The SD of a variable x is to be 10. SD of 50+5x is

Option a: 50. Solution: Given: SD(x) = 10 Find: SD(50 + 5x) Using the property: SD(a + bx) = |b| × SD(x) Here a = 50 , b = 5 : SD(50 + 5x) = |5| × 10 = 50 The constant 50 does not affect SD; only the multiplier 5 matters. Hence, Option A is the correct answer.

The SD of a variable $x$ is to be 10. SD of $50+5x$ is

The correct answer is Option a: 50. **Given:** $SD(x) = 10$ **Find:** $SD(50 + 5x)$ **Using the property:** $SD(a + bx) = |b| \cdot SD(x)$ Here $a = 50$, $b = 5$: $$SD(50 + 5x) = |5| \times 10 = 50$$ The constant 50 does not affect SD; only the multiplier 5 matters. Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 22Question 3186 of 473

All Questions

The SD of a variable $\displaystyle x$ is to be 10. SD of $\displaystyle 50+5x$ is

Options

A50

B100

C10

D500

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Correct Answer

✅ Option a — 50

All Options:

A50
B100
C10
D500

Detailed Solution & Explanation

**Given:**

\displaystyle SD(x) = 10

**Find:**

\displaystyle SD(50 + 5x)

**Using the property:**

\displaystyle SD(a + bx) = |b| \cdot SD(x)

Here

\displaystyle a = 50

\displaystyle b = 5

SD(50 + 5x) = |5| \times 10 = 50

The constant 50 does not affect SD; only the multiplier 5 matters. Hence, **Option A** 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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The SD of a variable x\displaystyle xx is to be 10. SD of 50+5x\displaystyle 50+5x50+5x is