The means of two samples of size 30 and 40 are 35 and 42 respectively. Then the mean of the combined sample of size 70 is
Show Hint
- \( 36 \)
- \( 37 \)
- \( 38 \)
- \( 39 \)
- \( 40 \)
The Correct Option is D
Solution and Explanation
Step 1: Formula for Combined Mean \[ \bar{x} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2} \] where: - \( n_1 = 30 \), \( \bar{x}_1 = 35 \) - \( n_2 = 40 \), \( \bar{x}_2 = 42 \)
Step 2: Compute the Combined Mean \[ \bar{x} = \frac{(30 \times 35) + (40 \times 42)}{30 + 40} \] \[ = \frac{1050 + 1680}{70} = \frac{2730}{70} = 39 \]
Final Answer: \[ \boxed{39} \]
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