Measures of Central Tendency and DispersionMCQMTP May 18Question 3082 of 473
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If the range of x\displaystyle x is 2\displaystyle 2, find range of −3x+50\displaystyle -3x + 50?

Options

A2
B6
C-6
D44
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Correct Answer

✅ Option b — 6

All Options:

  • A2
  • B6
  • C-6
  • D44

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Detailed Solution & Explanation

We are given the range of a variable x\displaystyle x is Rx=2\displaystyle R_x = 2. We want to find the range of the variable y=−3x+50\displaystyle y = -3x + 50. Range is a measure of dispersion, which is independent of change of origin (addition or subtraction of constants) but dependent on change of scale (multiplication by constants). For a linear transformation y=ax+b\displaystyle y = ax + b: Ry=∣a∣×RxR_y = |a| \times R_x Substitute the given values (a=−3\displaystyle a = -3 and Rx=2\displaystyle R_x = 2): Ry=∣−3∣×2=3×2=6R_y = |-3| \times 2 = 3 \times 2 = 6 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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