Measures of Central Tendency and DispersionPYQ May 25Question 4077 of 473
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The Arithmetic Mean (A.M.) and mode of the data are 32 and 26, respectively, then find the median of the data.

Options

A30
B12
C6
D29
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Correct Answer

✅ Option a — 30

All Options:

  • A30
  • B12
  • C6
  • D29

Detailed Solution & Explanation

We are given:
- Mean (A.M.)=32\displaystyle \text{Mean (A.M.)} = 32
- Mode=26\displaystyle \text{Mode} = 26

We use the empirical relationship between Mean, Median, and Mode for moderately skewed distributions:
Mean−Mode=3(Mean−Median)\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median}) Or equivalently:
Mode=3×Median−2×Mean\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} Let us substitute the given values into the formula:
26=3×Median−2×3226 = 3 \times \text{Median} - 2 \times 32 26=3×Median−6426 = 3 \times \text{Median} - 64 26+64=3×Median26 + 64 = 3 \times \text{Median} 90=3×Median90 = 3 \times \text{Median} Median=903=30\text{Median} = \frac{90}{3} = 30
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.

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