Measures of Central Tendency and DispersionMCQMTP Apr 21Question 2898 of 473
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At ABC Ltd, the average age of employees is 36. Average age of male employees is 38 and that of female is 32. Find the ratio of female to male in the company.

Options

A1:3
B2:1
C1:2
D3:1
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Correct Answer

✅ Option c — 1:2

All Options:

  • A1:3
  • B2:1
  • C1:2
  • D3:1

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Detailed Solution & Explanation

**Step 1: Set up the equation using the combined mean formula.** Let the number of females =f\displaystyle = f and males =m\displaystyle = m. 32f+38mf+m=36\frac{32f + 38m}{f + m} = 36 **Step 2: Solve.** 32f+38m=36f+36m32f + 38m = 36f + 36m 38m−36m=36f−32f38m - 36m = 36f - 32f 2m=4f2m = 4f fm=24=12\frac{f}{m} = \frac{2}{4} = \frac{1}{2} So female : male =1:2\displaystyle = 1 : 2 (Option C). **Note:** The computed ratio is 1:2 (Option C), not 2:1 (Option B). Verification: If f=1,m=2\displaystyle f = 1, m = 2: (32×1+38×2)/3=(32+76)/3=108/3=36\displaystyle (32 \times 1 + 38 \times 2)/3 = (32+76)/3 = 108/3 = 36 ✓ Hence, **Option C** 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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