Measures of Central Tendency and DispersionMCQPYQ Jun 23Question 2872 of 473
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A Professor has given assignment to students in a Statistics class. A student Jagan computes the arithmetic mean and standard deviation for a set of 100 observations as 50 and 5 respectively. Later on, Sonali points out to Jagan that he has made of mistake in taking one observation as 100 instead of 50. What would be the correct mean if the wrong observation is corrected?

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

✅ Option c — $49.5$

All Options:

  • A$50.5$
  • B$49.9$
  • C$49.5$
  • D$50.1$

Detailed Solution & Explanation

**Step 1: Find the wrong total sum.** Wrong sum=100×50=5000Wrong sum=100\displaystyle \text{Wrong sum} = 100 ×\displaystyle \times 50 = 5000 **Step 2: Compute the corrected sum.** Wrong observation: 100. Correct observation: 50. Correct sum=5000−100+50=4950Correct sum=5000−100+50=4950\displaystyle \text{Correct sum} = 5000 - 100 + 50 = 4950 **Step 3: Compute the correct mean.** Correct mean=4950100=49.5Correct mean=4950100=49\displaystyle \text{Correct mean} = \frac{4950}{100} = 49.5 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.

Key Concepts to Understand

Mistake

An erroneous belief about something material to the contract. A bilateral mistake of fact (both parties mistaken) renders a contract Void. A unilateral mistake (only one party) generally does not affect the validity of the contract.

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

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