If two variables x and y are related by 2x + 3y - 7 = 0 and the mean and mean deviation about mean of X are 1 and 0.3 respectively, then the co-efficient of mean deviation of Y about mean is.

Option c: .12. Solution: We are given: 2x + 3y - 7 = 0 3y = -2x + 7 y = -2/3x + 7/3 . - Mean of x ( x ) = 1 - Mean deviation of x ( M.D.x ) = 0.3 1. Find Mean of y ( y ): y = -2/3x + 7/3 = -2/3(1) + 7/3 = 5/3 ≈ 1.67 2. Find Mean deviation of y ( M.D.y ): M.D.y = ≤ft|-2/3| × M.D.x = 2/3 × 0.3 = 0.2 3. Calculate coefficient of mean deviation of y : Coefficient = .D.y|y| = 0.2/5/3 = 0.12 Hence, Option C is the correct answer.

If two variables $x$ and $y$ are related by $2x + 3y - 7 = 0$ and the mean and mean deviation about mean of $X$ are $1$ and $0.3$ respectively, then the co-efficient of mean deviation of $Y$ about mean is.

The correct answer is Option c: $.12$. We are given: $2x + 3y - 7 = 0 \implies 3y = -2x + 7 \implies y = -\frac{2}{3}x + \frac{7}{3}$. - Mean of $x$ ($\bar{x}$) = $1$ - Mean deviation of $x$ ($\text{M.D.}_x$) = $0.3$ 1. Find Mean of $y$ ($\bar{y}$): $$\bar{y} = -\frac{2}{3}\bar{x} + \frac{7}{3} = -\frac{2}{3}(1) + \frac{7}{3} = \frac{5}{3} \approx 1.67$$ 2. Find Mean deviation of $y$ ($\text{M.D.}_y$): $$\text{M.D.}_y = \left|-\frac{2}{3}\right| \times \text{M.D.}_x = \frac{2}{3} \times 0.3 = 0.2$$ 3. Calculate coefficient of mean deviation of $y$: $$\text{Coefficient} = \frac{\text{M.D.}_y}{|\bar{y}|} = \frac{0.2}{5/3} = 0.12$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IQuestion 3112 of 473

All Questions

If two variables $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 2x + 3y - 7 = 0$ and the mean and mean deviation about mean of $\displaystyle X$ are $\displaystyle 1$ and $\displaystyle 0.3$ respectively, then the co-efficient of mean deviation of $\displaystyle Y$ about mean is.

Options

\displaystyle .5

\displaystyle .4

\displaystyle .12

\displaystyle .50

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle .12$

All Options:

A $\displaystyle .5$
B $\displaystyle .4$
C $\displaystyle .12$
D $\displaystyle .50$

Detailed Solution & Explanation

We are given:

\displaystyle 2x + 3y - 7 = 0 \implies 3y = -2x + 7 \implies y = -\frac{2}{3}x + \frac{7}{3}

. - Mean of

\displaystyle x

(

\displaystyle \bar{x}

) =

\displaystyle 1

- Mean deviation of

\displaystyle x

(

\displaystyle \text{M.D.}_x

) =

\displaystyle 0.3

1. Find Mean of

\displaystyle y

(

\displaystyle \bar{y}

\bar{y} = -\frac{2}{3}\bar{x} + \frac{7}{3} = -\frac{2}{3}(1) + \frac{7}{3} = \frac{5}{3} \approx 1.67

2. Find Mean deviation of

\displaystyle y

(

\displaystyle \text{M.D.}_y

\text{M.D.}_y = \left|-\frac{2}{3}\right| \times \text{M.D.}_x = \frac{2}{3} \times 0.3 = 0.2

3. Calculate coefficient of mean deviation of

\displaystyle y

\text{Coefficient} = \frac{\text{M.D.}_y}{|\bar{y}|} = \frac{0.2}{5/3} = 0.12

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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