Measures of Central Tendency and DispersionMCQPYQ June 24Question 3006 of 473
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If the arithmetic mean of two numbers is 10\displaystyle 10 and the geometric mean is 6\displaystyle 6, then the difference in the numbers is

Options

A12
B14
C16
D8
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Correct Answer

✅ Option c — 16

All Options:

  • A12
  • B14
  • C16
  • D8

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Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be a\displaystyle a and b\displaystyle b. AM=a+b2=10⇒a+b=20\text{AM} = \frac{a+b}{2} = 10 \Rightarrow a + b = 20 GM=ab=6⇒ab=36\text{GM} = \sqrt{ab} = 6 \Rightarrow ab = 36 **Step 2: Find the difference.** Using the identity: (a−b)2=(a+b)2−4ab=400−144=256(a - b)^2 = (a + b)^2 - 4ab = 400 - 144 = 256 ∣a−b∣=256=16|a - b| = \sqrt{256} = 16 Hence, **Option C** 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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