Measures of Central Tendency and DispersionPYQ Jan 26Question 4588 of 473
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If two variables 'x' and 'y' are related by 3x+4y−7=0\displaystyle 3x + 4y - 7 = 0 and mean & mean deviation about mean of 'x' are 1.2 and 0.4 respectively then the coefficient of mean deviation of 'y' about its mean is?

Options

A34.3
B32.3
C35.3
D36.3
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Correct Answer

✅ Option c — 35.3

All Options:

  • A34.3
  • B32.3
  • C35.3
  • D36.3

Detailed Solution & Explanation

We are given the relationship between x\displaystyle x and y\displaystyle y: 3x+4y−7=03x + 4y - 7 = 0 We can express y\displaystyle y in terms of x\displaystyle x: 4y=7−3x  ⟹  y=74−34x4y = 7 - 3x \implies y = \frac{7}{4} - \frac{3}{4}x
We are given: - Mean of x\displaystyle x (xˉ\displaystyle \bar{x}) = 1.2\displaystyle 1.2 - Mean deviation of x\displaystyle x about its mean (MDx\displaystyle MD_x) = 0.4\displaystyle 0.4
**Step 1: Find the mean of y\displaystyle y (yˉ\displaystyle \bar{y})** Since the mean is affected by both change of origin and scale: yˉ=7−3xˉ4\bar{y} = \frac{7 - 3\bar{x}}{4} Substituting xˉ=1.2\displaystyle \bar{x} = 1.2: yˉ=7−3(1.2)4=7−3.64=3.44=0.85\bar{y} = \frac{7 - 3(1.2)}{4} = \frac{7 - 3.6}{4} = \frac{3.4}{4} = 0.85
**Step 2: Find the mean deviation of y\displaystyle y (MDy\displaystyle MD_y)** Mean deviation is independent of change of origin but is affected by the absolute value of the change of scale: MDy=∣−34∣×MDxMD_y = \left| -\frac{3}{4} \right| \times MD_x Substituting MDx=0.4\displaystyle MD_x = 0.4: MDy=34×0.4=0.3MD_y = \frac{3}{4} \times 0.4 = 0.3
**Step 3: Calculate the coefficient of mean deviation of y\displaystyle y** Coefficient of MDy=MDyyˉ×100\text{Coefficient of } MD_y = \frac{MD_y}{\bar{y}} \times 100 Coefficient of MDy=0.30.85×100=3008.5≈35.29%≈35.3\text{Coefficient of } MD_y = \frac{0.3}{0.85} \times 100 = \frac{300}{8.5} \approx 35.29\% \approx 35.3 Hence, **Option C** 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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