Measures of Central Tendency and DispersionMCQMTP Nov 18Question 2880 of 473
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The mean age of a group of 100 men and women is 25 years. If the mean age of the group of men is 26, then that of the group of women is 21 then the ratio of women and men in the group:

Options

A1:1
B1:2
C1:3
D1:4
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Correct Answer

✅ Option d — 1:4

All Options:

  • A1:1
  • B1:2
  • C1:3
  • D1:4

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Detailed Solution & Explanation

**Step 1: Set up equations.** Let number of men =m\displaystyle = m and women =w\displaystyle = w. Total =m+w=100\displaystyle = m + w = 100. **Step 2: Apply combined mean formula.** 26m+21wm+w=25\frac{26m + 21w}{m + w} = 25 26m+21w=25×100=250026m + 21w = 25 \times 100 = 2500 **Step 3: Solve the system.** From m+w=100⇒m=100−w\displaystyle m + w = 100 \Rightarrow m = 100 - w. 26(100−w)+21w=250026(100 - w) + 21w = 2500 2600−26w+21w=25002600 - 26w + 21w = 2500 2600−5w=25002600 - 5w = 2500 5w=100  ⟹  w=20,m=805w = 100 \implies w = 20, \quad m = 80 **Step 4: Compute the ratio.** wm=2080=14\frac{w}{m} = \frac{20}{80} = \frac{1}{4} So women : men =1:4\displaystyle = 1 : 4. **Note:** The computation gives ratio 1:4 (Option D), not 1:3. Verifying: 26(80)+21(20)=2080+420=2500\displaystyle 26(80) + 21(20) = 2080 + 420 = 2500 ✓. The correct ratio is **1:4**. 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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