Measures of Central Tendency and DispersionMCQMTP May 19 Series IIQuestion 3236 of 473
All Questions

Which measure is based on only the central fifty percent of the observations?

Options

AStandard deviation
BQuartile deviation
CMean deviation
DAll these measures
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Correct Answer

✅ Option b — Quartile deviation

All Options:

  • AStandard deviation
  • BQuartile deviation
  • CMean deviation
  • DAll these measures

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Detailed Solution & Explanation

The quartile deviation is defined as half of the difference between the third and first quartiles (Q3−Q12\displaystyle \frac{Q_3 - Q_1}{2}). Since Q1\displaystyle Q_1 is the 25th\displaystyle 25^{\text{th}} percentile and Q3\displaystyle Q_3 is the 75th\displaystyle 75^{\text{th}} percentile, the interval between them represents the central 50%\displaystyle 50\% of the observations. Therefore, quartile deviation is based on only the central fifty percent of the observations. 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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