Math Problem Statement
A group of 50 observations has A.M. 61 and S.D. 8. Another group of 100 observations have A.M. 70 and S.D. 9. Find A.M. and S.D. for the combined group of 150 observations.
Solution
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Math Problem Analysis
Mathematical Concepts
Arithmetic Mean
Standard Deviation
Variance
Formulas
Combined A.M. = (n1 * A.M.1 + n2 * A.M.2) / (n1 + n2)
Combined Variance = (n1 * σ1^2 + n2 * σ2^2 + n1 * (A.M.1 - Combined A.M.)^2 + n2 * (A.M.2 - Combined A.M.)^2) / (n1 + n2)
Combined S.D. = √(Combined Variance)
Theorems
Properties of Arithmetic Mean
Properties of Variance and Standard Deviation
Suitable Grade Level
Grades 10-12
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