Measures of Central Tendency and DispersionMCQPYQ Dec. 21Question 2866 of 473
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If average mark for a group of 30 girls is 80, a group of boys is 70 and combined average is 76, then how many are in the boy's group?

Options

A21\displaystyle 21
B20\displaystyle 20
C22\displaystyle 22
D19\displaystyle 19
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Correct Answer

✅ Option b — 20\displaystyle 20

All Options:

  • A21\displaystyle 21
  • B20\displaystyle 20
  • C22\displaystyle 22
  • D19\displaystyle 19

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Detailed Solution & Explanation

**Step 1: Set up variables.** Let the number of boys = nb\displaystyle n_b. Number of girls = 30. **Step 2: Apply combined mean formula.** xˉcombined=ng⋅xˉg+nb⋅xˉbng+nb\bar{x}_{combined} = \frac{n_g \cdot \bar{x}_g + n_b \cdot \bar{x}_b}{n_g + n_b} 76=30×80+nb×7030+nb76 = \frac{30 \times 80 + n_b \times 70}{30 + n_b} **Step 3: Solve for nb\displaystyle n_b.** 76(30+nb)=2400+70nb76(30 + n_b) = 2400 + 70n_b 2280+76nb=2400+70nb2280 + 76n_b = 2400 + 70n_b 6nb=1206n_b = 120 nb=20n_b = 20 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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