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10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of the…

The combined mean is the total of all observations divided by their number: \(\frac{7\times10 + 3\times5}{7+3} = \frac{70+15}{10} = 8.5\). Simply averaging the two means…

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10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of the combined set is given by

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The combined mean is the total of all observations divided by their number: 7×10+3×57+3=70+1510=8.5\frac{7\times10 + 3\times5}{7+3} = \frac{70+15}{10} = 8.5. Simply averaging the two means gives 7.5, which is wrong because the groups are of unequal size and the larger group must carry more weight.

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