Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 2929 of 473
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There were $50$ students in a class. $10$ failed whose average marks were $2.5$. The total marks of class were $281$. Find the average marks of students who passed?

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

✅ Option a — $6.4$

All Options:

  • A$6.4$
  • B$25$
  • C$256$
  • D$86$

Detailed Solution & Explanation

**Step 1: Find the sum of marks of failed students.** Sum of failed=10×2.5=25Sum of failed=10\displaystyle \text{Sum of failed} = 10 ×\displaystyle \times 2.5 = 25 **Step 2: Find sum of marks of passed students.** Passed students =50−10=40\displaystyle = 50 - 10 = 40. Sum of passed=281−25=256Sum of passed=281−25=256\displaystyle \text{Sum of passed} = 281 - 25 = 256 **Step 3: Average marks of passed students.** Average of passed=25640=6.4Average of passed=25640=6\displaystyle \text{Average of passed} = \frac{256}{40} = 6.4 **Note:** The computed average is **6.4** (Option A), not 25 (Option B). 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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