Measures of Central Tendency and DispersionMCQMTP Nov 19, ICAI SMQuestion 2885 of 473
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The average salary of a group of unskilled workers is Rs.10,000 and that of a group of skilled workers is Rs.15,000. If the combined salary is Rs.12,000, then what is the percentage of skilled workers?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 40%

All Options:

  • A40%
  • B50%
  • C60%
  • DNone of these

Detailed Solution & Explanation

**Step 1: Set up variables.** Let proportion of unskilled workers =p\displaystyle = p and skilled workers =(1−p)\displaystyle = (1-p). **Step 2: Apply combined mean equation.** 10000p+15000(1−p)=1200010000p + 15000(1-p) = 12000 10000p+15000−15000p=1200010000p + 15000 - 15000p = 12000 −5000p=−3000-5000p = -3000 p=30005000=0.6=60%p = 30005000=0\displaystyle \frac{3000}{5000} = 0.6 = 60\% So skilled workers =1−p=1−0.6=0.4=40%\displaystyle = 1 - p = 1 - 0.6 = 0.4 = 40\%. Hence, **Option A** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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