Measures of Central Tendency and DispersionMCQPYQ Dec 23Question 3042 of 473
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If the mean and median of a moderately asymmetrical series are 26.8 and 27.9 respectively, then the most probable mode is:

Options

A30.1
B30.4
C34.3
D70.8
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Correct Answer

✅ Option a — 30.1

All Options:

  • A30.1
  • B30.4
  • C34.3
  • D70.8

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Detailed Solution & Explanation

**Step 1: Apply the empirical formula.** Mode=3×Median−2×Mean\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} **Step 2: Substitute values.** - Mean = 26.8, Median = 27.9 Mode=3×27.9−2×26.8\text{Mode} = 3 \times 27.9 - 2 \times 26.8 =83.7−53.6=30.1= 83.7 - 53.6 = 30.1 The Mode = 30.1\displaystyle 30.1 = **Option A**. Note: The exam key says B (30.4\displaystyle 30.4), but the calculation gives 30.1\displaystyle 30.1 (Option A). 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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