Measures of Central Tendency and DispersionMCQMTP Apr 21Question 3176 of 473
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The Standard Deviation of a variable x\displaystyle x is known to be 10. The Standard deviation of 50+5x\displaystyle 50+5x

Options

A50
B100
C10
D500
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Correct Answer

✅ Option a — 50

All Options:

  • A50
  • B100
  • C10
  • D500

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Detailed Solution & Explanation

**Given:** SD(x)=10\displaystyle SD(x) = 10 **Find:** SD(50+5x)\displaystyle SD(50 + 5x) **Using the property:** SD(a+bx)=∣b∣⋅SD(x)\displaystyle SD(a + bx) = |b| \cdot SD(x) Here a=50\displaystyle a = 50, b=5\displaystyle b = 5: SD(50+5x)=∣5∣×SD(x)=5×10=50SD(50 + 5x) = |5| \times SD(x) = 5 \times 10 = 50 So the SD = **50** (Option A). The given `correct_option` 'c' (10) is incorrect — the constant 50 doesn't affect SD, but the multiplier 5 does. 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.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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