Measures of Central Tendency and DispersionMCQMTP Dec 23 - Series IQuestion 3260 of 473
All Questions

If the first quartile is 142\displaystyle 142 and semi-inter quartile range is 18\displaystyle 18, then the value of median is:

Options

A151\displaystyle 151
B160\displaystyle 160
C178\displaystyle 178
DNone of these
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Correct Answer

✅ Option b — 160\displaystyle 160

All Options:

  • A151\displaystyle 151
  • B160\displaystyle 160
  • C178\displaystyle 178
  • DNone of these

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Detailed Solution & Explanation

We are given: - First quartile: Q1=142\displaystyle Q_1 = 142 - Semi-interquartile range (Q.D.) = 18\displaystyle 18 For a symmetric distribution, the median lies exactly halfway between Q1\displaystyle Q_1 and Q3\displaystyle Q_3: Median=Q1+Q.D.=142+18=160\text{Median} = Q_1 + \text{Q.D.} = 142 + 18 = 160 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

Median

The middle value of a data set when arranged in ascending or descending order. It divides the distribution into two equal halves. For even n: Median = average of (n/2)th and (n/2 + 1)th values. It is NOT affected by extreme values.

Related Comparison Tables

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