two sets of sizes 40 and 50 respectively have the same mean 53 , but different standard deviations 19 and 8 respectively . find the standard deviation of the combined set of size 90
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Answer:
53.61902647.
Step-by-step explanation:
the variance is equal to the square of the standard deviation.
in the excel analysis, what happened was:
the standard deviation of the two samples was 50 and 61.23724.
the variance of the two samples was 2500 and 2750
the sum of squares of the two samples was 17500 + 11250.
the sum of square of the combined samples was 17500 + 11250 = 28750.
from the combined sum of squares, i could then calculate the variance and the standard deviation of the combined sample.
the variance was equal to 28750 / 10 = 2875
the standard deviation was equal to sqrt(2875) = 53.61902647.
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