Measures of Central Tendency and DispersionMCQMTP May 19 Series IIQuestion 3156 of 473

If $\displaystyle X$ and $\displaystyle Y$ are related by $\displaystyle 2X+3Y=4$ and SD of $\displaystyle X$ is 6, then SD of $\displaystyle Y$ is

Options

\displaystyle 22

\displaystyle 4

\displaystyle 40

\displaystyle 9

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Correct Answer

✅ Option b — $\displaystyle 4$

All Options:

A $\displaystyle 22$
B $\displaystyle 4$
C $\displaystyle 40$
D $\displaystyle 9$

Detailed Solution & Explanation

**Given:**

\displaystyle 2X + 3Y = 4

, SD of

\displaystyle X

= 6 **Step 1: Express

\displaystyle Y

in terms of

\displaystyle X

.**

3Y = 4 - 2X

Y = \frac{4 - 2X}{3} = \frac{4}{3} - \frac{2}{3}X

**Step 2: Use the property of SD for linear transformations.** For

\displaystyle Y = a + bX

\displaystyle SD(Y) = |b| \cdot SD(X)

Here

\displaystyle b = -\frac{2}{3}

, so:

SD(Y) = \left|{-\frac{2}{3}}\right| \times SD(X) = \frac{2}{3} \times 6 = 4

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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If X\displaystyle XX and Y\displaystyle YY are related by 2X+3Y=4\displaystyle 2X+3Y=42X+3Y=4 and SD of X\displaystyle XX is 6, then SD of Y\displaystyle YY is