Measures of Central Tendency and DispersionMCQMTP June 24 Series IIIQuestion 3072 of 473
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When the mean is 3.57\displaystyle 3.57 and mode is 2.13\displaystyle 2.13, then the value of median is _______.

Options

A3.09\displaystyle 3.09
B5.01\displaystyle 5.01
C5.01\displaystyle 5.01
DNone of these
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Correct Answer

✅ Option a — 3.09\displaystyle 3.09

All Options:

  • A3.09\displaystyle 3.09
  • B5.01\displaystyle 5.01
  • C5.01\displaystyle 5.01
  • DNone of these

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Detailed Solution & Explanation

**Step 1: Apply the empirical formula.** Mode=3Median−2Mean\text{Mode} = 3\text{Median} - 2\text{Mean} **Step 2: Substitute values.** 2.13=3Median−2(3.57)2.13 = 3\text{Median} - 2(3.57) 2.13=3Median−7.142.13 = 3\text{Median} - 7.14 3Median=9.273\text{Median} = 9.27 Median=3.09\text{Median} = 3.09 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

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.

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

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