Measures of Central Tendency and DispersionMCQPYQ Dec 23Question 3228 of 473
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If the quartile deviation is 12\displaystyle 12 and the first quartile is 25\displaystyle 25, then the value of the third quartile is:

Options

A37\displaystyle 37
B49\displaystyle 49
C61\displaystyle 61
D60\displaystyle 60
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Correct Answer

✅ Option b — 49\displaystyle 49

All Options:

  • A37\displaystyle 37
  • B49\displaystyle 49
  • C61\displaystyle 61
  • D60\displaystyle 60

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Detailed Solution & Explanation

We are given: - Quartile deviation (Q.D.) = 12\displaystyle 12 - First quartile (Q1\displaystyle Q_1) = 25\displaystyle 25 The formula for quartile deviation is: Q.D.=Q3−Q12\text{Q.D.} = \frac{Q_3 - Q_1}{2} Substitute the given values: 12=Q3−25212 = \frac{Q_3 - 25}{2} 24=Q3−25impliesQ3=4924 = Q_3 - 25 \\implies Q_3 = 49 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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