If the S.D. of the 1st n natural numbers is sqrt(30) then the value of n is

Option a: 19. Solution: The standard deviation (S.D.) of the first n natural numbers is given by the formula: S.D. = sqrt(n2 - 1/12) We are given the standard deviation is sqrt(30) . Set up the equation: sqrt(30) = sqrt(n2 - 1/12) Square both sides: 30 = n2 - 1/12 360 = n2 - 1 n2 = 361 n = 19 Hence, Option A is the correct answer.

If the S.D. of the $1^{st}$ $n$ natural numbers is $\sqrt{30}$ then the value of $n$ is

The correct answer is Option a: $19$. The standard deviation (S.D.) of the first $n$ natural numbers is given by the formula: $$\text{S.D.} = \sqrt{\frac{n^2 - 1}{12}}$$ We are given the standard deviation is $\sqrt{30}$. Set up the equation: $$\sqrt{30} = \sqrt{\frac{n^2 - 1}{12}}$$ Square both sides: $$30 = \frac{n^2 - 1}{12}$$ $$360 = n^2 - 1$$ $$n^2 = 361 \implies n = 19$$ Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ May 18Question 3115 of 473

All Questions

If the S.D. of the $\displaystyle 1^{st}$ $\displaystyle n$ natural numbers is $\displaystyle \sqrt{30}$ then the value of $\displaystyle n$ is

Options

\displaystyle 19

\displaystyle 20

\displaystyle 21

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 19$

All Options:

A $\displaystyle 19$
B $\displaystyle 20$
C $\displaystyle 21$
DNone of these

Detailed Solution & Explanation

The standard deviation (S.D.) of the first

\displaystyle n

natural numbers is given by the formula:

\text{S.D.} = \sqrt{\frac{n^2 - 1}{12}}

We are given the standard deviation is

\displaystyle \sqrt{30}

. Set up the equation:

\sqrt{30} = \sqrt{\frac{n^2 - 1}{12}}

Square both sides:

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

360 = n^2 - 1

n^2 = 361 \implies n = 19

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.

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If the S.D. of the 1st\displaystyle 1^{st}1st n\displaystyle nn natural numbers is 30\displaystyle \sqrt{30}30​ then the value of n\displaystyle nn is