Statistics
Combined Mean
Premium Question
Grade 11

Question:

Two groups of 10 and 15 observations have means 17 and 18 respectively. The combined mean of all 25 observations is:
(1) 17
(2) 17.6
(3) 18
(4) 17.5

Step-by-Step Solution

Key Concept: Use the combined-mean formula $\bar{x} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2}$, which weights each group's mean by the number of observations it contains.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)

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