Measures of Central Tendency and DispersionMCQPYQ Dec 22Question 3137 of 473
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If the coefficient of variation and standard deviation are 30 and 12 respectively, then the arithmetic mean of the distribution is:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $40$

All Options:

  • A$40$
  • B$36$
  • C$25$
  • D$19$

Detailed Solution & Explanation

**Given:** CV = 30, SD (σ\displaystyle σ\displaystyle \sigma) = 12 **Step 1: Use the formula for CV.** CV=σxˉ×100CV = σxˉ\displaystyle \frac{\sigma}{\bar{x}} ×\displaystyle \times 100 **Step 2: Substitute and solve for xˉ\displaystyle xˉ\displaystyle \bar{x}.** 30=12xˉ×10030 = 12xˉ\displaystyle \frac{12}{\bar{x}} ×\displaystyle \times 100 xˉ=12×10030=120030=40\displaystyle \bar{x} = \frac{12 ×\displaystyle \times 100}{30} = 120030=40\displaystyle \frac{1200}{30} = 40 **Result:** Arithmetic Mean = 40 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

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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