Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 3125 of 473
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Find SD of the following 1,2,3,4,5,6,7,8,9.\displaystyle 1, 2, 3, 4, 5, 6, 7, 8, 9.

Options

A2.56\displaystyle 2.56
B60/9\displaystyle 60/9
C60/3\displaystyle 60/3
D3.20\displaystyle 3.20
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Correct Answer

✅ Option a — 2.56\displaystyle 2.56

All Options:

  • A2.56\displaystyle 2.56
  • B60/9\displaystyle 60/9
  • C60/3\displaystyle 60/3
  • D3.20\displaystyle 3.20

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Detailed Solution & Explanation

We want to find the standard deviation (S.D.) of the first 9\displaystyle 9 natural numbers (1,2,…,9\displaystyle 1, 2, \dots, 9). The standard deviation of the first n\displaystyle n natural numbers is given by the formula: S.D.=n2−112\text{S.D.} = \sqrt{\frac{n^2 - 1}{12}} Substituting n=9\displaystyle n = 9: S.D.=92−112=81−112=8012=203≈6.67≈2.58\text{S.D.} = \sqrt{\frac{9^2 - 1}{12}} = \sqrt{\frac{81 - 1}{12}} = \sqrt{\frac{80}{12}} = \sqrt{\frac{20}{3}} \approx \sqrt{6.67} \approx 2.58 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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