Question

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

• A. \( 36 \)
• B. \( 37 \)
• C. \( 38 \)
• D. \( 39 \)
• E. \( 40 \)

Hint:

The combined mean is a weighted average, where each sample contributes according to its size.

Answer 1

The Correct Option is D

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: \[ \boxed{39} \]