Measures of Central Tendency and DispersionPYQ Jan 26Question 4535 of 473
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The two variables 'x' and 'y' are related by 2x−3y−3=0\displaystyle 2x - 3y - 3 = 0. If the mode of 'x' is 15, then the mode of 'y' is:

Options

A30
B3
C15
D9
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Correct Answer

✅ Option d — 9

All Options:

  • A30
  • B3
  • C15
  • D9

Detailed Solution & Explanation

Given the linear relationship between the variables x\displaystyle x and y\displaystyle y:
2x−3y−3=02x - 3y - 3 = 0

Since measures of central tendency (such as mean, median, and mode) are affected by both changes of origin and changes of scale, the mode of y\displaystyle y must satisfy the same linear relation as the variables themselves:
2×Mode(x)−3×Mode(y)−3=02 \times \text{Mode}(x) - 3 \times \text{Mode}(y) - 3 = 0

Given that the mode of x\displaystyle x is 15\displaystyle 15:
2(15)−3×Mode(y)−3=02(15) - 3 \times \text{Mode}(y) - 3 = 0
30−3×Mode(y)−3=030 - 3 \times \text{Mode}(y) - 3 = 0
27−3×Mode(y)=027 - 3 \times \text{Mode}(y) = 0
3×Mode(y)=273 \times \text{Mode}(y) = 27
Mode(y)=273=9\text{Mode}(y) = \frac{27}{3} = 9

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.

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