Standard deviation of first n natural number is 2. What is the value of n ?

Option a: 7. Solution: Formula for SD of first n natural numbers: sigma = sqrt(n2 - 1/12) Given: sigma = 2 Step 1: Set up equation. 2 = sqrt(n2 - 1/12) Step 2: Square both sides. 4 = n2 - 1/12 Step 3: Solve. n2 - 1 = 48 n2 = 49 n = 7 Verification: sigma = sqrt(49-1/12) = sqrt(48/12) = sqrt(4) = 2 ✓ Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 21Question 3179 of 473

All Questions

Standard deviation of first $\displaystyle n$ natural number is 2. What is the value of $\displaystyle n$ ?

Options

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Correct Answer

✅ Option a — 7

All Options:

Detailed Solution & Explanation

**Formula for SD of first

\displaystyle n

natural numbers:**

\sigma = \sqrt{\frac{n^2 - 1}{12}}

**Given:**

\displaystyle \sigma = 2

**Step 1:** Set up equation.

2 = \sqrt{\frac{n^2 - 1}{12}}

**Step 2:** Square both sides.

4 = \frac{n^2 - 1}{12}

**Step 3:** Solve.

n^2 - 1 = 48

n^2 = 49

n = 7

**Verification:**

\displaystyle \sigma = \sqrt{\frac{49-1}{12}} = \sqrt{\frac{48}{12}} = \sqrt{4} = 2

✓ Hence, **Option A** 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.

Key Concepts to Understand