Measures of Central Tendency and DispersionMCQPYQ Jun 23Question 2874 of 473
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The mean of a set of 20 observations is 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:

Options

A17.6\displaystyle 17.6
B18.9\displaystyle 18.9
C5.7\displaystyle 5.7
D24.6\displaystyle 24.6
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Correct Answer

✅ Option c — 5.7\displaystyle 5.7

All Options:

  • A17.6\displaystyle 17.6
  • B18.9\displaystyle 18.9
  • C5.7\displaystyle 5.7
  • D24.6\displaystyle 24.6

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Detailed Solution & Explanation

**Step 1: Compute the original total sum.** Sum of 20 observations=20×18.3=366\text{Sum of 20 observations} = 20 \times 18.3 = 366 **Step 2: Identify new mean and new total.** New mean =18.3−0.6=17.7\displaystyle = 18.3 - 0.6 = 17.7. Number of observations now =21\displaystyle = 21. New total sum=21×17.7=371.7\text{New total sum} = 21 \times 17.7 = 371.7 **Step 3: Find the new observation.** New observation=371.7−366=5.7\text{New observation} = 371.7 - 366 = 5.7 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

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.

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