Measures of Central Tendency and DispersionMCQMTP June 2023 Series IIQuestion 2921 of 473
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A student marks were wrongly entered as $85$ instead of $45$. Due to that the average marks for the whole class got increased by one-fourth. The no. of students in the class is?

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

✅ Option b — 160

All Options:

  • A80
  • B160
  • C40
  • D20

Detailed Solution & Explanation

**Step 1: Compute the error introduced.** Wrong entry: 85, Correct entry: 45. Excess added =85−45=40\displaystyle = 85 - 45 = 40. **Step 2: This excess caused average to increase by 14\displaystyle 14\displaystyle \frac{1}{4}.** Let n\displaystyle n = number of students. Increase in average =40n=14\displaystyle = 40n=14\displaystyle \frac{40}{n} = \frac{1}{4} **Step 3: Solve for n\displaystyle n.** n=40×4=160n = 40 ×\displaystyle \times 4 = 160 **Note:** The computed number of students is **160** (Option B), not 40 (Option C). 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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