Discussion
Arithmetic mean of salary of 100 males in a company is ₹ 20,000 per month and that of 50 females is ₹ 17,000 per month. The arithmetic mean of salary of the combined group of males and females in the company is .............. per month.
Answer: B
The combined mean salary is ₹ 19,000 per month.
The combined mean weights each group's mean by its size:
\[ \begin{aligned} \bar{x} &= \frac{100 \times 20000 + 50 \times 17000}{150} \\ &= \frac{28{,}50{,}000}{150} = 19{,}000 \end{aligned} \]
₹ 18,500 would be the simple average of the two means, which ignores that there are twice as many men; it is not even an option. ₹ 20,000 and ₹ 17,000 are the two group means.
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