Group A has 10 measurements with mean 35 and standard deviation 0.4. Group B has 15 measurements with mean 38 and standard deviation 0.6. Find the combined standard deviation to two decimals.
The combined mean is (10×35+15×38)/25=36.8. Using the source’s population-variance convention, total variance is [10(.4²+(35−36.8)²)+15(.6²+(38−36.8)²)]/25=2.44. Standard deviation=√2.44=1.56205, rounded 1.56. This includes between-group mean differences, not only within-group noise.
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