Measures of Central Tendency and DispersionPYQ Sept 25Question 4469 of 473
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If X\displaystyle X and Y\displaystyle Y are related by 4X+3Y+5=0\displaystyle 4X+3Y+5=0 and Mean of X\displaystyle X is 10, then the Mean of Y\displaystyle Y is

Options

A-23
B-15
C-20
D23
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Correct Answer

✅ Option b — -15

All Options:

  • A-23
  • B-15
  • C-20
  • D23

Detailed Solution & Explanation

Let Xˉ\displaystyle \bar{X} be the mean of X\displaystyle X and Yˉ\displaystyle \bar{Y} be the mean of Y\displaystyle Y.
1. **Property of Arithmetic Mean**: The arithmetic mean is affected by both change of origin and change of scale. If two variables X\displaystyle X and Y\displaystyle Y are related by a linear equation:
aX+bY+c=0aX + bY + c = 0
then their means satisfy the exact same linear relationship:
aXˉ+bYˉ+c=0a\bar{X} + b\bar{Y} + c = 0
2. **Given Data**: The relation is 4X+3Y+5=0\displaystyle 4X + 3Y + 5 = 0 and the mean of X\displaystyle X is Xˉ=10\displaystyle \bar{X} = 10.
3. **Calculation**:
Substitute Xˉ=10\displaystyle \bar{X} = 10 into the linear equation of the means:
4(10)+3Yˉ+5=04(10) + 3\bar{Y} + 5 = 0
40+3Yˉ+5=040 + 3\bar{Y} + 5 = 0
3Yˉ+45=03\bar{Y} + 45 = 0
3Yˉ=−453\bar{Y} = -45
Yˉ=−453=−15\bar{Y} = \frac{-45}{3} = -15
Therefore, the mean of Y\displaystyle Y is −15\displaystyle -15.
Hence, **Option B** 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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