Measures of Central Tendency and DispersionPYQ Jan 26Question 4286 of 473
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If mean is 21 and median is 25 then value of mode is

Options

A33
B25
C31
D21
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Correct Answer

✅ Option a — 33

All Options:

  • A33
  • B25
  • C31
  • D21

Detailed Solution & Explanation

For a moderately skewed distribution, there is an empirical relationship between mean, median, and mode: Mode=3×Median−2×Mean\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}
We are given: - Mean=21\displaystyle \text{Mean} = 21 - Median=25\displaystyle \text{Median} = 25
Substituting these values into the formula: Mode=3(25)−2(21)\text{Mode} = 3(25) - 2(21) Mode=75−42\text{Mode} = 75 - 42 Mode=33\text{Mode} = 33 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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