Measures of Central Tendency and DispersionMCQMTP March 22Question 2905 of 473
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If average marks for a group of 30\displaystyle 30 girls is 80\displaystyle 80, a group of boys is 70\displaystyle 70 and combined average is 76\displaystyle 76, then how many boys are in the group ?

Options

A21
B20
C22
D19
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Correct Answer

✅ Option b — 20

All Options:

  • A21
  • B20
  • C22
  • D19

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Detailed Solution & Explanation

**Step 1: Let number of boys = nb\displaystyle n_b.** Combined mean=30×80+nb×7030+nb=76\text{Combined mean} = \frac{30 \times 80 + n_b \times 70}{30 + n_b} = 76 **Step 2: Solve.** 2400+70nb=76(30+nb)=2280+76nb2400 + 70n_b = 76(30 + n_b) = 2280 + 76n_b 2400−2280=76nb−70nb2400 - 2280 = 76n_b - 70n_b 120=6nb120 = 6n_b nb=20n_b = 20 **Note:** The computed number of boys is **20** (Option B), not 19 (Option D). Verification: (30×80+20×70)/(30+20)=(2400+1400)/50=3800/50=76\displaystyle (30 \times 80 + 20 \times 70)/(30+20) = (2400+1400)/50 = 3800/50 = 76 ✓ 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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