Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 2926 of 473
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The average wages of a group of unexperienced labours is 1000\displaystyle 1000 and that of a group of experienced labours is 1,500\displaystyle 1,500. If the combined wage is 1200\displaystyle 1200, then what is the percentage of experienced labours?

Options

A60%\displaystyle 60\%
B40%\displaystyle 40\%
C50%\displaystyle 50\%
DNone of these
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Correct Answer

✅ Option b — 40%\displaystyle 40\%

All Options:

  • A60%\displaystyle 60\%
  • B40%\displaystyle 40\%
  • C50%\displaystyle 50\%
  • DNone of these

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Detailed Solution & Explanation

**Step 1: Let proportion of experienced labourers =p\displaystyle = p and unexperienced =(1−p)\displaystyle = (1-p).** 1000(1−p)+1500p=12001000(1-p) + 1500p = 1200 **Step 2: Solve.** 1000−1000p+1500p=12001000 - 1000p + 1500p = 1200 500p=200500p = 200 p=0.4=40%p = 0.4 = 40\% **Note:** The percentage of experienced labourers is **40%** (Option B). The `correct_option` given is A (60%), which would be the percentage of unexperienced, not experienced. Hence, **Option B** 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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