suspect that is impossible.


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