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

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

✅ Option b — 20

All Options:

  • A21
  • B20
  • C22
  • D19

Detailed Solution & Explanation

**Step 1: Let number of boys = nb\displaystyle n_b.** Combined mean=30×80+nb×7030+nb=76\displaystyle \text{Combined mean} = \frac{30 ×\displaystyle \times 80 + n_b ×\displaystyle \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 ×\displaystyle \times 80 + 20 ×\displaystyle \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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