Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 2914 of 473
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The mean annual salary of all employees in a company is $25,000$. The mean salary of male and female employees is $27,000$ and $17,000$ respectively. Find the percentage of males and females employed by the company.

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

✅ Option d — $80\%\displaystyle and $20\%

All Options:

  • A$60\%\displaystyle and $40\%
  • B$70\%\displaystyle and $25\%
  • C$70\%\displaystyle and $30\%
  • D$80\%\displaystyle and $20\%

Detailed Solution & Explanation

**Step 1: Let proportion of males =p\displaystyle = p and females =(1−p)\displaystyle = (1-p).** 27000p+17000(1−p)=2500027000p + 17000(1-p) = 25000 **Step 2: Solve.** 27000p+17000−17000p=2500027000p + 17000 - 17000p = 25000 10000p=800010000p = 8000 p=0.8=80%p = 0.8 = 80\% Females =1−0.8=0.2=20%\displaystyle = 1 - 0.8 = 0.2 = 20\%. **Note:** The computed percentages are **80% males and 20% females** (Option D). The `correct_option` is A (60% and 40%). Let us verify A: $27000 ×\displaystyle \times 0.6 + 17000 ×\displaystyle \times 0.4 = 16200 + 6800 = 23000 ≠\displaystyle \neq 25000\displaystyle . Verifying D: $27000 ×\displaystyle \times 0.8 + 17000 ×\displaystyle \times 0.2 = 21600 + 3400 = 25000 ✓ Hence, **Option D** 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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