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Two groups have 10 and 20 observations respectively. Their standard deviations are 2 and 3, and both are measured about the common mean value 5. What is the standard deviation of the combined set of 30 observations?
- 2/√3
- √6
- √(22/3)
- √3
Correct answer: √(22/3)
Solution
Since both SDs are about the common mean 5, combined variance = (n1*s1^2 + n2*s2^2)/(n1+n2) = (10*4 + 20*9)/30 = 220/30 = 22/3. So combined SD = sqrt(22/3).
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