Measures of Central Tendency and DispersionMCQPYQ June 22Question 2869 of 473
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The mean of 20 observation is 38. If two observation are taken as 84 and 36 instead of 48 and 63 find new means.

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

✅ Option c — $37.55$

All Options:

  • A$38.45$
  • B$41.15$
  • C$37.55$
  • D$40.05$

Detailed Solution & Explanation

**Step 1: Find the original total sum.** Original sum=20×38=760Original sum=20\displaystyle \text{Original sum} = 20 ×\displaystyle \times 38 = 760 **Step 2: Identify the error.** Wrong values used: 84 and 36 (instead of correct values 48 and 63). **Step 3: Compute the corrected sum.** Corrected sum=Original sum−Wrong values+Correct values\displaystyle \text{Corrected sum} = \text{Original sum} - \displaystyle \text{Wrong values} + \text{Correct values} =760−(84+36)+(48+63)= 760 - (84 + 36) + (48 + 63) =760−120+111= 760 - 120 + 111 =751= 751 **Step 4: Compute the new mean.** New mean=75120=37.55New mean=75120=37\displaystyle \text{New mean} = \frac{751}{20} = 37.55 Hence, **Option C** 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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