Measures of Central Tendency and DispersionMCQPYQ Jun 23Question 3037 of 473
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For a moderately skewed distribution of marks in statistics for a group of 200 students, the mean marks and median marks are 55.60 and 52.40, respectively. What are the modal marks?

Options

A54.43
B58
C53.56
D46
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Correct Answer

✅ Option d — 46

All Options:

  • A54.43
  • B58
  • C53.56
  • D46

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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 = 55.60, Median = 52.40 Mode=3×52.40−2×55.60\text{Mode} = 3 \times 52.40 - 2 \times 55.60 =157.20−111.20=46.00= 157.20 - 111.20 = 46.00 Hence, **Option D** 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.

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