Measures of Central Tendency and DispersionMCQPYQ Nov 18Question 3117 of 473
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Standard Deviation for the marks obtained by a student in monthly test in mathematic (out of 50\displaystyle 50) as 30,35,25,20,15\displaystyle 30, 35, 25, 20, 15 is

Options

A25\displaystyle \sqrt{25}
B50\displaystyle \sqrt{50}
C30\displaystyle \sqrt{30}
D10\displaystyle \sqrt{10}
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Correct Answer

✅ Option b — 50\displaystyle \sqrt{50}

All Options:

  • A25\displaystyle \sqrt{25}
  • B50\displaystyle \sqrt{50}
  • C30\displaystyle \sqrt{30}
  • D10\displaystyle \sqrt{10}

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Detailed Solution & Explanation

We are given the marks: 30,35,25,20,15\displaystyle 30, 35, 25, 20, 15. The number of observations is n=5\displaystyle n = 5. 1. Calculate the arithmetic mean (xˉ\displaystyle \bar{x}): xˉ=30+35+25+20+155=1255=25\bar{x} = \frac{30 + 35 + 25 + 20 + 15}{5} = \frac{125}{5} = 25 2. Calculate the deviations from the mean (xi−xˉ)\displaystyle (x_i - \bar{x}) and their squares (xi−xˉ)2\displaystyle (x_i - \bar{x})^2: - 30−25=5  ⟹  25\displaystyle 30 - 25 = 5 \implies 25 - 35−25=10  ⟹  100\displaystyle 35 - 25 = 10 \implies 100 - 25−25=0  ⟹  0\displaystyle 25 - 25 = 0 \implies 0 - 20−25=−5  ⟹  25\displaystyle 20 - 25 = -5 \implies 25 - 15−25=−10  ⟹  100\displaystyle 15 - 25 = -10 \implies 100 3. Calculate the sum of squared deviations: ∑(xi−xˉ)2=25+100+0+25+100=250\sum (x_i - \bar{x})^2 = 25 + 100 + 0 + 25 + 100 = 250 4. Calculate variance (σ2\displaystyle \sigma^2) and Standard Deviation (σ\displaystyle \sigma): σ2=2505=50  ⟹  σ=50\sigma^2 = \frac{250}{5} = 50 \implies \sigma = \sqrt{50} 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.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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