Question:
If the combined mean of two groups is \( \frac{40}{3} \) and if the mean of one group with 10 observations is 15, then the mean of the other group with 8 observations is equal to
If the combined mean of two groups is \( \frac{40}{3} \) and if the mean of one group with 10 observations is 15, then the mean of the other group with 8 observations is equal to
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Combined mean problems always reduce to weighted averages.
Updated On: May 8, 2026
- \( \frac{46}{3} \)
- \( \frac{35}{4} \)
- \( \frac{45}{4} \)
- \( \frac{41}{4} \)
- \( \frac{43}{4} \)
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The Correct Option is D
Solution and Explanation
Concept:
Combined mean:
\[
\bar{x} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1+n_2}
\]
Step 1: Substitute
\[ \frac{40}{3} = \frac{10 \cdot 15 + 8x}{18} \]
Step 2: Multiply
\[ 240 = 150 + 8x \]
Step 3: Solve
\[ 8x = 90 \Rightarrow x = \frac{45}{4} \]
Step 4: Final Answer
\[ \boxed{\frac{45}{4}} \]
Step 1: Substitute
\[ \frac{40}{3} = \frac{10 \cdot 15 + 8x}{18} \]
Step 2: Multiply
\[ 240 = 150 + 8x \]
Step 3: Solve
\[ 8x = 90 \Rightarrow x = \frac{45}{4} \]
Step 4: Final Answer
\[ \boxed{\frac{45}{4}} \]
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