Measures of Central Tendency and DispersionMCQMTP Mar 21, MTP Apr 21Question 2896 of 473
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The mean of the variable x\displaystyle x is 50, then the mean of u=10+5x\displaystyle u=10+5x will be

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — 260

All Options:

  • A250
  • B260
  • C265
  • D273

Detailed Solution & Explanation

**Step 1: Apply the linearity property of arithmetic mean.** Given: u=10+5x\displaystyle u = 10 + 5x and xˉ=50\displaystyle xˉ=50\displaystyle \bar{x} = 50. uˉ=10+5xˉ=10+5×50=10+250=260uˉ=10+5\displaystyle \bar{u} = 10 + 5xˉ=10+5\displaystyle \bar{x} = 10 + 5 ×\displaystyle \times 50 = 10 + 250 = 260 **Note:** The correct value is **260** (Option B). The `correct_option` D (273) is incorrect. The correct answer by first principles is 260. 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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