Measures of Central Tendency and DispersionMCQPYQ June 24 Series IQuestion 2938 of 473
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The Mean of a set of 20 observations on 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
B18.0
C5.7
D24.6
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Correct Answer

✅ Option c — 5.7

All Options:

  • A17.6
  • B18.0
  • C5.7
  • D24.6

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Detailed Solution & Explanation

We are given: - Number of initial observations: n1=20\displaystyle n_1 = 20 - Mean of initial observations: xˉ1=18.3\displaystyle \bar{x}_1 = 18.3 - Sum of initial observations: Sum1=20×18.3=366\displaystyle \text{Sum}_1 = 20 \times 18.3 = 366 When a new observation is added: - New number of observations: n2=21\displaystyle n_2 = 21 - The mean is reduced by 0.6\displaystyle 0.6, so the new mean is: xˉ2=18.3−0.6=17.7\displaystyle \bar{x}_2 = 18.3 - 0.6 = 17.7 - Sum of the new set of observations: Sum2=21×17.7=371.7\displaystyle \text{Sum}_2 = 21 \times 17.7 = 371.7 The value of the new observation is the difference between the new sum and the initial sum: New observation=Sum2−Sum1=371.7−366=5.7\text{New observation} = \text{Sum}_2 - \text{Sum}_1 = 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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