Measures of Central Tendency and DispersionPYQ Sept 25Question 4177 of 473
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If the sum of ten values is 20 and sum of squares of these values is 80, then the standard deviation is

Options

A1
B2
C1/2
D4
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Correct Answer

✅ Option b — 2

All Options:

  • A1
  • B2
  • C1/2
  • D4

Detailed Solution & Explanation

Let us calculate the standard deviation (σ\displaystyle \sigma) from the given data:
- Number of observations: n=10\displaystyle n = 10
- Sum of observations: ∑X=20\displaystyle \sum X = 20
- Sum of squares of observations: ∑X2=80\displaystyle \sum X^2 = 80
1. **Formula for Standard Deviation**:
σ=∑X2n−(∑Xn)2\sigma = \sqrt{\frac{\sum X^2}{n} - \left(\frac{\sum X}{n}\right)^2}
2. **Calculation**:
Substitute the given values into the formula:
σ=8010−(2010)2\sigma = \sqrt{\frac{80}{10} - \left(\frac{20}{10}\right)^2}
σ=8−(2)2\sigma = \sqrt{8 - (2)^2}
σ=8−4\sigma = \sqrt{8 - 4}
σ=4=2\sigma = \sqrt{4} = 2
Therefore, the standard deviation is 2\displaystyle 2.
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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