CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
Two branches of a retail firm have 50 employees each. In Branch A the mean daily sales per employee is ₹10 thousand with SD ₹3 thousand; in Branch B the mean is ₹18 thousand with SD ₹3 thousand. What is the standard deviation of the combined group of 100 employees (in ₹ thousand)?
The combined standard deviation is 5 thousand rupees. The combined mean is 14, each group mean is 4 away from it, so each contributes variance 9 + 16 = 25, giving combined variance 25. Ignoring the gap between the means would wrongly give 3.
- A3
- B4
- C5Correct
- D6
Explanation
Combined mean = 14. Deviations of the group means are d1 = −4 and d2 = 4. Combined variance = [50(9+16) + 50(9+16)]/100 = 25, so SD = 5. Answer 3 ignores the difference between the group means.
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