Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 2927 of 473
All Questions

If the arithmetic mean of 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 6n11\displaystyle \frac{6n}{11} then the value of 'n\displaystyle n' is:

Options

A10
B11
C14
DNone of these
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Correct Answer

✅ Option b — 11

All Options:

  • A10
  • B11
  • C14
  • DNone of these

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Detailed Solution & Explanation

**Step 1: Recall the AM of first n\displaystyle n natural numbers.** AM=n+12\text{AM} = \frac{n+1}{2} **Step 2: Set equal to given expression and solve.** n+12=6n11\frac{n+1}{2} = \frac{6n}{11} 11(n+1)=12n11(n+1) = 12n 11n+11=12n11n + 11 = 12n n=11n = 11 **Note:** The computed value is **n=11\displaystyle n = 11** (Option B), not 14 (Option C). Let us verify: AM of first 11 natural numbers =6/2=6\displaystyle = 6/2 = 6. Formula: 6×11/11=6\displaystyle 6 \times 11/11 = 6 ✓. 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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